nuclear spins on polybrominated catechol ligands and various complexes formed by coordination of the ligands to diamagnetic Ti^IV (Johnson, Jackson, and Zadrozny 2020) and magnetic V^IV (S = ½) (Jackson et al. 2019) ions reveals a pronounced modulation of the proton nuclear spin dynamics in the ligand shell. The V^IV example shows how the ¹H dynamics and, hence, the nuclear spin patterning can ultimately influence the electronic coherence, suggesting important design principles for molecular spin qubits (see Figure 3-2).

Beyond conventional NMR spectroscopy, several related resonance techniques show tremendous promise for interrogating nuclear spins in areas of interest to chemists working in the QIS field. Several electron and electron-nuclear double resonance (ENDOR) spectroscopies are described in later sections of this report (Goldfarb 2017; Greer et al. 2018; Harmer 2016; Kundu et al. 2023; Sato et al. 2007, 2009; Van Doorslaer 2017; Wang et al. 2018). A particular advantage of these methods is that they often inherit the far greater sensitivity of EPR, in comparison to NMR, and, in some cases, are capable of achieving extreme broadband sensitivity to a multitude of nuclei in a single experiment. Meanwhile, the sensitivity of NMR can also be enhanced greatly by means of dynamic nuclear polarization (DNP; Barnes et al. 2008), whereby electron polarization is dynamically transferred to nuclei via EPR excitation. Although most current applications of DNP-enhanced NMR are in the biophysical research arena (Can, Ni, and Griffin 2015), one can envision a wide range of areas where this blossoming technique can impact research in molecular QIS. First and foremost, DNP enhancement mechanisms (of which there are many) depend intimately on the nature of the coupling between electron and nuclear spins. Thus, DNP-NMR studies can provide valuable insights into decoherence processes associated with molecular spin qubits. Meanwhile, studies have shown that one can use DNP to initialize or control the nuclear environment, leading to a range of intriguing possibilities including massive electron-nuclear entanglement (Simmons et al. 2011), enhanced electronic coherence (Bluhm et al. 2010), and even execution of multiple electron–qubit gate operations (Foletti et al. 2009). While these examples have so far been limited to solid-state semiconductor platforms, application to the molecular QIS field is ripe for investigation. However, this will require cross-fertilization of ideas between chemists working on DNP-NMR and synthesis of molecular qubits, as well as wider access to state-of-the-art magnetic resonance instrumentation and expertise. Finally, DNP offers tremendous prospects for applying NMR to the study of molecules on surfaces (Rossini et al. 2013), where it can provide a means to overcome sensitivity limitations due to low areal concentrations. As illustrated in later sections of this chapter, the study of molecules deposited on solid substrates is an important and growing area of investigation, with potential for the development of scalable device architectures.

(Figure 3-4; Atzori et al. 2016; Bader et al. 2014; Bertaina et al. 2008; Warner et al. 2013; Zadrozny et al. 2015). The vast majority of these investigations have been carried out using high-end commercial EPR spectrometers operating in the X-band frequency range (9–10 GHz) down to liquid helium temperatures. One or two studies have been carried out at lower frequencies using both commercial (Zadrozny et al. 2017) and home-built (Collett et al. 2019) instruments. These concerted activities have significantly advanced the understanding of spin-lattice (Kazmierczak, Mirzoyan, and Hadt 2021; Kragskow et al. 2022; Lunghi and Sanvito 2020) and spin-spin (Canarie, Jahn, and Stoll 2020; Chen et al. 2020; Kundu et al. 2023) relaxation in magnetic molecules, leading to the various strategies for enhancing coherence that were described in detail in Chapter 2 of this report: minimization of

spin–orbit coupling (Ariciu et al. 2019; Graham et al. 2014), suppression of spin–vibrational coupling through the design of ligand field symmetry (Kazmierczak, Mirzoyan, and Hadt 2021), use of nuclear spin-free metals (Figure 3-5; Bader et al. 2017; Fataftah et al. 2016) and ligands (Yu et al. 2016), use of nuclear spin patterning (Jackson et al. 2019), and use of clock transitions (Collett et al. 2019; Gaita-Ariño et al. 2019; Harding et al. 2017; Kundu et al. 2022, 2023; McInnes 2022; Shiddiq et al. 2016; Zadrozny et al. 2017).

As with CW EPR, metal-based spin qubits frequently necessitate measurements at frequencies considerably higher than the X-band range. In most cases, this is due to the combined influences of spin–orbit coupling and the ligand field, which gives rise to a large ZFS of the 2S + 1 spin eigenstates, for S > ½ (Fataftah et al. 2020; Takahashi et al. 2009). Even for the S = ½ case, a recent lanthanide example demonstrates that the electron-nuclear hyperfine interaction is of a sufficient magnitude that the spectrum cannot be resolved in a commercial X-band instrument (Kundu et al. 2022). Measurements at higher frequencies are challenging due to the lack of available microwave sources with sufficient power to achieve short spin rotation pulses. Although very high-end commercial spectrometers operating at higher frequencies and magnetic fields are available, they have found little utility in this area of research, primarily due to a lack of power and a lack of flexibility for studying metals with broad EPR lines. One notable exception is the case of an Fe₄ molecule with a zero-field excitation that exactly matches the 94 GHz operating frequency (W-band) of a commercial instrument, thus enabling coherent spin manipulation in zero field (Schlegel et al. 2008). However, most if not all other notable high-field/frequency transient EPR studies have been conducted using custom-built hardware that is described in later sections of this chapter. An important early finding from these studies was a significant enhancement in coherence brought about by polarization of the electron spin bath at pumped liquid helium temperatures (Takahashi et al. 2008, 2009, 2011; Wang et al. 2011) (see Figure 3-6). A frequency of 240 GHz is equivalent to a thermal energy of ~11.5 K. Hence observing an EPR signal at low temperatures necessarily involves excitation from the ground spin projection state that is isolated from the first excited state by 11.5 K. Therefore, one can achieve an electron spin polarization exceeding 99.9 percent at a temperature of 1.5 K (pumped ⁴He). As a result, electron spin-spin fluctuations are almost completely suppressed, and one can observe coherent electron spin dynamics in a highly concentrated crystalline sample, as has been demonstrated for several polynuclear Fe clusters (Takahashi et al. 2011; Wang et al. 2011).

Besides measuring T₁ and demonstrating the possibility for coherent manipulation of spin states (e.g., Rabi oscillations) in a range of exotic molecular spin systems (see, e.g., Gould et al. 2021; Hu et al. 2018), pulsed

EPR provides access to a wealth of microscopic information via coherent multidimensional pump-probe techniques. In its most basic form, pulsed electron-electron double resonance (ELDOR) involves excitation at one frequency followed by a coherent detection (often by a standard π/2 – τ – π – τ – Hahn echo sequence) at a second frequency within an inhomogeneously broadened EPR spectrum. Such experiments can, for example, provide information on electron spectral diffusion by monitoring changes in polarization at one location/frequency in the spectrum brought about by saturation at another (Wang et al. 2018), thus yielding microscopic insights into electronic relaxation.

A fully coherent pulsed ELDOR sequence, also known as double electron-electron resonance (DEER), involves the execution of an inversion pulse at a frequency ν₂, during either a two-pulse Hahn echo sequence or a three-pulse sequence with a second refocusing π pulse at a frequency ν₁ (Jeschke 2018). This technique, which was developed for structural studies of biomolecules, precisely probes the weak dipolar coupling between two spin labels by monitoring changes in the coherence of one of the spins (at frequency ν₁) by inverting the polarization of the other spin (at frequency ν₂) as a function of delay time, t, within the echo sequence. The result is a modulation of the echo intensity, the Fourier transform of which corresponds to the dipolar coupling in frequency units. The coherent nature of the DEER technique enables the measurement of extremely weak dipolar couplings (~MHz) that would otherwise be buried (i.e., unresolvable) deep within the inhomogeneously broadened CW EPR spectra. Increased spectral resolution at high magnetic fields further permits enhanced orientation selectivity through excitation and detection at spectral locations corresponding to different components of the electron g-tensor. In this way, one obtains information not only on the distances between spins but also on the relative orientations of their g-tensors (Stevens et al. 2016). As depicted in Figure 3-7, DEER has recently been deployed to measure electron–electron coupling within dimers of {Cr₇Ni} spin qubits that have been proposed as molecular two-qubit gates (Ardavan et al. 2015), representing a first step toward the demonstration of electron quantum logic in molecules. Indeed, several proposals exist in the literature centered on the use of asymmetric dimers (or oligomers) as two-qubit gates (Aguilà et al. 2014; Collett et al. 2020; Ferrando-Soria, Moreno Pineda, et al. 2016; Uber et al. 2017; Ullah et al. 2022). The asymmetry is necessitated by the requirement that the spins be spectrally distinguishable. However, the demonstration of universal two-qubit logic gates remains a major outstanding goal, for which the primary obstacle is the limited bandwidths (~1 GHz) of current state-of-the-art transient EPR spectrometers (i.e., the limited ability to excite at two well-separated frequencies; Cruickshank et al. 2009). This issue is discussed further in Section 3.11.

study conducted at the W-band on a custom-built high-power spectrometer, Cruickshank and colleagues (2009) demonstrate the advantages of increased orientation selectivity at high fields, enabling correlation between the electron g- and hyperfine coupling tensors. Substitution of one of the ELDOR pulses with a radiofrequency (RF) NMR pulse leads to the ENDOR technique (Harmer 2016), which is useful at the interface between chemistry and QIS (Lutz et al. 2013; Sato et al. 2009; Weiden, Käss, and Dinse 1999). When combined, these multidimensional pump-probe EPR techniques provide access to complementary information about electron-electron and electron-nuclear spin-spin interactions, from which one may infer exquisite microscopic details of physical and electronic structures and spin relaxation behavior. However, more widespread deployment of these methods has likely been limited by the lack of available state-of-the-art transient EPR spectrometers and by the unfamiliarity with advanced (i.e., complex) EPR methodology among the synthetic chemistry community.

3.1.4 Neutron Scattering

The key advance in neutron scattering over the past decade has been the development of a new generation of high-flux cold-neutron time-of-flight spectrometers. They are equipped with arrays of position-sensitive detectors that enable efficient measurement of neutron scattering cross sections as a function of energy and the three components of the momentum transfer vector Q, and in vast portions of reciprocal space (Chiesa et al. 2017). The availability of large single crystals of magnetic molecules then permits very detailed four-dimensional (4D) inelastic neutron scattering (INS) spectroscopy, providing unprecedented insight into coherent spin dynamics (Figure 3-9). Indeed, 4D INS enables complete evaluation of the dynamical correlation function, S(Q,ω), without reliance on any spin Hamiltonian model.

accessible and populated via the Boltzmann distribution. The task of initializing a molecule into a single quantum state involves removing entropy associated with the Boltzmann distribution from a molecular system. Coupling molecular systems to light offers a convenient way to accomplish this: entropy can be transferred to light that propagates away from the system. If this process occurs on a timescale much shorter than that of thermalization with the environment, high-fidelity initialization of molecular qubits can occur even at room temperature, which is technologically desirable.

For optical initialization to occur, one first requires optically active molecules—those with high oscillator strength for an electric dipole transition between the ground and some optically excited state at technologically accessible wavelengths. Second, a configuration where certain quantum states are “dark” to incoming light is required. The molecule–light system must be engineered into such a configuration. When this occurs, repeated scattering of incoming photons “pump” molecules into the desired dark quantum state, a technique known as optical pumping. Concretely, the “darkness” required for internal state initialization can be achieved through spectral separation of optical transitions, or through control of the light polarization. Examples can be found in solid-state qubits formed by nitrogen-vacancy (NV) centers in diamond and chemically designed optical Cr⁺ spin qubits. The relevant qubit (“spin”) states in the ground electronic manifold are split by a large energy difference, allowing qubit states to be spectrally resolved (Awschalom et al. 2018; Jelezko and Wrachtrup 2006; Rodgers et al. 2021). By addressing a specific spin state with light, a qubit can be optically pumped into the unaddressed “dark” states. This form of optical pumping is also known as spectral hole burning. In gas-phase molecules that permit optical cycling (e.g., optical cycling centers [OCCs]), arrays of single diatomic molecules have been initialized through a polarization-sensitive optical pumping scheme (Holland, Lu, and Cheuk 2022).

3.2.2 Optical Quantum-State Readout

By repeatedly exciting a molecular qubit optically and collecting the resulting laser-induced fluorescence, the qubit can be detected. Quantum-state resolution is attained when the optical transitions to different spin states differ in energy and color. Through state-selective optical excitation, isolated OCCs individually trapped in optical tweezer arrays have been detected with quantum-state resolution and with high fidelity (Figure 3-10; Anderegg et al. 2019). In addition to the frequency of the emitted fluorescence, in certain systems, the polarization of an emitted photon can be entangled with the qubit state. This can be harnessed to create quantum networks of distant molecular qubits that are entangled, which can be a resource for quantum communication (Togan et al. 2010).

coherent quantum control of rotational states (Williams et al. 2018), and nondestructive fluorescent detection of ultracold molecules (Cheuk et al. 2018).

Notably, with relevance to quantum information processing and quantum simulation, recent work with laser-cooled diatomic molecules has demonstrated high-fidelity detection of arrays of single molecules held in optical tweezer traps (Anderegg et al. 2019; Holland, Lu, and Cheuk 2022). Recent work with molecular tweezer arrays has even demonstrated high-fidelity positioning and quantum-state initialization of single molecules within a large array (Holland, Lu, and Cheuk 2022). Very recently, on-demand entanglement between two molecules spatially separated on the micron scale was demonstrated for the first time, long coherence times on the 100 ms timescale were achieved, and a two-qubit gate sufficient for universal quantum computation was implemented in these arrays (Bao et al. 2022; Holland, Lu, and Cheuk 2022). These demonstrations establish the building blocks needed for quantum information processing and quantum simulation, and make molecular tweezer arrays a promising new platform for quantum science. Looking ahead, the platform of tweezer arrays with optically cyclable molecules could allow high-fidelity individual qubit addressing. By leveraging recent advances in optical tweezer arrays filled with single atoms, these molecular arrays could also be scalable in the near term to hundreds of qubits, as has been demonstrated in their atomic analogs (Ebadi et al. 2021; Scholl et al. 2021).

In the past few years, new work extending beyond diatomic radicals has explored whether optical cycling can be applied to more complex molecules and where new chemical principles can be found that guide the design of these molecules. On the physics front, the search for large molecules with favorable optical cycling properties is motivated by the fact that certain molecules are particularly sensitive to the potential for new fundamental physics beyond the standard model. If these same molecules can be optically controlled at the quantum level, they could offer significant improvements in fundamental physics searches, such as those that look for an electron electric dipole moment (Augenbraun et al. 2020) and ultralight dark matter (Kozyryev, Lasner, and Doyle 2021). The extension of similar techniques to larger molecules could open up possibilities including quantum-enhanced precision measurements and chemistry at ultracold temperatures with entangled matter.

The quest to identify molecules with favorable optical cycling properties along with the discovery of guiding chemical principles is where AMO physics and chemistry intersect. This is a rapidly evolving area. So far, a theme that has guided work on identifying OCCs successfully is the M-O-R motif, where an alkaline earth metal atom (M) is bonded to a halide (Kozyryev, Baum, Matsuda, Boerge, and Doyle 2016; Kozyryev et al. 2019). These systems behave as gas-phase M⁺ cation radicals. Optical excitations primarily involve orbitals localized on the metal atom that are minimally coupled to vibrational modes, thereby permitting optical cycling. Based on this principle, theoretical calculations and, in some cases, experiments have shown that more complex M—O—R (where O is oxygen, and R is the organic group) molecules can minimize the issue of vibrational branching and permit optical cycling (Dickerson et al. 2022; Dickerson, Guo, Shin, et al. 2021; Dickerson, Guo, Zhu, et al. 2021; Ivanov et al. 2020; Kłos and Kotochigova 2020; Kozyryev, Baum, Matsuda, and Doyle 2016; Mitra et al. 2022; Zhu et al. 2022). Experimental work has demonstrated optical cycling in the M-O-R polyatomics CaOH and CaOCH₃ (Hallas et al. 2023; Mitra et al. 2020; Vilas et al. 2022). Notably, the optical control over CaOH is rapidly approaching that of diatomic OCCs.

For even larger molecules, recent work has discovered new chemical principles that determine optical cycling properties. Theoretical work has shown that Franck–Condon factors in an M-O-R OCC can be tuned through chemical substitution in the R-ligand organic functional group (Figure 3-11; Dickerson, Guo, Shin, et al. 2021). Recent experiments have also verified that OCCs attached to aromatic groups can retain good cycling properties (Mitra et al. 2022; Zhu et al. 2022). Together, these works on M-O-R OCCs have also revealed a possible new chemical principle regarding optical cycling properties—the electron-withdrawing potential of the R ligand correlates well with the molecule’s electronic excitation energies and vibrational branching ratios.

The rapidly developing area of large OCCs has also increasingly emphasized the perspective of large OCCs as molecules functionalized with an optical cyclable quantum functional group. Viewing an OCC as a quantum functional group serving as a generic qubit moiety, there are proposals to attach optically controllable qubits to larger molecules and to surfaces (Guo et al. 2021; Zhu et al. 2022). If successful, these endeavors could open up new possibilities such as transducing information among several attached OCCs joined to a large molecule or surface and using attached OCCs as quantum sensors to probe the dynamics of their host molecules (Zhu et al. 2022).

transistor. The location in the magnetic field of this jump, therefore, provides a convenient readout of the nuclear state of the molecule. One can then perform logic operations on the nuclear spin via the application of selective microwave NMR pulses (see Figure 3-13), with the final readout achieved via the transistor. A quality factor can be deduced from the ratio of T₂/T_p (where T_p is the time taken to execute a p-pulse), which gives Q = (300 ms)/(0.12 ms) = 2,500, corresponding to a fidelity of about 99.9 percent. The next step would involve single-qubit gate randomized benchmarking which, to the best of our knowledge, has not been performed for a molecular system to date. These and other related studies (Jo et al. 2006; Perrin, Burzurí, and van der Zant 2015) clearly demonstrate the feasibility of realizing molecular-scale electronic devices for QIS.

this driving mode remains somewhat unclear) or via a separate RF antenna close to the tip. Detection is achieved by employing a magnetized STM tip that generates a spin-polarized tunneling current, enabling a projective readout of the state of the spin located below the tip. Averaging then yields the composition of the wave function (i.e., ∣ψ〉 = a∣↑〉 + b∣↓〉). By employing different excitation schemes, one can carry out all of the well-known pulsed EPR schemes (e.g., Rabi nutation, Ramsey fringe measurements, Hahn-echo decay measurements of the T_m associated with a single spin, and so on). The technique, which has been pioneered in Andreas Heinrich’s group at Ewha Womans University in Seoul, Korea, obviously requires access to high-end STM instruments along with considerable technical expertise. Most demonstrations until now have involved individual surface adatoms as well as pairs of atoms. However, one recent study focused on the coherent control of the spin associated with a single FePc molecule (Willke et al. 2021), emphasizing the tremendous potential of this relatively new method for coherent control of individual molecular qubits. An added powerful advantage of this technique is the possibility of moving atoms and molecules around on surfaces (Loth et al. 2012), enabling a very deliberate design of multispin architectures for studies of the physics associated with relatively simple model spin Hamiltonians. However, a potential drawback is the lack of an obvious pathway to scalable architectures with the possibility to manipulate large numbers of qubits. Nevertheless, EPR-STM offers a remarkably powerful tool for studying the quantum dynamics of individual (or small numbers of) molecules on surfaces. Limited availability of such instruments has resulted in a relatively low number of publications until now. Groups in Europe (Korvarik et al. 2022; Yan et al. 2020) and Asia (Chen, Bae, and Heinrich 2022; Kawaguchi et al. 2023) are increasingly turning to this technique, even though it was first developed in the United States (Baumann et al. 2015). Obviously, less exotic (and less costly) EPR techniques should be used to pre-screen candidate molecules. However, limited access to EPR-STM platforms, particularly in the United States, is preventing research at the intersection of QIS and chemistry to move forward.

3.3.3 Chemical Tailoring of Solid-State Spin Defects

Defects in semiconductors have become powerful hosts for spin-based qubits in the solid state within materials including diamond, silicon carbide, and silicon. By exploiting defects generated via electron or ion radiation as well as naturally occurring defects in these materials, researchers have demonstrated precise quantum control of individual electron and nuclear spins, robust entanglement, electron-nuclear quantum registers, and increasing control of the spin-optical interface at the level of single photons. For example, like NMR, the use of single NV centers close to the surface of diamond nanocrystals or nanopillars to sense single molecular spins deposited on their surfaces shows tremendous promise for chemical EPR investigations. Recent work by Pinto and colleagues (2020) has demonstrated coherent readout and control of an endohedral ¹⁴N@C₆₀ electronic spin via this method, including transient measurements. This approach can also be extended to nanoscale samples at high magnetic fields and frequencies (Fortman et al. 2020). In particular, NV-detected EPR offers the possibility to detect single electron spins and, therefore, to investigate biological processes at the single-molecule level. As such, NV-detected EPR with single-spin sensitivity can potentially eliminate ensemble averaging in heterogeneous systems (Giovannetti 2004).

Meanwhile, driven by predictive theoretical work, several defect-based states have been engineered for practical applications including quantum memories and optical emission in the telecom regime. Impressive quantum sensing of electric, magnetic, and strain fields has been shown along with dramatic improvements in small-volume and single-spin NMR. However, these material systems face considerable challenges for quantum science and engineering, including creating scalable and identical quantum states, mitigating the impact of strain and isotopic variations, as well as controlling decoherence-driven charge fluctuations from interfaces and unintentional dopants.

The selection of appropriate hosts and defects, and their mutual interactions with one another, remains both a challenge and an opportunity for QIS research. There have been considerable advances in understanding the mechanisms of spin decoherence in semiconductors and solid-state nanostructures. State-of-the-art synchrotron spectroscopies, coherent Bragg diffraction imaging, and high-resolution magnetic resonance techniques have proven to be powerful tools to improve the quality of host materials. In addition, improvements in first-principles approaches to understanding and predicting properties (e.g., density functional theory) have led to a deeper physical understanding of quantum decoherence and successful predictions in mitigating many sources of noise,

from dynamical decoupling to unique pulse sequences. In addition, there have been successful efforts aimed at harnessing the capabilities of today’s electronics technologies for quantum-state control, including electrical control and readout of single quantum states, the creation of decoherence-free subspaces to locally enhance coherence, and the integration of photonics to both enhance the efficiency of quantum emitters and entangle nearby quantum bits. Recently, rare-earth ions in oxide semiconductor hosts—including silicon-compatible materials—have emerged with encouraging properties as single quantum memories, with impressively long coherence times and single-shot photonic readout.

3.4 DEVELOP ENHANCED SPECTROSCOPIC AND MICROSCOPIC TECHNIQUES WITH NONCLASSICAL LIGHT

3.4.1 Quantum Light Spectroscopy and Entangled Photon Sources

As chemists push forward in their quest for deeper knowledge of the important processes and mechanisms of molecular interactions, great pressure is placed upon the nature of the measurements used to probe such processes. Indeed, the measurements themselves are also physical processes, and the accuracy to which these measurements may be performed to help better understand chemical processes is governed by the laws of physics. At the molecular level and for small systems, the processes involved in the measurements are governed by the laws of quantum mechanics that theoretically place limits on the accuracy to which the measurements can be performed. The intrinsic uncertainty of the results of the measurement of complementary observables is derived from the Heisenberg uncertainty relationship. Other quantum constraints combined with these uncertainty relations impose limits on how accurately we can measure quantities with the given physical resources of a measurement tool.

Nonlinear Entanglement Spectroscopy

New high-resolution, noninvasive spectroscopic and imaging methods for chemical processes have been developed over the past two decades. This success has allowed scientists to probe important chemical processes at the sub-femtosecond and sub-micron levels, which was not previously possible. However, better detection and imaging methods are still needed at the nanoscale at very low powers. Several impressive magnetic and optical techniques have been developed for this purpose. In the optical regime, both linear and nonlinear optical methods (see Figure 3-15) have been well illustrated in the literature. For example, nonlinear optical methods, such as two-photon absorption (TPA; and emission), have enjoyed great success in probing (at a very sensitive level) organic

and inorganic molecular systems as well as biological cellular (tissue) processes (Varnavski and Goodson 2020). The quadratic intensity dependence of TPA methods allows for very strong focusing and localization of the optical field, giving a much better effective resolution than their linear optical counterpart. The use of nonclassical sources of light such as squeezed states as well as entangled photons may provide an opportunity to exceed these quantum-imposed limits.

Great enthusiasm exists for exploring quantum information in molecular systems. Constructing a molecular system with the appropriate electronic states as well as inter- and intramolecular interactions for a desired quantum effect is a beneficial goal. This requires substantial advancement in both the synthesis and electronic structure of the proposed molecular systems. However, and perhaps of equal importance, this goal also requires advanced measurements at a very sensitive level for the desired detection of the spectroscopic or microscopic signal. New measurements are now being developed to probe the molecular properties of molecules at an enhanced level, which may one day provide new insights into the molecular design of systems for QIS applications as well as provide a more fundamental understanding of the nature of electronic interactions and mechanisms. In describing quantum phenomena in molecular systems, one usually is seeking behavior that lies outside the norm of classical behavior. For example, one is interested in the processes of coherence and decoherence in optical spectroscopy. These processes are being further defined and developed continually by time-resolved and nonlinear spectroscopic techniques. Chemists are developing the instrumentation and theory for new frontiers in this direction. Molecular systems typically suffer from a loss of coherence (amplitude and phase) at room temperature on ultrafast timescales (femtoseconds). A difficulty in measuring quantum states in molecular systems stems from the fast decoherence or mixing with a homogeneous broadening ensemble environment that is typical in solutions or solids. The development of new experimental techniques to provide new information through nonlinear signals, ultrafast multidimensional systems, and entangled photon interactions could enable improvement in the measurement of quantum-defined processes in molecular systems.

3.4.2 Quantum Light in Molecular Spectroscopy

The use of nonclassical states of light for spectroscopy may provide new approaches toward understanding the physical properties of molecules beyond quantum coherences to include entanglement. There are several ways that one may generate a quantum light source. Photon entanglement occurs between two beams of light when the quantum state of each field cannot be described in the individual parameter space of that field (Mukamel et al. 2020). While there are different parameters of light that can be entangled, the most commonly reported methods involve time and energy, polarization, and position and momentum. Along with the generation of squeezed states of light, these methods provide the bulk of the experimental techniques with nonclassical states of light. The interest in utilizing nonclassical states of light (e.g., entangled photons) stems from the potential advantages they may provide in comparison to classical laser excitation. It may be possible to take advantage of the high degree of temporal and spatial correlations in quantum light resulting from entangled pairs of photons (i.e., the signal and idler). These correlations can provide a sensing tool for chemists to detect potential molecular systems at very low levels of light, which is useful for investigations of chemical and biological systems. The pairs of photons are typically created by the process of spontaneous parametric down-conversion (SPDC) (Figure 3-16). These entangled pairs have shown different and low noise characteristics when compared to classical photon sources. This feature of entangled light can also be utilized in new linear and nonlinear spectroscopic approaches. All light fields have fluctuations in their amplitudes and phases, are subject to a stochastic indeterminacy beyond environmental influences, and involve a quantum indeterminacy. There has been a great deal of progress in producing light fields with fluctuations lower than the shot noise limit (SNL). One of these is amplitude squeezing, which may be produced by an interaction that preferentially removes the large amplitude fluctuations, resulting in a radiation field below the SNL. Both amplitude and photon number squeezing have attracted new applications in sensing and spectroscopy (Ispasoiu and Goodson 2000; Loudon and Knight 1987). Nonlinear four-wave mixing approaches have been carried out to produce bright squeezed states of light. Measurements are achievable with sensitivity beyond the standard classical limit and can be performed at low excitation fluxes for exciting photosensitive materials. With the advent of novel theoretical predictions and models, new measurements have been proposed that may suggest

an enhanced spectral resolution. Additionally, by utilizing the unique features of entangled photon pairs, one may also pursue the possibility of targeted entangled or coherent control of photochemical processes (Eshun et al. 2022). In the context of imaging (in biological systems), the highly correlated light provides the opportunity to probe chemical and biological systems at extremely low photon flux, avoiding the typically detrimental light toxicity issue. Entangled photon pairs provide a very powerful way to evaluate fundamental quantum mechanical principles such as Bell’s inequalities or in Hong–Ou–Mandel (HOM) photon correlation experiments (Schlawin et al. 2013).

Other intriguing properties of entangled photon spectroscopies include a non-Fourier-related spectral and temporal resolution. The spectral resolution is determined by the linewidth of the down-converted pump, whereas the temporal resolution is determined by the spectral width of the non-degenerate, down-converted photon pairs. This is because only the two entangled photons in a pair will interact with each other in an entangled photon spectroscopy measurement, whereas in a classical laser, any two photons can interact. Along these same lines is the ability to measure one photon using another wavelength or to image an object without spatially detecting the photons hitting the target. These “ghost” measurement techniques rely on the quantum correlations between the two photons in the entangled pair to determine the property of one photon using the other. It is notable that the photons must still be interfered with or measured by coincidence counting circuits to determine these properties. Such techniques are promising because extremes such as measuring an X-ray photon using a visible light photon are possible, all while gaining the quantum advantages of the entangled photons.

As depicted in Figure 3-16, SPDC is the most common method for creating nonclassical, entangled light. In the case of SPDC, a strong pump beam of frequency ω_p interacts with a χ⁽²⁾ nonlinear crystal to create a pair of lower-energy photons (the signal ω_s and idler ω_i photon), whose energy adds up to that of the pump, ω_s + ω_i = ω_p (Eshun et al. 2022). In addition to energy, momentum also must be conserved, which leads to “phase-matching” conditions defined by k_s + k_i = k_p. The phase-matching conditions determine the spatial correlations, efficiency, bandwidth, and temporal constants of the generated entangled photon pair. The most common nonlinear crystals used for SPDC are bulk β-barium borate (BBO) and potassium dideuterium phosphate (KDP). Because of said phase-matching

conditions, bulk crystals usually have efficiencies on the order of 10⁻¹⁰ to 10⁻¹². The phase-matching conditions of bulk BBO and KDP also dictate tens of nanometer bandwidths and hundreds of femtosecond correlation times. These parameters put constraints on potential measurements to be performed with entangled photons.

The efficiency, bandwidth, and temporal correlations of an entangled photon source can be improved by using periodic poling of ferroelectric materials to create quasi–phase matching. Materials made popular by telecom entangled photon experiments include potassium titanyl phosphate and lithium niobate. Switching the poling of the crystals on the micrometer scale allows for artificial optimization of the phase-matching conditions. Higher-strength nonlinear tensors can also be used for type 0 SPDC. This results in a dramatic increase of the SPDC efficiency, to as high as 10⁻⁶, while also allowing a broader tuning of the central wavelength and bandwidth (and therefore temporal correlations) of the SPDC. Octave-spanning bandwidths with ~10 fs correlation times have been achieved with μW fluxes that are visible by eye. The greater bandwidth is accomplished by the introduction of a chirp in the poling field, which allows more wavelengths to be phase matched while also retaining the benefits associated with longer crystals (Szoke et al. 2021). Quasi–phase matching can be achieved in bulk crystals as well as waveguided sources to provide accessibility in both on-chip and free-space measurements.

A unique aspect of chemistry that is different from quantum information is the ability to create entangled photons over a broad range of central wavelengths. New proposals to use lithium tantalate have been published, offering the ability to pump SPDC down to ~350 nm where lithium niobate begins to suffer from self-absorption issues (Figure 3-17). Of course, even with lithium tantalate, the down-converted entangled photons are still in the 700 nm range, which is too high for most molecular dyes. Recent work has shown the creation of deep ultraviolet entangled photons using LaBGeO₅ (LBGO). Entangled photons can also be created in the IR to terahertz regions using lithium niobate (<5 μm) and up to the terahertz range using orientationally patterned GaAs. Future work involves the use of sub-wavelength structures to further enhance the entangled photon generation rate (Price 2022).

As entangled light sources continue to be developed, attention has increased recently toward carrying out spectroscopy with the available entangled photons by current methods. The interest in utilizing entangled photons as spectroscopic tools first emerged in 1990, when scientists theoretically predicted a linear, rather than quadratic, scaling of the TPA rate with the pump photon intensity. One may rationalize this effect by comparing the interaction of the three-level atom with ordinary coherent light and with SPDC entangled light. If the atom interacts with coherent light tuned to the two-photon resonance, the two-photon transition rate may be estimated as the rate of excitation from the (virtual or real) intermediate state multiplied by the probability that the atom is in the intermediate state. At low intensity, both these quantities are proportional to the intensity, and one obtains the usual quadratic dependence of the two-photon rate on intensity. With the SPDC light, on the other hand, the excitation is accomplished in a single step: one photon of the pair promotes the atom to the virtual intermediate state, while its twin immediately (in a time less than the virtual-state lifetime) completes the two-photon transition. One may estimate the two-photon transition rate as the probability of excitation by a photon pair multiplied by the rate of arrival of photon pairs (proportional to intensity). The rate should be linear in intensity. The experimental verification of this effect in atomic and molecular systems established entangled photons as unique light sources for nonlinear spectroscopy with low photon fluxes (Figure 3-18). Measurements in atomic and molecular systems have been carried out for this form of entangled two-photon spectroscopy. Measurements of the entangled two-photon fluorescence with as few as 10⁷ photons/sec have been carried out with this method. This gives rise to the possibility of doing spectroscopy with a small number of photons. The exact manner in which the entangled photons interact with particular molecular states and its impact on our understanding of the fundamental photochemical mechanisms could have important ramifications in our ability to excite and possibly control photochemical processes. Theoretical proposals for entangled virtual-state spectroscopy or entanglement-induced two-photon transparency have pointed out the highly unusual bandwidth properties of entangled photons and how this may be used further in understanding and possibly controlling chemical processes (Burdick, Schatz, and Goodson 2021; Eshun et al. 2022; Georgiades et al. 1995; Giri and Schatz 2022; Guzman et al. 2010; Harpham et al. 2009; Kang et al. 2020; Lee and Goodson 2006; Li et al. 2020; Parzuchowski et al. 2021; Raymer et al. 2013; Saleh et al. 1998; Schlawin, Dorfman, and Mukamel 2018; Svidzinsky et al. 2021; Tabakaev et al. 2021, 2022; Upton et al. 2013; Varnavski, Pinsky, and Goodson 2017; Villabona-Monsalve et al. 2018; Ye and Mukamel 2020).

Schlawin, Dorfman, and Mukamel (2018) have been instrumental in making theoretical predictions involving entangled photon spectroscopy. Nonclassical intensity fluctuations can enhance nonlinear optical signals relative to

linear absorption. This enables nonlinear quantum spectroscopy of, for example, photosensitive biological samples at low light intensities. In addition to the signal’s scaling with intensity, the use of entangled photons may also provide a new approach to shaping and controlling excitation pathways in molecular aggregates in ways that cannot be achieved with shaped classical pulses. For example, in some cases the use of entangled photons may suppress background signals and enhance others. In one proposed experiment, time–energy entangled photons produced by SPDC are employed to calculate vibrational hyper-Raman (HR) signals of a conjugated organic chromophore. Compared with classical light, Schlawin, Dorfman, and Mukamel (2018) found that time–energy entanglement can provide selectivity of Liouville-space pathways and will suppress the broad electronic-Raman background arising from one-photon resonances of the intermediate states. They showed that one-photon resonances can significantly

enhance classical HR signals; however, the electronic-Raman background is also introduced. By pathway selectivity, time-energy entangled photons can suppress this background while retaining the intense and narrow HR peaks (Figure 3-19). Another advantage of entangled light for HR spectroscopy is that the signal scales linearly with the pump intensity rather than quadratically. At low field intensities, entangled photons give stronger signals than

classical light, making this tool valuable for experiments using fragile biological samples (Dorfman, Schlawin, and Mukamel 2014; Roslyak, Marx, and Mukamel 2009; Schlawin, Dorfman, and Mukamel 2018).

Other proposals from Dorfman, Schlawin, and Mukamel (2014) include using interferometric signals for pathway selectivity; applying multidimensional spectroscopy to suppress uncorrelated background signals; and employing interferometric TPA techniques with a triphoton entangled state, which will give stronger spectrally dispersed photon-counting signals than a typical biphoton state. The fundamental idea behind these proposed techniques is two-photon interferometry, which is best described with a HOM interferometer (Hong, Ou, and Mandel 1987). In a HOM interferometer, the entangled photon pairs are separated, and a time delay is introduced between them via differences in their propagation paths. Next, the photons meet and interfere at a 50:50 beam splitter, where single-photon detectors measure whether the photons emerge from the same or opposite sides of the beam splitter. The indistinguishability of the photon pair leads to destructive interference of the indistinguishable paths and a subsequent drop in the coincidence counts known as the “HOM dip” (Figure 3-20). Factors that distinguish the photon pair will affect the shape of the “HOM dip.” The dip reflects any matter interactions that the entangled photons encountered, which is an important feature for spectroscopic measurements. The increased sensitivity of quantum interferometers can improve the accuracy of measurements of material linear and nonlinear susceptibilities. This technique was first demonstrated in solid-state crystals and nanostructures with relatively narrow absorption lines. Earlier reports described coherent dynamics and dephasing processes in these systems. More recently, the HOM experiment was utilized to extract a dephasing time in an organic of ~102 fs upon coherent excitation and quantum interference with a path of entangled photons in the HOM interferometer. With theoretical modeling of the coincidence rate of the HOM dip by Eshun and colleagues (2021), the experiment and theory were analyzed and showed good agreement. The proof-of-concept report gives encouragement for further measurements of nonlinear signals with this quantum interferometry tool.

For entangled two-photon absorption (ETPA), and other processes where the photon entanglement is destroyed as a result of the excitation process, uncertainties remain about which proper final-state density to use in Fermi’s golden rule for determining the rate of absorption. For classical (unentangled) TPA, this state density is determined by the states of the molecule associated with the doubly excited state; normally, this is dominated by the density

of phonons associated with this state, as this leads to the known rapid dephasing (in ~10 fs) after photoexcitation. However, for entangled photon excitation, Kang and colleagues (2020) proposed that entanglement fidelity can constrain the state density, such that the radiative lifetime of the doubly excited state rather than phonon dephasing determines this density. This result, which previously had been used in atomic physics modeling (Fei et al. 1997; Kojima and Nguyen 2004), leads to a much narrower lineshape for ETPA, and much larger cross sections are obtained from electronic structure calculations that are similar to what has been found in experiments (Kang et al. 2020). However, this assumes that fidelity of the entanglement constrains coupling to phonons, which is an assumption of unknown validity. Further work is needed to relate this result to known electronic and electron-vibrational entanglement properties of molecules (McKemmish et al. 2011; Plasser 2016).

There have been reports of utilizing nonclassical states of light in spectroscopy and microscopy in the linear optical regime. The use of quantum optical approaches in the linear regime could be of great interest to chemists in providing sensitive detection schemes for possible remote detection of chemical and biological systems. For example, there have been reports of quantum imaging with undetected photons. In this quantum interference effect, the photons that pass through the imaged object are never detected. The entangled photons that never interacted with the object provide the image. Here, it is not necessary to detect the photons that illuminate the object at all. This could be very useful for chemical and biological samples, where the material could lead to very opaque and high scattering of the illuminating light (Lemos et al. 2014). There have been other uses of quantum interferometers for linear optical effects in the IR regions. For example, reports have shown that by detecting the signal photons one can acquire the amplitude or phase information of the idler photons. Research has shown that the measured transmission spectrum of a polymer sample is in good agreement with a conventionally measured reference spectrum by detecting the correlated visible light of the SPDC process. Again, this approach could be useful for chemists interested in collecting IR spectral signatures of molecules using a visible laser light source and a silicon-based detector (Lindner et al. 2020; Mukai, Okamoto, Takeuchi 2022). This approach has even been extended to the terahertz region, where terahertz photons interact with a sample in free space and information about the sample thickness is obtained by the detection of visible photons. The ability to do terahertz spectroscopy with detection of visible photons would impact the investigation of thick opaque materials and samples (Kutas et al. 2020).

The use of entangled photons for coherent control has been reported as well by Gu and colleagues (2021). Recent theoretical work revealed that entangled light may provide a coherent control scheme for nuclear wave packets in a one-photon dark excited state of a molecule. This is demonstrated by nonadiabatic conical intersection wave packet dynamics for the trans–cis photoisomerization of azobenzene (Figure 3-21) (Casacio et al. 2021). This control leads to a substantial difference in the transient coherences during the passage through the intersection (the transition-state structure of the photochemistry), which is proposed to be detected by a stimulated X-ray Raman signal. Additionally, it was suggested that the photoisomerization yield is noticeably affected by modulating the photon entanglement time. The essential role of energy–time entanglement in the control is clearly demonstrated by contrasting the quantum light–excited wave packets to the wave packets created by classical light. Varying the bandwidth alone for both classical nonchirped and chirped pulses leads to minor differences in the two-photon excitation process. These results may provide a strategy for coherent quantum light control of the photoexcitation of electronic dark states of molecules (Gu et al. 2021).

3.4.3 Use of Quantum Light in Microscopy

One of the most recent applications of nonclassical states of light in chemistry involves microscopy, which is essential in broad areas of science from physics to biology. Using nonclassical states of light, chemists can open possibilities of realizing low-intensity microscopy at intensity levels not achievable with classical resources. For example, using quantum states of light for illumination, precise phase and linear absorption measurements in a microscopic format have been previously reported, and precision beyond the standard quantum limit has been achieved in a microscope (Casacio et al. 2021). These experiments also will be useful in overcoming photodamage, which is important for biological systems. Through the use of quantum correlations in nonclassical light, Casacio and colleagues (2021) demonstrated a highly selective coherent Raman microscope. They observed a 35 percent improved signal-to-noise ratio (SNR) compared to conventional classical light microscopy. This improvement

translates to a 14 percent enhancement in concentration sensitivity, which reduces phototoxicity levels and allows for increased resolution of otherwise unobservable biological structures. The Raman microscope shows the vibrational spectra of biomolecules. Furthermore, quantum light eases the photon budget because it increases the SNR, as Raman scattering can be observed with even less than a single photon within the measurement time frame. Quantum-enhanced images of samples of both dry polystyrene beads and living Saccharomyces cerevisiae yeast were obtained (Figure 3-22) with 23 to 35 percent enhanced SNR, leading to increased image contrast. As such Casacio and colleagues (2021) were able to view features that were uncovered below the SNL.

Another approach toward the use of entangled photons in molecular and biological microscopy involves TPA (Eshun et al. 2022; Mukamel et al. 2020; Varnavski and Goodson 2020; Varnavski et al. 2022). Here, the microscopic image created by the fluorescence selectively excited by the process of the entangled TPA was reported. Entangled two-photon microscopy offers nonlinear imaging capabilities at an unprecedented low excitation intensity, 10⁷, which is six orders of magnitude lower than the excitation level for the classical two-photon image. The nonmonotonic dependence of the image on the femtosecond delay between the components of the entangled photon pair is demonstrated. This delay dependence is a result of specific quantum interference effects associated with the entanglement, and this is not observable with classical excitation light. Additionally, fluorescent images of breast cancer cells were captured using entangled TPA in a scanning microscope (Figure 3-23; Varnavski et al. 2022). These images were generated at an excitation intensity orders of magnitude lower than the conditions necessary for classical two-photon microscopy. Quantum-enhanced entangled two-photon microscopy has shown cancer cell imaging capabilities at an unprecedented low excitation intensity of ~3.6 × 10⁷ photons/sec, which is one million times lower than the excitation level for the classical two-photon fluorescence image obtained in the same microscope. The entangled two-photon microscope images resolving specific features of breast cancer cells in different stages of mitosis have been obtained. Varnavski and colleagues (2022) also illustrated the impact of

the low light excitation with entangled photons on the photodamage of the cancer cells. This is encouraging in the development of methods with extremely low light probe intensity with entangled two-photon microscopy critical to minimizing photobleaching during repetitive imaging and damage to cells in live-cell applications.

3.4.4 Measurement of Coherence in Molecular Systems

The measurement of coherence in chemical systems has a long history. The development of better methods to resolve more information about the molecular system is a significant part of modern physical chemistry. The instrumentation utilized in measuring the relatively fast dephasing times in molecules was significantly improved with the advent of the femtosecond laser, the use of which is now rather commonplace. As an example, one can utilize short laser pulses to excite ladders of states in phase, thereby making a superposition that can be detected using 2D spectroscopy. In the past decade, the number of research groups with the experience and equipment to carry out electronic and vibrational 2D spectroscopy has significantly increased. In this approach, a cross-peak in the 2D map labels the excited and detected transitions (Figure 3-24), while oscillations in the cross-peaks as a function of pump–probe waiting time reveal coherences involving those transitions occurring together. However, over time the oscillations damp away as a function of waiting time (Figure 3-24c). This spectral characteristic is a consequence of dephasing, giving a lower bound for the decoherence time of the quantum superposition. Figure 3-24a shows an example of electronic coherence for a semiconductor “nanoplatelet” colloid dispersed in

an ambient-temperature solution. Here, the broadband femtosecond pulses (red curve) overlap with the first two exciton states, which are the heavy-hole (HX) and light-hole (LX) exciton. As demonstrated in Figure 3-24b, the amplitudes of the cross-peaks, HX-LX and LX-HX, in the 2D signal map oscillate as a function of excitation-detection time delay, showing that the amplitudes of HX and LX bands indeed are correlated until the superposition dephases. The dephasing of this ensemble happens with a time constant of 13 fs, which is aligned with previous observations for similar systems (Figure 3-24c). Electronic coherences at ambient temperature typically decohere with a time constant of ≤100 fs.

3.4.5 Coherence and Biological Function Is the Future

In the past 10 years, electronic and vibrational coherence experiments have improved significantly with the use of time-resolved nonlinear spectroscopic techniques. Mukamel and colleagues (2020) have been instrumental in the theory and prediction of spectroscopic signals under this context. Chemists have investigated the electronic coherences in organic and biological systems in impressive detail. According to Scholes and colleagues (2017), it might be appropriate for the field to move beyond measuring the coherence lifetimes. The use of multidimensional spectroscopic methods to probe other parameters related to the excited-state properties could provide new insights into the connection between biological function and chemical structure. For example, time-resolved ultrafast optical probes of chiral dynamics may provide a new window to explore how interactions with structured environments drive electronic dynamics. Incorporating optical activity into time-resolved spectroscopies has proven challenging owing to the small signal and large achiral background. Higgins, Allodi, and colleagues (2021) demonstrate that 2D electronic spectroscopy (ES) can be adapted to detect chiral signals and that these signals reveal how excitations delocalize and contract following excitation. They dynamically probe the evolution of the chiral electronic structure in the light-harvesting complex 2 of purple bacteria (Figure 3-25) following photoexcitation by creating a

chiral 2D mapping. The dynamics of the chiral 2D signal directly report on changes in the degree of delocalization of the excitonic states following photoexcitation. The mechanism of energy transfer in this system may enhance transfer probability owing to the coherent coupling among chromophores while suppressing fluorescence that arises from populating delocalized states. This generally applicable spectroscopy will provide an incisive tool to probe ultrafast transient molecular fluctuations that are obscured in non-chiral experiments. Although coherence has been shown to yield transformative ways for improving function, advances have been confined to pristine matter and coherence was considered fragile. However, recent evidence of coherence in chemical and biological systems suggests that the phenomena are robust and can survive in the face of disorder and noise. Chemists are still assessing the variability of this process and the possibility that coherence experiments and mechanisms can be used effectively in more complex chemical systems. A key missing point is the role of coherence as a design element in realizing function.

Most recently, quantum coherences observed as time-dependent beats in ultrafast spectroscopic experiments arise when light–matter interactions prepare systems in superpositions of states with differing energy (e.g., redox states) and fixed phases across the ensemble. These measurements reveal important variations when compared to previous reports, suggesting that redox conditions tune vibronic coupling in the Fenna–Matthews–Olson (FMO) pigment–protein in green sulfur bacteria; this raises the question of whether redox conditions may also affect the long-lived (>100 fs) quantum coherences observed in this very important complex. Higgins, Lloyd, and colleagues (2021) performed ultrafast 2DES on the FMO complex under both oxidizing and reducing conditions (Figure 3-26). They observed that many excited-state coherences are exclusively present in reducing conditions and are absent or attenuated in oxidizing conditions. Reducing conditions mimic the natural conditions of the complex more closely. Furthermore, the presence of these coherences correlates with the vibronic coupling that produces faster, more efficient energy transfer through the complex under reducing conditions. The growth of coherences across the waiting time and the number of beat frequencies across hundreds of wavenumbers in the power spectra suggest that the beats are excited-state coherences with a mostly vibrational character whose phase relationship is maintained through the energy transfer process. These results suggest that excitonic energy transfer proceeds through a coherent mechanism in this complex and that the coherences may provide a tool to disentangle coherent relaxation from energy transfer driven by stochastic environmental fluctuations.

As this field shifts its focus from confirming the existence of coherence to exploring the connection between coherence and function, new methods are being extended to provide new insights. As expected, this area of investigation will require extensive feedback between theory and experiment, synthesis and measurement, and the development of systematic methods to quantify the influence of coherence in specific processes or devices. Exploring function requires controlled perturbation, and establishing this essential methodology requires new control mechanisms and clear assessment tools. For instance, new and improved experimental techniques will enhance capabilities such as measuring the delocalization of wave functions or measuring the collapse of delocalized states. In this regard, attosecond laser sources have enhanced the ability to study coherent electronic motion, such as charge migration and quantum interference between electrons, as well as electron-nuclear wave packet motion. Similarly, advances in time-resolved X-ray spectroscopies open up new probes of electronic structure by delineating dynamics into element-specific contributions. Inspired by coherent multiple scattering and molecular transport junctions, the reactivity of metal centers might be directed or redox chemistry tuned by interference effects to modify the electron density at an active site of a catalyst. In coherent backscattering, which provides scattering that is twice as bright as diffuse scattering, substantial gains are possible when robust coherence phenomena are exploited. Such gains warrant future research into coherence as a potential force for enhancing function.

3.4.6 High-Finesse Cavities and Nanophotonics for Molecular Qubit Systems

In addition to understanding and designing molecular systems with favorable optical properties, a different and complementary approach is to engineer optical control by modifying the molecule–light coupling, by changing the vacuum field of the light itself. One way to accomplish this is by surrounding a molecule with an optical cavity (Figure 3-27). Light resonant with the cavity recirculates and repeatedly interacts with matter located in the cavity modes, leading to enhanced light–matter coupling. In addition, the cavity can also modify the decay rate of optically excited molecular states by modifying the density of states of the electromagnetic field.

viable path toward emission factors exceeding 90 percent (Riedel et al. 2017). Second, optical cavities can provide coherent interactions between matter spaced over large distances. For atomic systems, this has been proposed as a way to produce entanglement and teleportation of quantum information over long distances. The same principles apply to optically active molecular systems.

Although we have focused above on how optical cavities can be used to produce more favorable qubits, combining the QIS technique of optical cavities with molecules also opens a potential new way to control chemical reactions. In the presence of strong light–matter coupling, molecules within a cavity inherit photonic character and form so-called polaritons, which are quantum superpositions of light and matter. This has led to much interest recently in polariton chemistry (see below), where new possibilities abound. With dense highly absorbing molecular ensembles in microfluidic cavities and dye lasers, experiments already have seen polaritons affect chemical reactivity and optoelectronic properties (Ebbesen 2016; Ribeiro et al. 2018). New types of molecular polaritons with unique properties could be synthesized (Gu and Franco 2018), and novel catalysts might be found. For example, with molecules in cavities, it could be possible to control photochemistry remotely simply by tuning a “remote catalyst” in a distant cavity that is coupled to the system of interest via photons (Du, Ribeiro, and Yuen-Zhou 2019). The many new possibilities with molecular systems in optical cavities come with some technical and material challenges, including fabricating cavities with low loss (i.e., high reflectance and low scatter) and integrating cavities with molecular systems.

Analogous to the work with optical cavities described above, demonstrations of strong spin–photon coupling in resonant microwave devices is another area of significant exploration (Bonizzoni, Ghirri, and Affronte 2018; Eddins et al. 2014; Gimeno et al. 2020; Jenkins et al. 2013). All of these investigations have been in a regime far from the quantum limit, involving macroscopic numbers of spins and photons. Nevertheless, strong coupling effects have been reported for a number of different molecular systems and resonator types. This is an area ripe for further development in order to reach a point where entanglement between microwave photons and a small ensemble of molecular spins (or even a single molecular spin) is achieved.

Cavity Polaritons

When strongly coupled, material states and optical cavity modes transform into a single quantum entity—a polariton—with its own distinct and modifiable physics and chemistry, fundamentally altering the behavior of both matter and the electromagnetic field. Cavities may provide a nondestructive and versatile way to control energy, charge, and coherence transfer in molecular systems, which underlie reactivity, photochemistry, and catalysis. To

establish the fundamental scientific understanding of cavity-enabled molecular control, it is necessary to establish basic principles that can guide future chemical innovation. With these essential concepts identified, the modular nature of external cavity control will usher in the rapid technological development of cavity-enabled chemistry. By leveraging, for example, microfluidic and lab-on-a-chip platforms, it will be possible to carry out complex, high-value chemical transformations that are key to the production of pharmaceutical and industrial chemicals. This could indeed be another avenue for chemistry in QIS.

The use of cavities is already under way in chemical research, with two parallel but related efforts in the polaritonic chemistry community. One thrust has been to apply ultrafast laser spectroscopy methods to monitor the complex energy transfer and relaxation processes in molecular polaritons, both in the vibrational and electronic domains. While considerable basic science interest certainly exists, there are also many possibilities for applications in QIS using molecular polaritons as quantum resources, particularly in the case of quantum transduction. Vibrational polaritons are especially promising in this context because of the relatively long coherence times achievable using molecular vibrations coupled to resonant optical cavities. The use of ultrafast 2D optical spectroscopy, both in the visible and mid-IR spectral regions, has revealed nonlinear optical effects of potential use for optical switching, polaritonic energy ladders, and the exchange of energy between bright polariton states and nearly inactive dark states (Figure 3-28). There are clearly challenges that require advanced cavity designs, as suggested by a recent study showing considerable contributions to the measured two-dimensional infrared (2DIR) response from molecules that are neither polaritons nor dark states but instead comprise a non-polaritonic background (Duan et al. 2021). These fundamental dynamics studies are important because they directly probe the underlying physics of all the components present in a molecule-cavity construct.

The other major thrust in polaritonic chemistry is arguably the most promising avenue for future investigation and discovery. Following the first observation of a cavity-controlled photochemical reaction by Laboratoire des Nanostructures at the University of Strasbourg, there are now several examples of chemical reactions whose kinetics and equilibria can be altered through coupling to a resonant optical cavity (George et al. 2015). An important recent finding showed that the selectivity and rate of bond cleavages in an alkyl silane compound can be modified within a cavity tuned to specific resonances of the reacting species (Nagarajan, Thomas, and Ebbesen 2021). This observation implies that cavities can exert both thermodynamic control (e.g., altering the equilibrium constant of a reaction) as well

as kinetic control by selectively lowering the barrier for one reaction channel relative to another. Perhaps an exciting recent development is a report that shows that a urethane addition reaction can be controlled by strong coupling to a cavity (Ahn, Herrera, and Simpkins 2022). Though no more fundamental chemically than the alkyl silane example, this latter work is the first by a research group that is completely independent of the University of Strasbourg team. Indeed, challenges in reproducing some cavity results have cast some doubt on the robustness of cavity control, but the recent urethane addition reaction provides ample evidence that cavity control is possible in other laboratories. Theoretically, scientists such as Gu and Mukamel (2021) are working to describe this process in detail.

Perhaps the key outstanding challenge that the field must confront is the lack of a clear set of guiding principles that underlie the mechanism(s) of cavity control. Whereas the physics of strong coupling between molecules and cavity modes are understood, no consensus exists regarding the reasons why creating delocalized states with energies slightly above and below the uncoupled energies would cause reaction rate constants to increase or decrease to the degree reported in the literature. Statistical theories, such as transition-state theory, that routinely apply broadly in chemistry seem to be completely inconsistent with polaritonic effects on reactivity. Dynamical approaches based on quantum electrodynamic density functional theory are feasible but are extremely demanding and are unlikely to be helpful for the broader chemistry community. A set of experimental results on tractable chemically reactive systems that can be studied to provide inspiration and inputs to theoretical analyses will deepen this research area. Ideally, these reactions will be elementary and will not rely on complicated multistep mechanisms. Reactions that are phototriggered will enable direct dynamical investigation rather than more coarse-grained kinetics measurements. In some sense, polaritonic chemistry, especially when coupling vibrational transitions to cavity modes, is the fulfillment of a dream that began with the advent of lasers in the 1960s that we would be able to do chemistry precisely using mode selectivity. A promising aspect of the present situation is that it is highly likely that basic principles will be established quickly—particularly with enhanced funding support—paving the way for accelerated chemical technologies that will offer entirely new ways to conceive of and carry out chemistry.

Another area of research that has received primarily theoretical attention in the chemistry community is the use of quantum light in the context of polaritonic effects in cavities. Gu and Mukamel (2020) have shown that nonlinear quantum light spectroscopy can be employed for probing two-photon excitations in polaritonic systems. Theoretical investigations have identified the combined signatures of a cavity photon mode strongly coupled to molecules and entangled photons on collective bipolariton resonances. Initial studies focused on TPA signals with an entangled photon pair to a polaritonic system consisting of N two-level molecules strongly coupled to a single cavity photon mode. By comparing the TPA spectra with classical and quantum light, Gu and Mukamel (2020) have demonstrated that entangled photons can create two-photon excitations in polaritonic systems that are drastically different from the classical two-photon excitations. Entangled photons can reveal classically dark bipolariton states by modifying the quantum interference among transition pathways leading to TPA (Figure 3-29). These exciting predictions have yet to be examined experimentally and provide a novel opportunity for chemists working in QIS.

example involves the application to clock transitions associated with a Ho(III) molecular spin qubit (Liu, Mrozek, et al. 2021). Crystals contain two electrically polar molecules related by inversion. Importantly, the structural distortion that gives rise to the electric dipole moment is also responsible for the symmetry breaking that induces the clock transition (the avoided level crossing between the Zeeman levels corresponding to electronic spin-up and -down states)—that is, the clock transition frequency is directly coupled to the molecular dipole moment. In turn, this implies linear coupling of an electric field to the clock transition frequency. However, the frequency shift is opposite for the two inversion-related molecules. Consequently, the application of an electric field pulse during the first half of a Hahn-echo sequence results in an eventual phase-shifted refocusing of the two populations at angles ±φ relative to the magnetic pulses within the rotating frame, where the magnitude of φ scales linearly with the duration and amplitude of the electric field pulse. Thus, a periodic modulation and decay of the echo is observed in the in-phase echo signal, with no echo detected in the quadrature channel (due to cancelation of the ±φ shifted echoes from each subpopulation). The decay is caused by the inhomogeneous response of the ensemble to the electric field pulse. Since these inhomogeneities are static, the spin echo is completely recovered if the electric field pulse spans the second (refocusing) half of the Hahn-echo sequence (see Figure 3-32). It is then possible to perform a 2D experiment, after which the electric field pulse is applied only during the refocusing magnetic π pulse while scanning the frequency of the π pulse. Refocusing is only effective for one of the subpopulations

(i.e., half of the molecules) when the π-pulse frequency matches the shift caused by the electric field. Hence, the echo signal drops in intensity by a factor of two and shifts linearly both up and down in frequency in response to the magnitude of the electric field (see Figure 3-32). In this way, the electric field breaks the inversion symmetry inherent to the crystal, enabling selective excitation of the two inversion-related molecules. More generally, these studies clearly demonstrate coherent spin-electric control in molecular nanomagnets that exhibit long coherence times due to clock transitions (Shiddiq et al. 2016), paving the way toward local electrical control of molecular spin qubits at the nanometer scale with low dissipation (Ullah et al. 2022). These methods are now finding more general utility in the chemical study of magnetoelectric materials (Liu, Mrozek, et al. 2021).

3.6 EXTEND QUANTUM TELEPORTATION AMONG MOLECULAR QUBITS

Quantum communication is a rapidly growing area of QIS and engineering, with quantum network test beds appearing around the world. In contrast to classical communication, quantum communication takes place by sending or receiving information transmitted using the quantum states of a specific quantum system (e.g., a photon). Such “flying qubits” offer built-in security given that the (unwanted) observation of these states collapses the information. A quantum internet is being developed using entangled qubits to create a unique mode of information processing utilizing teleportation. In addition to security, a quantum network may enable quantum computing clusters, connecting multiple quantum computers to create more powerful machines for applications in science and engineering. Ultimately, one imagines a quantum ecosystem where sensors, communications (wiring), and computers exchange quantum information without exposure to the classical world. This new paradigm for communications requires the community to address a growing number of significant challenges, including the creation of quantum repeaters and robust quantum memories. These needs sit at the interface of fundamental physics and chemistry, representing exciting and important scientific research areas.

Today’s internet is driven by the existence of repeaters that circumvent our current limits in materials science. Digital optical pulses travel through optical fibers until their amplitude is diminished through scattering processes in the glass. At that point, the signal is read, amplified, and repeated downstream. This process is repeated until the signal reaches its destination. Given the laws of quantum physics, quantum repeaters will require a different operational mode given the inherent information collapse upon observation. To that end, the community currently envisions new concepts such as exploiting and combining different quantum degrees of freedom, as well as mixing photons, phonons, magnons, and spins in an effort to amplify one mode in lieu of another. Devising and constructing atomically engineered materials that enable quantum transduction at the single spin–photon and/or single phonon–photon level may be greatly advanced through molecular chemistry, where advanced theory and synthesis may be used to manipulate local bond strengths and spin–orbit interactions, integrate single ion memories, tune optical levels, and design integration pathways with optical communication pathways (fibers). In addition to a high degree of spatial control and tunable emission energies, there are opportunities to multiplex quantum signals within single structures given molecular length scales and existing organic molecular frameworks. The remarkable precision, placement, and tunability of molecular qubits and potential memories make molecular quantum systems powerful candidates to accelerate research in science and engineering (Baek et al. 2005).

Use Molecular Systems to Teleport Quantum Information Over Distances Greater than 1 μm with High Fidelity

Control of the coherence times of quantum states is currently one of the major challenges in QIS (Wasielewski et al. 2020). Spin-state decoherence can be accelerated greatly by interactions such as spin exchange, hyperfine coupling, spin–orbit coupling, and magnetic dipolar coupling. By controlling the structure and composition of molecular qubits, many of these decoherence sources can be mitigated and/or controlled (Krzyaniak et al. 2015; Yu et al. 2016). For example, purely organic molecular qubits have the advantages of weak spin–orbit coupling and well-defined electron–electron and electron–nuclear spin exchange interactions (Nelson et al. 2017). Moreover, ultrafast photochemical electron transfer within an organic donor-bridge-acceptor (D-B-A) molecule can produce a radical pair that can function as two entangled spin qubits (D^•+–A^•−), giving rise to an entangled two-spin singlet or triplet state (Krzyaniak et al. 2015; Yu et al. 2016).

biomolecules, especially enzymes, in real time. The difficulty arises when one needs to increase the light intensity to levels required to probe the important mechanistic molecules, risking changing their behavior—or even damaging them. In some cases, ordered arrays of quantum sensors that are individually addressable and densely packed in a small volume are used to produce hyper-resolved images or maps that would far exceed the diffraction limit or even room-temperature super-resolution. Creating such an array requires a rigidly organized collection of qubits that are individually optically addressable. These arrays can be organized into a molecular structure, within a single crystal, or in a larger cross-braced scaffold of many solid-state quantum nanoparticles. In other NMR-related experiments, different isotopes such as deuterium, ¹³C, and ¹⁵N are used. Imaging spectroscopies sensitive to molecular vibrations can be used to detect deuterium but have low sensitivity for ¹³C or ¹⁵N. However, ¹³C and ¹⁵N have nuclear magnetic moments that can be detected in conventional NMR spectrometers, raising the intriguing possibility of using high-resolution and high-sensitivity quantum-enhanced magnetometry for detection. Such a tool would enable, for instance, maps of candidate drug distributions through different tissues and, perhaps, even which organelles the drug localizes to, or maps of protein synthesis upregulation in the brain in response to learning or memory formation. To achieve spatially dense measurements with high time resolution using quantum sensors, one will need to integrate the measurements with complementary classical sensing modalities that can provide nanoscale chemical information across an entire cell. These methods will exploit the exquisite sensitivity of enzymes to the local biochemical environment.

3.8.2 Quantum Light and Biological Processes

Other scientists interested in this difficult issue regarding the measurement or tracking of enzymatic activity in biological systems with low light intensities have invoked quantum metrology as a solution. In a proof of concept, conducted by Cimini and colleagues (2019), N00N states were employed to observe and measure enzyme

activity. First, N00N states that are in circular-polarization basis are created from single photons with orthogonal polarizations (using SPDC) that underwent interference through a polarizing beam splitter (Figure 3-35). This interference is an important step because it generates photons in superposed states, hence exhibiting indistinguishable spatial and temporal degrees of freedom, which allows the creation of the N00N states. After the desired photon state is generated, it is then passed through a solution containing enzymes undergoing catalytic activity. In this example, the enzymes are hydrolyzing sucrose and producing mixtures of chiral products. Due to the chiral states, the molecule’s interactions with the photon creates a phase shift between the different N00N states. The extent of the phase shift is a function of the concentration of sucrose. Two avalanche photodiodes were used to measure these shifts. There are still challenges making this technique feasible for use (signal-to-noise detection ratio). However, this proof-of-principle work demonstrated researchers’ ability to study biocatalytic reactions to track enzymes’ activity in real time by taking advantage of different chiral systems and their distinct optical properties.

as metal tips, to localize an incident electromagnetic field to a sub-wavelength regime (Figure 3-37) (Anlage et al. 2001; Farina and Hwang 2020; Hecht et al. 2000; Mauser and Hartschuh 2014; Rosner and van der Weide 2002; Seo and Kim 2022). Common abbreviations for the techniques are near-field scanning optical microscopy for visible light to terahertz characterization and near-field scanning microwave microscopy for the long-wavelength microwave version. The main difference is the source: visible to terahertz light can be generated by nonlinear frequency generation from a laser, whereas microwaves are created using electronic signal generators and antennas or waveguides when needed. Scanning near-field techniques can reach tens of nanometers in resolution to isolate single molecules or look at interactions between nearest-neighbor molecules. The methods are also easily converted into transient measurements, wherein an optical or microwave pump is used to initiate an excited state of the molecular qubit and then another wavelength region is used as the probe. This allows for measurements of the underlying dephasing mechanisms that are controlling the molecular magnet or qubit operation.

While not as elegant as ion trap measurements, scanning near-field microscopies will be an emergent tool for molecular QIS systems. Multiple companies now sell instruments adaptable for chemistry in QIS work. Depending on the complexity and options selected, the instruments range from the hundreds of thousands to the million-dollar range. The instruments also have multiple applications and therefore can be invested as user facilities. Cutting-edge methods that use STM feedback circuits are now also allowing for sub-nanometer resolution, even with microwave frequencies, and are emergent tools that allow true quantum readout between different spin centers of a molecule (Imtiaz, Wallis, and Kabos 2014). Furthermore, by combining scanning probe microscopy methods with entangled photon spectroscopy, how molecules control or rely on entanglement can be directly measured on the atomic scale.

Combined, the application of single-molecule characterization tools to chemistry in QIS can (1) measure the quantum state of a molecular qubit after being initialized and its decoherence time; (2) use steady-state and ultrafast characterization techniques to measure spin-lattice, spin-spin, and other interactions to understand decoherence mechanisms; and (3) repeat these measurements with nearby molecular qubits to understand coupling mechanisms. These types of measurements would give clues as to how to delineate and achieve multiple qubit interactions in molecular quantum sensors and other QIS systems.

3.10.1b Control and Detection of Ensembles of Molecular Qubits

The application of molecular qubits in quantum scenarios requires the delineation of interactions in an ensemble. Multiple molecular qubits, molecular magnets, or molecular sensors will need to be addressed individually and measured in a complicated environment. While some differentiation can be achieved through synthetic means, as demonstrated by sensing with diamond and other vacancy centers, emerging instrumentation will also play a dominant role.

Shi, Fung, and Zhou 2021). In this case, a molecular qubit would be imaged by its unique Raman spectral profile. Since Raman scattering can measure individual bonds, methods may be developed that can measure decoherence indirectly by vibrational dynamics or, more challengingly, directly through their fine structure. Other nonlinear microscopy techniques, like second and third harmonic generation or sum frequency generation, are also sensitive to local polarizations and vibrational populations and can be used as label-free methods for molecular qubit characterization and interaction (Lim 2019; Rehberg et al. 2011; Wang and Xiong 2021).

3.10.1c Advanced Spectroscopy of Entangled and Classical Interactions for Molecular Qubits

Previous sections have focused on ways to measure or control individual molecular qubits or networks thereof. However, instrumentation development on the ensemble level presents an opportunity to help understand how molecular qubits operate and transduce quantum information. Although microwaves have been used for the control and readout of most molecular qubits to date, how a molecule decoheres and its quantum coupling are often explored using ultrafast lasers. As mentioned throughout this report, techniques like sum frequency generation and stimulated Raman scattering can be used to understand time domain information about bond vibrations; the optical Kerr effect can be used to measure spin polarizations; and multidimensional spectroscopy (2DIR and 2DES) or transient EPR can be used to create and measure molecular spin center coupling within a molecule.

Further development of existing nonlinear optical techniques to operate in conjunction with magnetic fields, microwave access, and optical readout of spin will advance the field. Conventional pulsed EPR cannot measure rapid electron spin relaxation (less than ~5 ns) and does not provide the spatial resolution of optical techniques. Ultrafast spin relaxation processes have been studied in spin-½ systems using all-optical methods such as Faraday rotation to measure optical induction of ground-state magnetization dynamics and subsequent observation of quantum-beat free-induction decay (Furue et al. 2005). While long T₁ and T₂ times are required for quantum information processing applications, measurement of ultrafast spin dynamics still enables fundamental insight into molecular spin–phonon coupling and decoherence mechanisms. A particularly powerful way to explore these mechanisms that need to be developed is probing variable-temperature, variable-field regimes that are typically inaccessible to EPR and AC magnetometry.

Although ensemble based, these techniques remain prominent because high-purity synthesis products can be created. The methods of this section are more mature and accessible, but continued development could further simplify the tools to the level that a synthetic laboratory could use them for rapid characterization without needing a laser spectroscopist collaborator. While these collaborations are highly encouraged and productive, they create a

barrier for universities and laboratories that do not have the funds for complex laser tools. This report concludes that the development of new specialized techniques is needed, but simultaneous efforts to simplify and lower the cost of existing nonlinear or entangled spectroscopy techniques are critical for accelerating molecular qubit design rules. These developments will also increase ready access to user facilities housing the needed tools.

3.11 IMPROVE INFRASTRUCTURE FOR CHEMICAL MEASUREMENTS IN QIS

Physical resources are required to support the range of established and emerging tools for the experimental characterization of quantum behavior discussed in this chapter. This section reviews available infrastructure in the United States today and makes recommendations for the prioritization of future resources to advance the field of QIS.

This section divides user facilities into three main categories that are based on the scale of the infrastructure. Box 3-1 briefly defines these categories as they are used in the remainder of this section. Although the National Science Foundation (NSF) has established funding ranges (in dollars) that are defined using similar terms, the committee acknowledged the continuously changing costs of various techniques and elected not to assign dollar values to these scale definitions.

Another key element of establishing and maintaining a strong infrastructure for QIS chemistry research in the United States is workforce development. The cultivation of an educated, well-equipped human resources pipeline to support the maintenance and operation of user facilities is discussed in Chapter 5.

3.11.1 Laboratory-Scale, Single–Principal Investigator Centers

A need exists to develop chemistry-oriented QIS laboratories if the field is going to progress. As of now, most single–principal investigator (PI) laboratories do not have access to the basic tools needed to characterize microwave qubit interactions, such as transient EPR, nor the ability to characterize optical qubits. Most chemistry in QIS research has been accomplished by the partnering of synthetic chemistry laboratories with physics or physical chemistry laboratories that specialize in quantum optics or transient EPR techniques. However, these collaborations do not exist at every university and present a barrier to development. Standardized and commercial instruments need to be developed for basic qubit characterization, especially for measuring properties like coherence times or spin-coupling interactions in multiqubit architectures, to allow any synthetic laboratory access to chemistry in QIS research.

Even for quantum optics and optics laboratories, a need for investment remains. Magnetic field and microwave generators are not commonly associated with ultrafast laser optics, and, at the same time, advanced optical capabilities are rarely integrated with transient EPR spectrometers. These capabilities, along with cryostats, represent significant investments. Physical chemists have developed a broad range of nonlinear and linear spectroscopies that can measure almost all of the details of the molecular interaction Hamiltonian. However, these techniques are not yet optimized for measurements of molecular qubits. Ultracold atoms and optical lattice research is currently focused in the physics community, and extension to molecular systems beyond a few atoms will enhance this area of research greatly.

While custom instrument development is needed, multiple tools can already be purchased commercially and adapted to the chemistry in QIS tasks. For example, the multiphoton and tagless Raman imaging microscopes

developed for biology can be used to isolate and measure molecular quantum sensors in complex environments. Optical tweezer systems can be purchased for isolating single-molecular qubits and exploring factors like strain and stiffness on the molecular qubit’s dephasing time. Near-field scanning probe microscopies like NSOM and NSMM have reached maturity and can be used for single- and multiple-qubit interaction studies with atomic resolution. Scanning probe methods can also be used to arrange molecules on surfaces. Transient EPR is a dominant tool that is commercially available, albeit at a high cost and on a limited basis. All of these instruments represent significant investments in the hundreds of thousands to several-million-dollar range, but they can be leveraged for multiple experiments across multiple departments to help their adoption.

Driven by communications industries, rapid advances in microwave technologies are such that the hardware employed in transient EPR spectrometers is becoming more advanced, more widely available, and more affordable. Indeed, perhaps with the exception of the magnet, the components needed to assemble quite advanced transient EPR spectrometers can be acquired at a fraction of the current cost of a fully assembled turnkey instrument. Of course, most research groups do not possess the technical expertise to build their own transient EPR spectrometers. Nevertheless, the increased need for these capabilities motivates creative solutions to the significant financial barrier that currently limits the availability of such systems.

There are encouraging signs that several new startups, often supported by Small Business Innovation Research–type federal funding, are entering this scientific space. In turn, this is leading to exciting new routes to reduce costs such as Open Source Hardware,¹ where all relevant information required to produce a given hardware item can be posted and made available to the wider research community at no cost. Indeed, one can already find examples of extremely low-cost components relevant to transient EPR spectroscopy. Another area of rapid progress is the development of advanced on-chip EPR spectrometers that employ tiny permanent magnets (Hassan et al. 2021, 2022; Künstner et al. 2021; Lotfi et al. 2022), with the main spectrometer hardware often having a footprint no larger than a thumb drive. Such systems offer the added advantage of exceptional sample sensitivity. Although still developmental, these instruments are starting to demonstrate some of the capabilities of commercial spectrometers and could soon become commercially available at low cost. Therefore, the prospects for more widespread access to transient EPR capabilities over the next 10 years are promising and should be encouraged by funding agencies, although it is clear that these capabilities will remain somewhat limited in comparison to the most advanced systems (see below). It will be important to ensure that issues related to precision, reproducibility, and safety are addressed if such low-cost instruments become more widely available. However, it should be noted that the international EPR community successfully polices such issues upon the emergence of any new hardware or methodology.

3.11.2 Mid-Scale University User Facilities and Centers

While the prospects for low-cost hardware described in the previous section are exciting, there will always be a need for high-end instrumentation, as well as one-of-a-kind spectrometers offering truly unique capabilities, developed by the leading instrument builders. State-of-the-art commercial spectrometers are essential for benchmarking promising molecular systems and enabling measurements (e.g., of coherence and weak spin–spin interactions) that are simply not possible by other means (Kundu et al. 2023). As noted in a recent article in the International EPR (ESR) Society newsletter (Gallez 2022), “Those universities with modern pulsed EPR systems are currently swamped with demand.” However, there are significant barriers to accessing instrumentation in the leading EPR laboratories. Typically, these instruments are operated in support of targeted research programs with relatively narrow scope, and access is limited to collaborators on these projects. The best way to remove these barriers is to locate high-end instrumentation and promote the development of new methodologies (e.g., those discussed in Section 3.11.3) at national user facilities. These organizations are truly open to the wider research community through merit-based proposal processes that are reviewed externally. They support world-leading staff scientists who can optimize the measurement time even for the most inexperienced user (from running the measurements to the data analysis, interpretation, and drafting of manuscripts); they educate their users, thus greatly

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¹ The website for Open Source Hardware is www.oshwa.org, accessed April 27, 2023.

expanding intellectual resources within the wider chemistry community; and they enforce policies related to, for example, FAIR data principles.

Although several EPR facilities are scattered across the United States (see Figure 3-40), most of them are supported by the National Institutes of Health, and their mission is focused on biomedical, biochemical, and biophysical research (e.g., Cornell [ACERT]; University of Wisconsin, Milwaukee [National Biomedical EPR Center]; Miami University in Ohio [Ohio Advanced EPR Laboratory]; and the University of Denver [EPR Center]). These facilities generally are not open to chemists working on QIS problems, even though a handful of experiments have been performed using instruments located at these centers (Zadrozny et al. 2017). The Department of Energy also supports facilities focused on environmental and energy-related research (e.g., Argonne National Laboratory, National Renewable Energy Laboratory, Pacific Northwest National Laboratory, and University of California, Davis). The only U.S. EPR user facility that currently supports research at the interface between chemistry and QIS is the NSF Division of Materials Research–funded NHMFL, where the majority of experiments are conducted at magnetic fields and frequencies that are considerably higher than those of commercial instruments (Baker et al. 2015; Morley, Brunel, and van Tol 2008). However, users of the facility also have access to commercial X- (9–10 GHz) and W-band (94 GHz) transient spectrometers as well as a high-power W-band transient spectrometer developed at St. Andrews University (Cruickshank et al. 2009), resources that are highly valued by the user community. The facility is also staffed with internationally renowned EPR support scientists. Therefore, it serves as a model facility for carrying out research on molecular spin qubits of the kinds discussed in Chapter 2, with more than two-thirds of its users drawn from the chemistry community. It is a resource not only for U.S. scientists but also for international researchers, with about 50 percent of its users coming from overseas—particularly from Europe, where a large and active chemistry QIS community already exists. Indeed, the strong demand from overseas users is a testament to the world-leading stature of the NHMFL EPR facility, as similar user centers exist in Europe and Asia. The downside is that limited resources (both in terms of staffing and instrumentation) are making it more difficult for the facility to keep up with user demand, with considerable growth in activity deriving from chemistry-inspired QIS research.

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² The website for the European Magnetic Field Laboratory is https://emfl.eu, accessed April 28, 2023.

same molecule (e.g., a qudit) or among multiple coupled spin centers, thereby facilitating execution of multiqubit gate operations, initially among molecular ensembles. In the longer term (5 to 10 years), efforts would be directed toward arrays of molecules on surfaces. The costs for such developments will be considerable, likely requiring new source/amplifier technologies that extend beyond the current 5G frequency band. Therefore, design criteria must be carefully formulated and based on a viable chemical approach, involving teams of instrument builders, engineers, and synthetic QIS chemists. Significant benchmarking of proposed molecular species represents an important first step in the design process so that future instrument developments do not fail simply because the molecules do not perform as expected. The scale and complexity of these development projects are comparable to those typically associated with national facilities. Moreover, staffing requirements, both during development and upon deployment, suggest that these projects be managed through national facilities. This will ensure availability of necessary expertise, project management, and maximum eventual access.

3.11.3 Large-Scale User Facilities

The committee did not identify any need for new large-scale national facilities. However, barriers to access were clearly identified. Current facilities are oversubscribed, and clearly a need exists to support efforts that increase access—for example, by creating regional instrumentation hubs that relieve national facilities of some of their more routine user demand, increasing availability of magnet/beam time at national facilities to the chemistry QIS community, and developing new beamlines and resonance magnets. However, as noted in the previous section, available user end-station instrumentation also represents a major current barrier to access at national facilities. Therefore, a steady funding stream is needed to develop and sustain support for chemistry QIS instrumentation at national facilities, as has been the case for other large-scale entities such as synchrotrons.

3.11.3a Magnet Laboratories

As noted in earlier sections of this report, strong spin–orbit coupling and ligand field effects can give rise to situations where metal-based spin qubits are EPR-silent at the conventional low frequencies (<50 GHz) and fields (<1.5 T) employed in commercial spectrometers, thus necessitating measurements at high magnetic fields and at frequencies stretching into the terahertz and far-IR regimes. The same is true for NMR, where the most advanced spectrometers capable of targeting quadrupolar nuclei spanning much of the periodic table operate at magnetic fields in excess of 30 T (Gan et al. 2017). For this reason, a large body of work in the molecular QIS field has been performed at large-scale user facilities such as NHMFL.

Much of the high-field research performed today involves powered (resistive) magnets, and the power supplies ultimately limit the amount of time available to the user community at the very highest fields. The current situation at NHMFL is that costs prohibit 24/7 operations. Therefore, some scope exists for increasing user operations without the need for significant investment in infrastructure, although the associated staffing and electricity costs would be quite considerable. Recently, however, the laboratory successfully brought online the first all-superconducting 32 T user magnet, with high-temperature superconducting inner coils (Weijers et al. 2016). Compared to resistive magnet technologies, it provides a lower noise environment for precision measurements, as well as a larger sample space. This magnet is now part of the user NHMFL program, although it is not currently instrumented for EPR or solid-state NMR experiments. Even though this magnet runs independently of the high-power resistive magnets (that require a 56 MW supply), it would not be easy to operate outside of the facility due to a very high helium consumption and complex supporting infrastructure (not to mention that this technology remains developmental). The resonance users of the facility (both EPR and NMR) recognize the tremendous opportunities that such a magnet provides in terms of increased access to the very highest magnetic fields. The current version does not provide the homogeneity needed for high-resolution solid-state NMR, but it is more than adequate for most EPR applications as well as certain specialized NMR applications (and further development of methodologies such as DNP). The development of a second all-superconducting magnet dedicated to resonance applications as well as the future development of high-resolution all-superconducting NMR magnets would serve as a very significant research resource for the chemistry QIS community.

electron–photon pairs (Wong and Kaminer 2021). Given that specialized detectors and long experimental times are needed for most X-ray experiments, the creation of dedicated beamlines could revolutionize nonlinear X-ray source creation as well as exploration of the use of entanglement.

3.11.4 Limited Natural Resources

Applications of rare-earth and actinide elements in the area of optically addressable qubits are discussed in Section 2.2.2 of this report. An important consideration in many of these examples is the availability of naturally occurring isotopes with a variety of nuclear spin quantum numbers, I. A perfect example is the I = ½ ¹⁷¹Yb⁺ ion that is employed in ion trap quantum computers (Wright et al. 2019), where the hyperfine interaction involving the lone unpaired 6s electron gives rise to a hydrogenic-like situation and a massive 12.6 GHz clock transition. Similar targets may be anticipated in pursuit of ideal molecular qubit candidates, necessitating isotopic purifications or the production of particular isotopes at nuclear reactor facilities. Access to such isotopes will likely be limited and costly, with sub-milligram syntheses precluding many standard characterization techniques that lack sensitivity. Sample recycling will therefore be essential. Such approaches are already employed—for example, in QIS studies of endohedral metallofullerenes, which are typically extracted and purified via chromatographic techniques. Indeed, several gadolinium endohedral metallofullerenes have recently shown great promise as potential molecular qudits (d-dimensional qubits) (Fu et al. 2022; Hu et al. 2018), where the fullerene cage provides added protection from environmental decoherence sources.

Finally, the ongoing helium crisis represents a very significant challenge for researchers working in the QIS field, where many studies are conducted at temperatures in the sub-10 K range. Moreover, many groups continue to rely on older liquid helium–based cryogenic systems. It goes without saying that continued efforts must be pursued to reduce reliance on such cryogenic approaches, by furnishing researchers with closed-cycle refrigeration systems.

3.12 SUMMARY OF RESEARCH PRIORITIES AND RECOMMENDATION

The following fundamental research priorities have been identified by the committee and extensively discussed in Chapter 3 as those that the Department of Energy and NSF should prioritize within the target research area of “measurement and control of molecular quantum systems.”

Research Priorities:

• Develop new approaches and techniques for addressing and controlling multiple electron and nuclear spins and optical cycling centers in molecular systems.
• Develop techniques to probe molecular qubits at complex interfaces to inform their systematic control.

• Develop enhanced spectroscopic and microscopic techniques by creating
  1. entangled photon sources with higher yield and better spectral coverage, and
  2. high-finesse cavities and nanophotonics for molecular qubit systems.
• Develop and exploit alternative approaches to spin polarization and coherence control (e.g., chirality-induced spin selectivity and electric field effects).
• Use molecular systems to teleport quantum information over distances greater than 1 μm with high fidelity.
• Develop molecular quantum transduction schemes that take advantage of entangled photons as well as entangled electrons and nuclear spins.
• Advance quantum sensing techniques to further understand biological systems.
• Use bio-inspired quantum processes for the development of new quantum technologies.

In sum, in this chapter the committee discussed infrastructure and instrumentation needs at various levels. The committee provides Recommendation 3-1 to ensure that the infrastructure needs and instrumentation support required to drive chemistry QIS research in the United States are met on a competitive timescale.