A Molecular Approach to Quantum Sensing.

The second quantum revolution hinges on the creation of materials that unite atomic structural precision with electronic and structural tunability. A molecular approach to quantum information science (QIS) promises to enable the bottom-up creation of quantum systems. Within the broad reach of QIS, which spans fields ranging from quantum computation to quantum communication, we will focus on quantum sensing. Quantum sensing harnesses quantum control to interrogate the world around us. A broadly applicable class of quantum sensors would feature adaptable environmental compatibility, control over distance from the target analyte, and a tunable energy range of interaction. Molecules enable customizable "designer" quantum sensors with tunable functionality and compatibility across a range of environments. These capabilities offer the potential to bring unmatched sensitivity and spatial resolution to address a wide range of sensing tasks from the characterization of dynamic biological processes to the detection of emergent phenomena in condensed matter. In this Outlook, we outline the concepts and design criteria central to quantum sensors and look toward the next generation of designer quantum sensors based on new classes of molecular sensors.

We are living in the second quantum revolution. The realization of the quantum nature of the universe instigated the first quantum revolution; in this second quantum revolution, we are harnessing unprecedented control of those quantum properties to transform our universe. Control over quantum properties is at the core of the broad field of quantum information science (QIS),[1−10] which includes fantastical-sounding ideas such as the quantum Internet, quantum computing, and quantum metrology. Among these emerging quantum technologies, quantum sensing has demonstrated early successes, with discoveries across fields from condensed matter physics to molecular biology.[11−16] In these areas, quantum sensing exploits the sensitivity of quantum states to detect minute environmental fluctuations or perturbations to gain increased information about the natural world. Within this area, scientists are leveraging quantum coherence and entanglement between nuclear and electronic states (Figure A),[17] between electronic states of exotic matter (Figure B), (18−20)or between photon degrees of freedom (Figure C)[22] to accomplish sensing tasks inaccessible with their classical analogues. Further, quantum sensor arrays built on entangled quantum states could surpass classical sensing limits, allowing us to probe theoretically predicted phenomena or matter.[21] This has been elegantly demonstrated by the Advanced Light Interferometer Gravitational-Wave Observatory (aLIGO) to further enhance the detection limits of gravitational waves.[22]

Figure 1

Examples of existing sensing protocols that leverage quantum mechanical properties such as coherence and entanglement to detect (A) electron–nuclear hyperfine interactions, (B) electric fields, and (C) space–time perturbations.

While there are many candidates for quantum sensors, the joint features of atomic-scale tunability, reproducibility, and chemical specificity make paramagnetic molecules a paradigm-shifting category of materials.[23−28] Fundamentally, the same chemical design features that facilitate targeted drug design with molecules afford chemical selectivity and enable proximity to their sensing target in quantum sensors. These features enhance the sensing interaction, maximizing resolution while minimizing noise and detection limits. Molecules also support the additional design requirements of quantum sensors beyond those of classical sensors: a mechanism to prepare the initial sensor state and lifetimes that are long enough to facilitate high-fidelity sensing and read-out. Molecules offer a tunable electronic structure, enabling control of coherent quantum state lifetimes and making them ideal hosts for electronic manifolds that enable optical initialization and read-out of spin information. A specific class of electronic structure enables numerous defects in semiconductors to offer optical single-spin read-out, a critical feature for nanoscale sensing.[29,30] A molecule designed to mimic this electronic structure can seamlessly interface with the spectroscopic infrastructure built up for defect-based systems, thereby catapulting forward the application of molecules as quantum sensors. We recently demonstrated all optical initialization and read-out with three spin-triplet molecular systems, a first important step toward this goal.[31]

Molecular quantum sensors would have broad applicability, impacting fields ranging from structural biology to dark matter detection. One key example is the visionary goal of single-molecule magnetic resonance. The modularity of molecules could enable targeted interactions to precisely position sensors on biological substrates. Localizing molecular quantum sensors is the first step toward mapping out protein structures and dynamics with single-molecule magnetic resonance techniques (Figure ).[14,15] Further exploiting the electric and magnetic field detection capabilities of quantum sensors, molecular quantum sensors proximal to extended solids may be used to detect and characterize emergent phenomena in condensed matter physics, such as fundamental excitations like spinons and magnons.[34,35] Alternatively, in astrophysics, the detection of dark matter necessitates sensors with exceptionally high sensitivities, tunable energy responses, and orientation information.[36] In each of these areas, chemical synthesis provides a powerful method for both tuning quantum states and controlling multisensor interactions that underpin quantum entanglement to achieve unparalleled sensitivities.

Figure 2

(Bottom) Calculated sensitivities of nitrogen-vacancy (NV) centers to the 1H nuclear spin magnetic moment quantified by the number of detectable 1H spins using a published formula.[14] Orange circles, green squares, and purple triangles represent NV center data from refs (14), (32), and (33) respectively. For consistency, we included only NV centers with directly measured depths whose coherence times (T2) were measured through XY8-k pulse sequences, assumed a read-out fidelity F = 0.03, and excluded quantum logic-based read-out from ref (14). The yellow region highlights the distance regime in which molecular quantum sensors can localize near target nuclei. The boxed region represents the localization and sensitivity requirements necessary for single-molecule and single-nuclei sensing, opening exciting possibilities such as single protein studies of membrane protein dynamics in vivo (top).

Realizing the promise of molecular quantum sensors necessitates understanding and controlling several key features simultaneously. Molecular sensors precisely tailored to the desired sensing task and imbued with analyte specificity through targeted conjugation or noncovalent binding could outperform existing quantum sensors. Colocalization of molecular sensors to their targets with Ångström-scale proximity would maximize the sensor response and detection resolution. At the same time, molecules targeted to the specific environments that are compatible with temperature, opacity of the environment, and intended time scale of the measurement will enable translating quantum-enhanced measurements into new applications. The immense potential of chemical synthesis perfectly positions molecules to deliver a new class of broadly tunable quantum sensors with unparalleled sensitivity and specificity.

In this Outlook, we highlight key considerations for quantum sensors, review several proof-of principle demonstrations that are critical for the use of molecular quantum sensor candidates, and describe exciting applications for quantum sensing. In addition, we outline how these new classes of designer materials may deliver transformative quantum sensor capabilities while comparing to them the state-of-the-art within the field.

Requirements for Quantum Sensors

The requirements for quantum sensors[21] are similar to those for quantum bits, or qubits.[37] Much like qubits, quantum sensors must (1) have discrete, well-defined quantum states, such as polarization of photons, quantized currents in superconducting circuits, and electronic or nuclear spin states;[21,38] (2) be initialized into a single, well-known state such that the desired stimulus produces a specific, predictable, and measurable signal; (3) be addressable for manipulation, for example, via optical, microwave, or radiofrequency excitation; and (4) incorporate a sensor read-out pathway to measure the signal response. However, unlike qubits that interact minimally with the surrounding environment, quantum sensors must (5) interact strongly with their sensing target. This interaction needs to induce changes in the quantum state of the sensor or transition rates between states or modulate the quantum coherence of the sensor.[21,39−41] Judicious selection of the quantum system is imperative to maximize sensitivity to the desired physical quantity while mitigating background noise. Toward this end, molecular systems offer the requisite chemical specificity to achieve unprecedented quantum sensor–analyte proximity via covalent attachment or van der Waals interactions, maximizing the potential sensor response.

Quantum sensors also share many requirements with classical sensing systems. Both classical and quantum sensors require a well-defined state that, upon interacting with an external perturbation or analyte, undergoes a signal transduction event to create a sensing response. However, the requirements stated above for quantum sensors include additional considerations that classical sensors do not have. Quantum sensors must have mechanisms to prepare the initial sensor state and generate coherent quantum state lifetimes long enough to facilitate high-fidelity sensing and read-out. Achieving these prerequisites of quantum sensors, specifically a well-defined, two-level quantum system, enables the use of entanglement to boost sensor performance in multisensor or ensemble measurements.[9] Quantum entanglement is a phenomenon in which the quantum states of the systems cannot be defined independently and are intrinsically linked. Entangled sensor arrays have the potential to surpass the standard quantum limit: for N measurements of a quantity, the uncertainty usually scales with N–1/2. For N entangled sensors, however, the lower Heisenberg limit applies where uncertainty scales with N–1.[21,42−44] Entanglement has already been employed in a range of quantum systems, including photons, atomic clocks, quantum dots, trapped ions, and nuclear spins.[40,45−54] Managing the more rapid decoherence of entangled states is critical to realize these statistical gains but represents an opportunity for quantum sensing to reach precisions and sensitivities beyond the limit of classical systems.[55−58]

Toward the Next Generation of Quantum Sensors

To meet their promise, molecular quantum sensors must address several key challenges. First, molecular quantum sensor candidates need to demonstrate long-lived coherence times. Sufficiently long coherence times are crucial to maximize the sensor response to a given analyte and to achieve optimal sensor read-out. Quantum sensor state lifetimes establish the upper bound on both the time the sensor can interact with its target and the time scale for read-out. These lifetimes also establish a floor for sensitivity, limiting the minimum perturbation of the quantum sensor that can be detected. Second, sensors must incorporate mechanisms for initialization, such as thermal, optical, or electrical pathways,[21,59,60] and read-out,[61−63] ideally at the single-sensor level. Individual sensor read-out mechanisms may be most readily achieved via optical and electrical methods.

To address these challenges, we and others are employing coordination chemistry to rationally control both the physical and electronic structure as well as coherence properties including quantum state lifetimes (T1) and coherence times (Tm).[25,31,64−92] Ligand design provides an immediate route to achieve long T1 and Tm or optical initialization and read-out pathways. Further tuning parameters such as spin–orbit coupling, crystal field splitting, and electron–nuclear hyperfine interaction provide additional handles to optimize the requisite sensor criteria mentioned above.[25,79,86,93] In addition, harnessing parameters such as spin–orbit coupling and hyperfine interactions can elicit detection of physical parameters beyond magnetic fields, including electric fields and pressure.[79,94,95] Lastly, employing anisotropic electronic structures of transition metals can provide orientation information during sensing, enhancing the spatial resolution of the molecular sensor.[96,97]

Over the last five years, our group has made significant inroads to understand and optimize the molecular design for quantum sensors. We identified a system with a ligand environment comprised of nearly nuclear spin-free elements, such as carbon, sulfur, and oxygen. This ligand design mitigated environmental magnetic noise originating from nearby nuclear spins that reduce Tm.[98] Using this approach, we synthesized a vanadium(IV) complex (PPh4-d20)2[V(C8S8)3] that, when dissolved in a similarly nuclear spin-free carbon disulfide matrix, exhibited quantum state coherence times of 675(7) μs, a time scale on par with nitrogen-vacancy (NV) centers (Figure ).[69] This proof-of-concept study demonstrated that synthetic chemistry can enable long coherent quantum state lifetimes in coordination complexes.

Figure 3

Environmental nuclear spins represent a major source of decoherence in molecular quantum systems. By judicious design of ligand and solvent environments with nuclear spin-free elements (carbon and sulfur), we achieved a nearly millisecond coherence time in a molecular vanadium(IV) complex (PPh4-d20)2[V(C8S8)3] dissolved in carbon disulfide. Data were reproduced from ref (69).

Progressing beyond demonstration of long coherence times within a highly controlled environment requires a different approach. To achieve long coherence times in magnetically noisy environments, such as those present in biological systems, we sought to mitigate decoherence pathways caused by nearby spin-active nuclei in these environments using so-called “clock-like” transitions (Figure ). Within a clock-like transition, the slope of the transition relative to magnetic field is zero, thereby insulating transitions from ambient magnetic noise. This principle has been extensively used in solid-state and atomic qubits and is the core idea behind atomic clocks. Creating these transitions requires precise engineering of the ligand field to access hyperfine coupling-induced electron–nuclear state mixing.[99,100] To achieve this, we sought a S = 1/2 spin coupled with a large nuclear spin and a large hyperfine coupling term. Specifically, we selected a square planar coordination environment around cobalt(II) ions in a porphyrinic metal–organic framework [(TCPP)Co0.07Zn0.93]3[Zr6O4(OH)4(H2O)6]2.[101] The square planar environment generates a low spin S = 1/2 state in a mixed 4s-3dz orbital. The 4s character of the orbital enables strong Fermi contact with the I = 7/2 nuclear spin of the 59Co nucleus, thereby engendering strong mixing (large hyperfine term). With this system, we were able to observe coherence times of 1.96(1) μs despite the magnetically noisy framework environment. Notably, coherence times at the clock transition were seven times longer than that at nonclock transitions.

Figure 4

To achieve strong electron–nuclear hyperfine coupling for clock transitions, we designed square planar cobalt(II) complexes in a porphyrinic metal–organic framework [(TCPP)Co0.07Zn0.93]3[Zr6O4(OH)4(H2O)6]2. The clock transition exhibited seven-fold longer coherence times compared to the nonclock transition at 15 K. Data were reproduced from ref (101).

As described above, current state-of-the-art spin-based quantum sensors offer optical read-out and initialization of spin information. There is a sophisticated infrastructure built up to address these defect-based spins. From an electronic structure perspective, one can envision a defect within a semiconductor as an analogue to a molecule. By mimicking the electronic structure of these materials within a tunable molecular scaffold, it should be possible to interface molecules with established read-out protocols. Initialization and read-out of sensor spin states with light are particularly attractive, as this leverages existing optical technologies for integration into a variety of sensing environments.[102] For example, read-out through optically detected magnetic resonance can enable atomic spatial resolution and single-sensor read-out.[103] To accomplish this goal, we drew inspiration from the electronic structure of defect sites such as the anionic NV center in diamond and chromium(IV) ions in silicon carbide, which exhibit optical pathways for initialization and read-out. Our molecular design included three key targets: a spin-triplet ground state, a first excited state of spin-singlet character exhibiting radiative decay, and a sufficiently small ground state zero-field splitting to achieve microwave manipulation.[104] Toward this end, tetrahedral chromium(IV) complexes in strong ligand fields (Figure a) offer the targeted excited state structure and zero-field splitting values (e.g., D < 0.3 cm–1 in Figure b). For these systems, ground state spin polarization was achieved through resonant optical excitation from the spin-triplet ground state to the spin-singlet excited state, while photoluminescence from the spin-singlet excited state enabled optical read-out of the ground state (Figure b).[31] While such mechanisms were previously considered exclusive to defect-based systems, this work illustrates how synthetic chemistry may confer molecules with optical initialization and read-out pathways. Moreover, the electronic structures that give rise to optical addressability can be readily translated into biologically compatible ions[70] or heteroleptic molecular architectures.[105] The insights gleaned from this work paves the way toward imbuing optical initialization and single-spin read-out in molecular quantum sensors in an effort to maximize spatial resolution and sensitivity.

Figure 5

(a) Molecular structure of tetra-o-tolylchromium(IV) complex. (b) Energy level diagram of the Cr(IV) center depicting photoluminescence of the S = 0 state after excitation with a resonant laser source. Data were reproduced from ref (31).

Opportunities for Molecular Quantum Sensors

The rapid development of quantum sensing technology over the past decade has yielded impressive discoveries across a range of fields. For example, in biology, quantum sensors detected the nuclear spins of individual proteins and the action potentials of neurons in living organisms.[14,16] In astrophysics, the advanced Laser Interferometer Gravitational-wave Observatory (aLIGO) employs a type of entangled state in photons, “squeezed light”, to enhance signal-to-noise in the detection of gravitational waves from exotic astrophysical events (Figure B).[22,106,107] In condensed matter physics, phenomena such as spin waves and skyrmions have been mapped and measured at the nanometer scale with quantum sensors on the tips of atomic force microscopes.[11,13] These discoveries illustrate the revolutionary cross-discipline capabilities and potential of quantum sensors. Building on the fundamental insights from these and other studies, we highlight key areas where molecular quantum sensors may aid in future discovery across disparate fields such as materials science, chemistry, biology, and particle physics.

Quantum sensing provides a characterization modality to probe dynamic biological structures and processes with subcellular resolution and impressive sensitivities. Notable accomplishments include both mapping magnetic ions and nanostructures in living cells and noninvasive detection of neuronal action potentials.[16,108−114] The current state-of-the-art quantum sensor in this arena, the NV center in diamond, has demonstrated sensing at the single-cell and, with complementary targeting strategies, even the single-molecule level.[14,16,113] Furthermore, these sensors have detected individual nuclear and electronic spins in individual proteins and, with recent advancements in single nuclear spin detection by NV centers, point the way toward single-molecule and single -spin magnetic resonance techniques in biological systems.[14,15,115,116] The combination of an optical read-out, chemical inertness, and compatibility with nanofabrication has been central to many of the NV center-based applications.[117] These demonstrations highlight the exceptional sensitivity and resolution for detecting magnetic signatures in biological media with atomic defect-based quantum sensors.

Building upon such impressive demonstrations, molecular quantum sensors with engineered specificity to cellular or molecular targets and optical read-out will enable targeted analyte sensing down to the single molecule. The nanometer size of molecules is commensurate with that of biomolecules from amino acids to proteins, enabling precise colocalization of the sensor to maximize sensitivity (Figure ). Highly dynamical systems such as cellular membranes and intrinsically disordered proteins would be prime targets for single-molecule magnetic resonance studies with quantum sensors since their time-dependent properties are lost or averaged out in ensemble measurements.[118,119]

Strategies that imbue quantum sensors with single-molecule sensitivities, such as optical or electrical read-out, could also reveal chemical species undetectable with ensemble magnetic resonance methods. Current efforts have utilized entangled photons and NV centers in diamond for nanoscale and single-molecule magnetic resonance of various chemical species.[120−124] Single-molecule detection by quantum sensors can greatly benefit chemical separation and analysis devices. For example, merging the sensitivity of quantum sensors with microfluidic devices could enable miniaturization of devices for chemical separations and analysis on the molecular scale.[125,126] Species such as ortho/para hydrogen, ortho/para water, chiral molecules, and transient intermediates are exciting targets for quantum sensors.[127−129] The tunability of molecular quantum sensors to merge analyte specificity with various sensing modalities can enable new understanding toward fundamental chemical reactivity.

In condensed matter physics, accessing new sensing modalities with quantum sensors offers a powerful method to develop correlations between multiple physical phenomena with the same sensor. Designing quantum sensors for nanoscale electrometry can enable high-resolution electric field imaging to map charged phenomena in two-dimensional electronics such as polar skyrmions and charged quasiparticles.[130−132] Furthermore, quantum sensors that can detect both electric and magnetic fields can provide new insights into the coupling between charge and spin in condensed matter phenomena, such as the current-induced motion of skyrmions and magnetoelectric coupling in multiferroic domains.[133−140] Among electric field sensors (Figure ), single NV centers in diamond are highly attractive for nanoscale electric field detection when used as a probe in atomic force microscopy. However, the sensitivity of NV centers toward electric fields is two orders of magnitude lower than that of existing techniques such as single-electron transistors (Figure ).[141] While the lower sensitivity can be compensated for by using shallower NV centers in closer proximities to the electric field targets, their coherence times rapidly degrade as their depth decreases. In contrast, molecular quantum sensors may be placed much closer to the substrate or material of interest for improved electric field sensitivity. Critically, molecular systems may be easily deposited on or near the target substrate through processing techniques, such as spin coating, dropcasting, or thermal evaporation, which are challenging to use with defect-based systems. Thus, using this sensor portability and the structural flexibility to design sensors with long lifetimes on magnetically noisy surfaces (Figure ), we envision an immediate pathway for molecular systems to create the desired sensor-substrate interactions and achieve optimal electric field read-out.

Figure 6

Electric field sensitivity V m–1 Hz–1/2 of existing sensing candidates. Spatial resolution is defined as the characteristic length scale over which the electric field is detected. The gray region marks the sensitivity and spatial resolution goals for single charge detection at single-molecule resolutions. For each candidate, spatial resolution was defined as follows. SET: half distance of the junction. Rydberg atoms: gas cell length. Trapped ions: electrode width. Ensemble NV centers: diamond substrate thickness. Single NV centers: NV center depth. Sensitivity data were taken from refs (141)−[152]. SET sensitivities were calculated using the gate capacitance and junction length.

Detecting dark matter represents another untapped opportunity for molecular quantum sensors with atomic control over sensor orientation and energy states. Theory predicts a range of potential dark matter candidates, directing the search for these particles to several different energy regimes (Figure ).[153] Molecule-based sensors offer a unique approach for creating tunable dark matter detectors. By appropriately tuning nuclear or electronic energy levels, molecules could detect dark matter via transitions between spin sublevels or electronic states or by measuring phase changes in superpositions of quantum states.[154] For example, in the search for ultralight dark matter candidates such as axions, molecular sensors can employ electronic or nuclear spin states to couple to the axion, inducing energy or spin coherence changes that can be measured.[155−157] Toward this goal, recent experimental studies have initiated searches for dark matter using nuclear spin states, such as 199Hg, 13C, and 1H, in molecular quantum sensors.[158,159]

Figure 7

Experimental (solid blue areas) and projected (dashed lines) sensitivities of dark matter detection strategies that utilize interactions with a dark photon. Solid green regions depict stellar constraints on sensitivity. Sensitivity limits taken from refs (36), (154), (162), and (165)−[168].

One particularly attractive region for molecular sensors that has yet to be experimentally explored is low-mass dark matter candidates within the 10–3 to 106 eV, known as hidden sector dark matter. One well-established candidate in this mass regime is dark photons.[160,161] While current dark photon detection proposals rely on dark photon scattering in superconductors or absorption of dark photons through phonons and electron excitations in semiconductors and polar materials,[36,162−164] a recent intriguing proposal for dark photon detection employs single-molecule magnets. Here, energy deposited by dark matter excites intramolecular vibrational modes and charge transfer transitions, inducing a change in the magnetic relaxation time of local molecules. This change in magnetic relaxation can then cause a runaway avalanche of spin relaxation, generating a net change in magnetization signal that can be detected.[154] This approach has been recently demonstrated with single crystals of Mn12-acetate molecular magnets, providing a first key step toward broadly tunable molecular sensors for dark matter.[169] The sensitivity of these molecules to dark photons depends on the transition probability of a given vibrational or electronic transition, which can be quantified by the spectral intensity of infrared or UV–vis spectra. By harnessing these transitions in dark photon detection, the Mn12-acetate molecular magnet has projected sensitivities exceeding any other proposed strategy in this energy range (Figure ). Thus, the design of ligand vibrational modes and coordination symmetry can enable further enhancements in sensitivity toward discovering these dark matter candidates. Broadly tunable molecular quantum sensors are poised to help unravel this great mystery of particle physics.

Conclusion

A molecular approach to quantum sensing offers tremendous promise for creating a new class of designer quantum sensors, with each sensor specifically targeted to an analyte and environment. Quantum sensing has already delivered incredible achievements in precision, sensitivity, and spatiotemporal resolution previously unimaginable with conventional measurements. New designer quantum sensors, built from the bottom-up with their sensing target in mind, will expand this scope and deliver brand new capabilities. We as a community have an opportunity to collaborate to identify the key scientific questions that would benefit from the next generation of sensors, to create such systems, and to execute sensing measurements. Achieving these goals will require a truly interdisciplinary approach that will benefit an equally interdisciplinary community. The next generation of quantum sensors will bring unprecedented capabilities and deliver the second quantum revolution into laboratories around the world.