Cavity Born-Oppenheimer approximation for molecules and materials via electric field response.

We present an ab initio method for computing vibro-polariton and phonon-polariton spectra of molecules and solids coupled to the photon modes of optical cavities. We demonstrate that if interactions of cavity photon modes with both nuclear and electronic degrees of freedom are treated on the level of the cavity Born-Oppenheimer approximation, spectra can be expressed in terms of the matter response to electric fields and nuclear displacements, which are readily available in standard density functional perturbation theory implementations. In this framework, results over a range of cavity parameters can be obtained without the need for additional electronic structure calculations, enabling efficient calculations on a wide range of parameters. Furthermore, this approach enables results to be more readily interpreted in terms of the more familiar cavity-independent molecular electric field response properties, such as polarizability and Born effective charges, which enter into the vibro-polariton calculation. Using corresponding electric field response properties of bulk insulating systems, we are also able to obtain the Γ point phonon-polariton spectra of two dimensional (2D) insulators. Results for a selection of cavity-coupled molecular and 2D crystal systems are presented to demonstrate the method.

Emergent Optical Resonances in Atomically Phase-Patterned Semiconducting Monolayers of WS2.

Atomic-scale control of light-matter interactions represents the ultimate frontier for many applications in photonics and quantum technology. Two-dimensional semiconductors, including transition-metal dichalcogenides, are a promising platform to achieve such control due to the combination of an atomically thin geometry and convenient photophysical properties. Here, we demonstrate that a variety of durable polymorphic structures can be combined to generate additional optical resonances beyond the standard excitons. We theoretically predict and experimentally show that atomic-sized patches of the 1T phase within the 1H matrix form unique electronic bands that lead to the emergence of robust optical resonances with strong absorption, circularly polarized emission, and long radiative lifetimes. The atomic manipulation of two-dimensional semiconductors opens unexplored scenarios for light harvesting devices and exciton-based photonics.

Photoinduced Charge Injection from Shallow Point Defects in Diamond into Water.

Thanks to its low or negative surface electron affinity and chemical inertness, diamond is attracting broad attention as a source material of solvated electrons produced by optical excitation of the solid-liquid interface. Unfortunately, its wide bandgap typically imposes the use of wavelengths in the ultraviolet range, hence complicating practical applications. Here, we probe the photocurrent response of water surrounded by single-crystal diamond surfaces engineered to host shallow nitrogen-vacancy (NV) centers. We observe clear signatures of diamond-induced photocurrent generation throughout the visible range and for wavelengths reaching up to 594 nm. Experiments as a function of laser power suggest that NV centers and other coexisting defects─likely in the form of surface traps─contribute to carrier injection, though we find that NVs dominate the system response in the limit of high illumination intensities. Given our growing understanding of near-surface NV centers and adjacent point defects, these results open new perspectives in the application of diamond-liquid interfaces to photocarrier-initiated chemical and spin processes in fluids.

Probing Correlation of Optical Emission and Defect Sites in Hexagonal Boron Nitride by High-Resolution STEM-EELS.

Optically bright emitters in hexagonal boron nitride (hBN) often acting as a source of a single-photon are mostly attributed to point-defect centers, featuring localized intra-bandgap electronic states. Although vacancies, anti-sites, and impurities have been proposed as candidates, the exact physical and chemical nature of most hBN single-photon emitters (SPEs) within the visible region are still up for debate. Combining site-specific high-angle annular dark-field imaging (HAADF) with electron energy loss spectroscopy (EELS), we resolve and identify a few carbon substitutions among neighboring hBN hexagons, all within the same sample region, from which typical defect emission is observed. Our experimental results are further supported by first-principles calculations, through which the stability and possible optical transitions of the proposed carbon-defect complex are assessed. The presented correlation between optical emission and defects provides valuable information toward the controlled creation of emitters in hBN, highlighting carbon complexes as another probable cause of its visible SPEs.

Ab Initio Calculations of Quantum Light-Matter Interactions in General Electromagnetic Environments.

The emerging field of strongly coupled light-matter systems has drawn significant attention in recent years because of the prospect of altering both the physical and chemical properties of molecules and materials. Because this emerging field draws on ideas from both condensed-matter physics and quantum optics, it has attracted the attention of theoreticians from both fields. While the former often employ accurate descriptions of the electronic structure of the matter, the description of the electromagnetic environment is often oversimplified. In contrast, the latter often employs sophisticated descriptions of the electromagnetic environment while using oversimplified few-level approximations of the electronic structure. Both approaches are problematic because the oversimplified descriptions of the electronic system are incapable of describing effects such as light-induced structural changes in the electronic system, while the oversimplified descriptions of the electromagnetic environments can lead to unphysical predictions because the light-matter interactions strengths are misrepresented. In this work, we overcome these shortcomings and present the first method which can quantitatively describe both the electronic system and general electromagnetic environments from first principles. We realize this by combining macroscopic QED (MQED) with Quantum Electrodynamical Density-Functional Theory. To exemplify this approach, we consider the example of an absorbing spherical cavity and study the impact of different parameters of both the environment and the electronic system on the transition from weak-to-strong coupling for different aromatic molecules. As part of this work, we also provide an easy-to-use tool to calculate the cavity coupling strengths for simple cavity setups. Our work is a significant step toward parameter-free ab initio calculations for strongly coupled quantum light-matter systems and will help bridge the gap between theoretical methods and experiments in the field.

Simulating Polaritonic Ground States on Noisy Quantum Devices.

The recent advent of quantum algorithms for noisy quantum devices offers a new route toward simulating strong light-matter interactions of molecules in optical cavities for polaritonic chemistry. In this work, we introduce a general framework for simulating electron-photon-coupled systems on small, noisy quantum devices. This method is based on the variational quantum eigensolver (VQE) with the polaritonic unitary coupled cluster (PUCC) ansatz. To achieve chemical accuracy, we exploit various symmetries in qubit reduction methods, such as electron-photon parity, and use recently developed error mitigation schemes, such as the reference zero-noise extrapolation method. We explore the robustness of the VQE-PUCC approach across a diverse set of regimes for the bond length, cavity frequency, and coupling strength of the H2 molecule in an optical cavity. To quantify the performance, we measure two properties: ground-state energy, fundamentally relevant to chemical reactivity, and photon number, an experimentally accessible general indicator of electron-photon correlation.

Detection and Modeling of Hole Capture by Single Point Defects under Variable Electric Fields.

Understanding carrier trapping in solids has proven key to semiconductor technologies, but observations thus far have relied on ensembles of point defects, where the impact of neighboring traps or carrier screening is often important. Here, we investigate the capture of photogenerated holes by an individual negatively charged nitrogen-vacancy (NV) center in diamond at room temperature. Using an externally gated potential to minimize space-charge effects, we find the capture probability under electric fields of variable sign and amplitude shows an asymmetric-bell-shaped response with maximum at zero voltage. To interpret these observations, we run semiclassical Monte Carlo simulations modeling carrier trapping through a cascade process of phonon emission and obtain electric-field-dependent capture probabilities in good agreement with experiment. Because the mechanisms at play are insensitive to the characteristics of the trap, we anticipate the capture cross sections we observe─largely exceeding those derived from ensemble measurements─may also be present in materials platforms other than diamond.

Shining light on the microscopic resonant mechanism responsible for cavity-mediated chemical reactivity.

Strong light-matter interaction in cavity environments is emerging as a promising approach to control chemical reactions in a non-intrusive and efficient manner. The underlying mechanism that distinguishes between steering, accelerating, or decelerating a chemical reaction has, however, remained unclear, hampering progress in this frontier area of research. We leverage quantum-electrodynamical density-functional theory to unveil the microscopic mechanism behind the experimentally observed reduced reaction rate under cavity induced resonant vibrational strong light-matter coupling. We observe multiple resonances and obtain the thus far theoretically elusive but experimentally critical resonant feature for a single strongly coupled molecule undergoing the reaction. While we describe only a single mode and do not explicitly account for collective coupling or intermolecular interactions, the qualitative agreement with experimental measurements suggests that our conclusions can be largely abstracted towards the experimental realization. Specifically, we find that the cavity mode acts as mediator between different vibrational modes. In effect, vibrational energy localized in single bonds that are critical for the reaction is redistributed differently which ultimately inhibits the reaction.

Chemical reactivity under collective vibrational strong coupling.

Recent experiments of chemical reactions in optical cavities have shown great promise to alter and steer chemical reactions, but still remain poorly understood theoretically. In particular, the origin of resonant effects between the cavity and certain vibrational modes in the collective limit is still subject to active research. In this paper, we study the unimolecular dissociation reactions of many molecules, collectively interacting with an infrared cavity mode, through their vibrational dipole moment. We find that the reaction rate can slow down by increasing the number of aligned molecules, if the cavity mode is resonant with a vibrational mode of the molecules. We also discover a simple scaling relation that scales with the collective Rabi splitting, to estimate the onset of reaction rate modification by collective vibrational strong coupling and numerically demonstrate these effects for up to 104 molecules.

Simple Exchange-Correlation Energy Functionals for Strongly Coupled Light-Matter Systems Based on the Fluctuation-Dissipation Theorem.

Recent experimental advances in strongly coupled light-matter systems have sparked the development of general ab initio methods capable of describing interacting light-matter systems from first principles. One of these methods, quantum-electrodynamical density-functional theory (QEDFT), promises computationally efficient calculations for large correlated light-matter systems with the quality of the calculation depending on the underlying approximation for the exchange-correlation functional. So far no true density-functional approximation has been introduced limiting the efficient application of the theory. In this Letter, we introduce the first gradient-based density functional for the QEDFT exchange-correlation energy derived from the adiabatic-connection fluctuation-dissipation theorem. We benchmark this simple-to-implement approximation on small systems in optical cavities and demonstrate its relatively low computational costs for fullerene molecules up to C_{180} coupled to 400 000 photon modes in a dissipative optical cavity. This Letter now makes first principle calculations of much larger systems possible within the QEDFT framework effectively combining quantum optics with large-scale electronic structure theory.

Frequency-Dependent Sternheimer Linear-Response Formalism for Strongly Coupled Light-Matter Systems.

The rapid progress in quantum-optical experiments, especially in the field of cavity quantum electrodynamics and nanoplasmonics, allows one to substantially modify and control chemical and physical properties of atoms, molecules, and solids by strongly coupling to the quantized field. Alongside such experimental advances has been the recent development of ab initio approaches such as quantum electrodynamical density-functional theory (QEDFT), which is capable of describing these strongly coupled systems from first principles. To investigate response properties of relatively large systems coupled to a wide range of photon modes, ab initio methods that scale well with system size become relevant. In light of this, we extend the linear-response Sternheimer approach within the framework of QEDFT to efficiently compute excited-state properties of strongly coupled light-matter systems. Using this method, we capture features of strong light-matter coupling both in the dispersion and absorption properties of a molecular system strongly coupled to the modes of a cavity. We exemplify the efficiency of the Sternheimer approach by coupling the matter system to the continuum of an electromagnetic field. We observe changes in the spectral features of the coupled system as Lorentzian line shapes turn into Fano resonances when the molecule interacts strongly with the continuum of modes. This work provides an alternative approach for computing efficiently excited-state properties of large molecular systems interacting with the quantized electromagnetic field.

Error rate reduction of single-qubit gates via noise-aware decomposition into native gates.

In the current era of Noisy Intermediate-Scale Quantum (NISQ) technology, the practical use of quantum computers remains inhibited by our inability to aptly decouple qubits from their environment to mitigate computational errors. In this paper, we introduce an approach by which knowledge of a qubit's initial quantum state and the standard parameters describing its decoherence can be leveraged to mitigate the noise present during the execution of a single-qubit gate. We benchmark our protocol using cloud-based access to IBM quantum processors. On ibmq_rome, we demonstrate a reduction of the single-qubit error rate by 38%, from [Formula: see text] to [Formula: see text], provided the initial state of the input qubit is known. On ibmq_bogota, we prove that our protocol will never decrease gate fidelity, provided the system's [Formula: see text] and [Formula: see text] times have not drifted above 100 times their assumed values. The protocol can be used to reduce quantum state preparation errors, as well as to improve the fidelity of quantum circuits for which some knowledge of the qubits' intermediate states can be inferred. This paper presents a pathway to using information about noise levels and quantum state distributions to significantly reduce error rates associated with quantum gates via optimized decomposition into native hardware gates.

Cavity-Modified Unimolecular Dissociation Reactions via Intramolecular Vibrational Energy Redistribution.

While the emerging field of vibrational polariton chemistry has the potential to overcome traditional limitations of synthetic chemistry, the underlying mechanism is not yet well understood. Here, we explore how the dynamics of unimolecular dissociation reactions that are rate-limited by intramolecular vibrational energy redistribution (IVR) can be modified inside an infrared optical cavity. We study a classical model of a bent triatomic molecule, where the two outer atoms are bound by anharmonic Morse potentials to the center atom coupled to a harmonic bending mode. We show that an optical cavity resonantly coupled to particular anharmonic vibrational modes can interfere with IVR and alter unimolecular dissociation reaction rates when the cavity mode acts as a reservoir for vibrational energy. These results lay the foundation for further theoretical work toward understanding the intriguing experimental results of vibrational polaritonic chemistry within the context of IVR.

Ab Initio Linear-Response Approach to Vibro-Polaritons in the Cavity Born-Oppenheimer Approximation.

Recent years have seen significant developments in the study of strong light-matter coupling including the control of chemical reactions by altering the vibrational normal modes of molecules. In the vibrational strong coupling regime, the normal modes of the system become hybrid modes which mix nuclear, electronic, and photonic degrees of freedom. First-principles methods capable of treating light and matter degrees of freedom on the same level of theory are an important tool in understanding such systems. In this work, we develop and apply a generalized force constant matrix approach to the study of mixed vibration-photon (vibro-polariton) states of molecules based on the cavity Born-Oppenheimer approximation and quantum-electrodynamical density-functional theory. With this method, vibro-polariton modes and infrared spectra can be computed via linear-response techniques analogous to those widely used for conventional vibrations and phonons. We also develop an accurate model that highlights the consistent treatment of cavity-coupled electrons in the vibrational strong coupling regime. These electronic effects appear as new terms previously disregarded by simpler models. This effective model also allows for an accurate extrapolation of single and two molecule calculations to the collective strong coupling limit of hundreds of molecules. We benchmark these approaches for single and many CO2 molecules coupled to a single photon mode and the iron pentacarbonyl Fe(CO)5 molecule coupled to a few photon modes. Our results are the first ab initio results for collective vibrational strong coupling effects. This framework for efficient computations of vibro-polaritons paves the way to a systematic description and improved understanding of the behavior of chemical systems in vibrational strong coupling.

Cavity-Modulated Proton Transfer Reactions.

Proton transfer is ubiquitous in many fundamental chemical and biological processes, and the ability to modulate and control the proton transfer rate would have a major impact on numerous quantum technological advances. One possibility to modulate the reaction rate of proton transfer processes is given by exploiting the strong light-matter coupling of chemical systems inside optical or nanoplasmonic cavities. In this work, we investigate the proton transfer reactions in the prototype malonaldehyde and Z-3-amino-propenal (aminopropenal) molecules using different quantum electrodynamics methods, in particular, quantum electrodynamics coupled cluster theory and quantum electrodynamical density functional theory. Depending on the cavity mode polarization direction, we show that the optical cavity can increase the reaction energy barrier by 10-20% or decrease the reaction barrier by ∼5%. By using first-principles methods, this work establishes strong light-matter coupling as a viable and practical route to alter and catalyze proton transfer reactions.

Polaritonic Unitary Coupled Cluster for Quantum Computations.

In the field of polaritonic chemistry, strong light-matter interactions are used to alter chemical reactions inside optical cavities. To understand these processes, the development of reliable theoretical models is essential. While traditional methods have to balance accuracy and system size, new developments in quantum computing offer a path for accurate calculations on currently available quantum devices. Here, we introduce the quantum electrodynamics unitary coupled cluster (QED-UCC) method combined with the Variational Quantum Eigensolver algorithm, as well as the quantum electrodynamics equation-of-motion (QED-EOM) method formulated in the qubit basis that allow accurate calculations of ground-state and excited-state properties of strongly coupled light-matter systems suitable for quantum computers. These methods show excellent agreement with the exact reference results and can outperform their traditional counterparts when strong electronic correlations become significant. This work sets the stage for future developments of polaritonic quantum chemistry methods suitable for both classical and quantum computers.

Defect Polaritons from First Principles.

Control over the optical properties of defects in solid-state materials is necessary for their application in quantum technologies. In this study, we demonstrate, from first principles, how to tune these properties via the formation of defect polaritons in an optical cavity. We show that the polaritonic splitting that shifts the absorption energy of the lower polariton is much higher than can be expected from a Jaynes-Cummings interaction. We also find that the absorption intensity of the lower polariton increases by several orders of magnitude, suggesting a possible route toward overcoming phonon-limited single-photon emission from defect centers. These findings are a result of an effective continuum of electronic transitions near the lowest-lying electronic transition that dramatically enhances the strength of the light-matter interaction. We expect our findings to spur experimental investigations of strong light-matter coupling between defect centers and cavity photons for applications in quantum technologies.

Light-matter interaction of a molecule in a dissipative cavity from first principles.

Cavity-mediated light-matter coupling can dramatically alter opto-electronic and physico-chemical properties of a molecule. Ab initio theoretical predictions of these systems need to combine non-perturbative, many-body electronic structure theory-based methods with cavity quantum electrodynamics and theories of open-quantum systems. Here, we generalize quantum-electrodynamical density functional theory to account for dissipative dynamics of the cavity and describe coupled cavity-single molecule interactions in the weak-to-strong-coupling regimes. Specifically, to establish this generalized technique, we study excited-state dynamics and spectral responses of benzene and toluene under weak-to-strong light-matter coupling. By tuning the coupling, we achieve cavity-mediated energy transfer between electronically excited states. This generalized ab initio quantum-electrodynamical density functional theory treatment can be naturally extended to describe cavity-mediated interactions in arbitrary electromagnetic environments, accessing correlated light-matter observables and thereby closing the gap between electronic structure theory, quantum optics, and nanophotonics.

Hybridized Defects in Solid-State Materials as Artificial Molecules.

Two-dimensional materials can be crafted with structural precision approaching the atomic scale, enabling quantum defects-by-design. These defects are frequently described as "artificial atoms" and are emerging optically addressable spin qubits. However, interactions and coupling of such artificial atoms with each other, in the presence of the lattice, warrants further investigation. Here we present the formation of "artificial molecules" in solids, introducing a chemical degree of freedom in control of quantum optoelectronic materials. Specifically, in monolayer hexagonal boron nitride as our model system, we observe configuration- and distance-dependent dissociation curves and hybridization of defect orbitals within the bandgap into bonding and antibonding orbitals, with splitting energies ranging from ∼10 meV to nearly 1 eV. We calculate the energetics of cis and trans out-of-plane defect pairs CHB-CHB against an in-plane defect pair CB-CB and find that in-plane defect pair interacts more strongly than out-of-plane pairs. We demonstrate an application of this chemical degree of freedom by varying the distance between CB and VN of CBVN and observe changes in the predicted peak absorption wavelength from the visible to the near-infrared spectral band. We envision leveraging this chemical degree of freedom of defect complexes to precisely control and tune defect properties toward engineering robust quantum memories and quantum emitters for quantum information science.

Quantum Information and Algorithms for Correlated Quantum Matter.

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.