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.

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.

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.

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.

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.

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.

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.

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.

Ab initio polaritonic potential-energy surfaces for excited-state nanophotonics and polaritonic chemistry.

Advances in nanophotonics, quantum optics, and low-dimensional materials have enabled precise control of light-matter interactions down to the nanoscale. Combining concepts from each of these fields, there is now an opportunity to create and manipulate photonic matter via strong coupling of molecules to the electromagnetic field. Toward this goal, here we demonstrate a first principles framework to calculate polaritonic excited-state potential-energy surfaces, transition dipole moments, and transition densities for strongly coupled light-matter systems. In particular, we demonstrate the applicability of our methodology by calculating the polaritonic excited-state manifold of a formaldehyde molecule strongly coupled to an optical cavity. This proof-of-concept calculation shows how strong coupling can be exploited to alter photochemical reaction pathways by influencing avoided crossings with tuning of the cavity frequency and coupling strength. Therefore, by introducing an ab initio method to calculate excited-state potential-energy surfaces, our work opens a new avenue for the field of polaritonic chemistry.

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems.

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light-matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).

Atoms and molecules in cavities, from weak to strong coupling in quantum-electrodynamics (QED) chemistry.

In this work, we provide an overview of how well-established concepts in the fields of quantum chemistry and material sciences have to be adapted when the quantum nature of light becomes important in correlated matter-photon problems. We analyze model systems in optical cavities, where the matter-photon interaction is considered from the weak- to the strong-coupling limit and for individual photon modes as well as for the multimode case. We identify fundamental changes in Born-Oppenheimer surfaces, spectroscopic quantities, conical intersections, and efficiency for quantum control. We conclude by applying our recently developed quantum-electrodynamical density-functional theory to spontaneous emission and show how a straightforward approximation accurately describes the correlated electron-photon dynamics. This work paves the way to describe matter-photon interactions from first principles and addresses the emergence of new states of matter in chemistry and material science.

Variational Theory of Nonrelativistic Quantum Electrodynamics.

The ability to achieve ultrastrong coupling between light and matter promises to bring about new means to control material properties, new concepts for manipulating light at the atomic scale, and new insights into quantum electrodynamics (QED). Thus, there is a need to develop quantitative theories of QED phenomena in complex electronic and photonic systems. In this Letter, we develop a variational theory of general non-relativistic QED systems of coupled light and matter. Essential to our Ansatz is the notion of an effective photonic vacuum whose modes are different than the modes in the absence of light-matter coupling. This variational formulation leads to a set of general equations that can describe the ground state of multielectron systems coupled to many photonic modes in real space. As a first step toward a new ab initio approach to ground and excited state energies in QED, we apply our Ansatz to describe a multilevel emitter coupled to many optical modes, a system with no analytical solution. We find a compact semianalytical formula which describes ground and excited state energies very well in all regimes of coupling parameters allowed by sum rules. Our formulation provides a nonperturbative theory of Lamb shifts and Casimir-Polder forces, as well as suggest new physical concepts such as the Casimir energy of a single atom in a cavity. Our method thus give rise to highly accurate nonperturbative descriptions of many other phenomena in general QED systems.

Cavity-Correlated Electron-Nuclear Dynamics from First Principles.

The rapidly developing and converging fields of polaritonic chemistry and quantum optics necessitate a unified approach to predict strongly correlated light-matter interactions with atomic-scale resolution. Toward this overarching goal, we introduce a general time-dependent density-functional theory to study correlated electron, nuclear, and photon interactions on the same quantized footing. We complement our theoretical formulation with the first ab initio calculation of a correlated electron-nuclear-photon system. For a CO_{2} molecule in an optical cavity, we construct the infrared spectra exhibiting Rabi splitting between the upper and lower polaritonic branches, time-dependent quantum-electrodynamical observables such as the electric displacement field, and observe cavity-modulated molecular motion. Our work opens an important new avenue in introducing ab initio methods to the nascent field of collective strong vibrational light-matter interactions.

Kohn-Sham approach to quantum electrodynamical density-functional theory: Exact time-dependent effective potentials in real space.

The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we numerically construct the exact electron-photon Kohn-Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light-matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account.

Optimized Effective Potential for Quantum Electrodynamical Time-Dependent Density Functional Theory.

We propose an orbital exchange-correlation functional for applying time-dependent density functional theory to many-electron systems coupled to cavity photons. The time nonlocal equation for the electron-photon optimized effective potential (OEP) is derived. In the static limit our OEP energy functional reduces to the Lamb shift of the ground state energy. We test the new approximation in the Rabi model. It is shown that the OEP (i) reproduces quantitatively the exact ground-state energy from the weak to the deep strong coupling regime and (ii) accurately captures the dynamics entering the ultrastrong coupling regime. The present formalism opens the path to a first-principles description of correlated electron-photon systems, bridging the gap between electronic structure methods and quantum optics for real material applications.

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.

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.

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.

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.

Modeling loop backbone flexibility in receptor-ligand docking simulations.

The relevance of receptor conformational change during ligand binding is well documented for many pharmaceutically relevant receptors, but is still not fully accounted for in in silico docking methods. While there has been significant progress in treatment of receptor side chain flexibility sampling of backbone flexibility remains challenging because the conformational space expands dramatically and the scoring function must balance protein-protein and protein-ligand contributions. Here, we investigate an efficient multistage backbone reconstruction algorithm for large loop regions in the receptor and demonstrate that treatment of backbone receptor flexibility significantly improves binding mode prediction starting from apo structures and in cross docking simulations. For three different kinase receptors in which large flexible loops reconstruct upon ligand binding, we demonstrate that treatment of backbone flexibility results in accurate models of the complexes in simulations starting from the apo structure. At the example of the DFG-motif in the p38 kinase, we also show how loop reconstruction can be used to model allosteric binding. Our approach thus paves the way to treat the complex process of receptor reconstruction upon ligand binding in docking simulations and may help to design new ligands with high specificity by exploitation of allosteric mechanisms.