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.
Energy transfer in terms of excitation or charge is one of the most basic processes in nature, and understanding and controlling them is one of the major challenges of modern quantum chemistry. In ...this work, we highlight that these processes as well as other chemical properties can be drastically altered by modifying the vacuum fluctuations of the electromagnetic field in a cavity. By using a real-space formulation from first principles that keeps all of the electronic degrees of freedom in the model explicit and simulates changes in the environment by an effective photon mode, we can easily connect to well-known quantum-chemical results such asDexter charge-transfer and Förster excitation-transfer reactions, taking into account the often-disregarded Coulomb and self-polarization interaction. We find that the photonic degrees of freedom introduce extra electron–electron correlations over large distances and that the coupling to the cavity can drastically alter the characteristic charge-transfer behavior and even selectively improve the efficiency. For excitation transfer, we find that the cavity renders the transfer more efficient, essentially distance-independent, and further different configurations of highest efficiency depending on the coherence times. For strong decoherence (short coherence times), the cavity frequency should be in between the isolated excitations of the donor and acceptor, while for weak decoherence (long coherence times), the cavity should enhance a mode that is close to resonance with either donor or acceptor. Our results highlight that changing the photonic environment can redefine chemical processes, rendering polaritonic chemistry a promising approach toward the control of chemical reactions.
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.
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.
In conventional quantum optimal control theory, the parameters that determine an external field are optimised to maximise some predefined function of the trajectory, or of the final state, of a ...matter system. The situation changes in the case of quantum electrodynamics, where the degrees of freedom of the radiation field are now part of the system. In consequence, instead of optimising an external field, the optimal control question turns into a optimisation problem for the many-body initial state of the combined matter-photon system. In the present work, we develop such an optimal control theory for quantum electrodynamics. We derive the equation that provides the gradient of the target function, which is often the occupation of some given state or subspace, with respect to the control variables that define the initial state. We choose the well-known Dicke model to study the possibilities of this technique. In the weak coupling regime, we find that Dicke states are the optimal matter states to reach Fock number states of the cavity mode with large fidelity, and vice versa, that Fock number states of the photon modes are the optimal states to reach the Dicke states. This picture does not prevail in the strong coupling regime. We have also considered the extended case with more than one mode. In this case, we find that increasing the number of two-level systems allows reaching a larger occupation of entangled photon targets.
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We introduce a simple scheme to efficiently compute photon exchange-correlation contributions due to the coupling to transversal photons as formulated in the newly developed quantum-electrodynamical ...density-functional theory (QEDFT). − Our construction employs the optimized-effective potential (OEP) approach by means of the Sternheimer equation to avoid the explicit calculation of unoccupied states. We demonstrate the efficiency of the scheme by applying it to an exactly solvable GaAs quantum ring model system, a single azulene molecule, and chains of sodium dimers, all located in optical cavities and described in full real space. While the first example is a two-dimensional system and allows to benchmark the employed approximations, the latter two examples demonstrate that the correlated electron-photon interaction appreciably distorts the ground-state electronic structure of a real molecule. By using this scheme, we not only construct typical electronic observables, such as the electronic ground-state density, but also illustrate how photon observables, such as the photon number, and mixed electron-photon observables, for example, electron–photon correlation functions, become accessible in a density-functional theory (DFT) framework. This work constitutes the first three-dimensional ab initio calculation within the new QEDFT formalism and thus opens up a new computational route for the ab initio study of correlated electron–photon systems in quantum cavities.
In recent years significant experimental advances in nano-scale fabrication techniques and in available light sources have opened the possibility to study a vast set of novel light-matter interaction ...scenarios, including strong coupling cases. In many situations nowadays, classical electromagnetic modeling is insufficient as quantum effects, both in matter and light, start to play an important role. Instead, a fully self-consistent and microscopic coupling of light and matter becomes necessary. We provide here a critical review of current approaches for electromagnetic modeling, highlighting their limitations. We show how to overcome these limitations by introducing the theoretical foundations and the implementation details of a density-functional approach for coupled photons, electrons, and effective nuclei in non-relativistic quantum electrodynamics. Starting point of the formalism is a generalization of the Pauli-Fierz field theory for which we establish a one-to-one correspondence between external fields and internal variables. Based on this correspondence, we introduce a Kohn-Sham construction which provides a computationally feasible approach for ab-initio light-matter interactions. In the mean-field limit, the formalism reduces to coupled Ehrenfest-Maxwell-Pauli-Kohn-Sham equations. We present an implementation of the approach in the real-space real-time code Octopus using the Riemann-Silberstein formulation of classical electrodynamics to rewrite Maxwell's equations in Schrödinger form. This allows us to use existing very efficient time-evolution algorithms developed for quantum-mechanical systems also for Maxwell's equations. We show how to couple the time-evolution of the electromagnetic fields self-consistently with the quantum time-evolution of the electrons and nuclei. This approach is ideally suited for applications in nano-optics, nano-plasmonics, (photo) electrocatalysis, light-matter coupling in 2D materials, cases where laser pulses carry orbital angular momentum, or light-tailored chemical reactions in optical cavities just to name but a few.
We develop coupled-cluster theory for systems of electrons strongly coupled to photons, providing a promising theoretical tool in polaritonic chemistry with a perspective of application to all types ...of fermion-boson coupled systems. We show benchmark results for model molecular Hamiltonians coupled to cavity photons. By comparing to full configuration interaction results for various ground-state properties and optical spectra, we demonstrate that our method captures all key features present in the exact reference, including Rabi splittings and multiphoton processes. Furthermore, a path on how to incorporate our bosonic extension of coupled-cluster theory into existing quantum chemistry programs is given.
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