Ground-State Quantum-Electrodynamical Density-Functional Theory

In this work we establish a density-functional reformulation of coupled matter-photon problems subject to general external electromagnetic fields and charge currents. We first show that for static minimally-coupled matter-photon systems an external electromagnetic field is equivalent to an external charge current. We employ this to show that scalar external potentials and transversal external charge currents are in a one-to-one correspondence to the expectation values of the charge density and the vector-potential of the correlated matter-photon ground state. This allows to establish a Maxwell-Kohn-Sham approach, where in conjunction with the usual single-particle Kohn-Sham equations a classical Maxwell equation has to be solved. In the magnetic mean-field limit this reduces to a current-density-functional theory that does not suffer from non-uniqueness problems and if furthermore the magnetic field is zero recovers standard density-functional theory

Global fixed point proof of time-dependent density-functional theory

We reformulate and generalize the uniqueness and existence proofs of time-dependent density-functional theory. The central idea is to restate the fundamental one-to-one correspondence between densities and potentials as a global fixed point question for potentials on a given time-interval. We show that the unique fixed point, i.e. the unique potential generating a given density, is reached as the limiting point of an iterative procedure. The one-to-one correspondence between densities and potentials is a straightforward result provided that the response function of the divergence of the internal forces is bounded. The existence, i.e. the v-representability of a density, can be proven as well provided that the operator norms of the response functions of the members of the iterative sequence of potentials have an upper bound. The densities under consideration have second time-derivatives that are required to satisfy a condition slightly weaker than being square-integrable. This approach avoids the usual restrictions of Taylor-expandability in time of the uniqueness theorem by Runge and Gross [Phys.Rev.Lett.52, 997 (1984)] and of the existence theorem by van Leeuwen [Phys.Rev.Lett. 82, 3863 (1999)]. Owing to its generality, the proof not only answers basic questions in density-functional theory but also has potential implications in other fields of physics.Comment: 4 pages, 1 figur

Time-dependent Kohn-Sham approach to quantum electrodynamics

We prove a generalization of the van Leeuwen theorem towards quantum electrodynamics, providing the formal foundations of a time-dependent Kohn-Sham construction for coupled quantized matter and electromagnetic fields. Thereby we circumvent the symmetry-causality problems associated with the action-functional approach to Kohn-Sham systems. We show that the effective external four-potential and four-current of the Kohn-Sham system are uniquely defined and that the effective four-current takes a very simple form. Further we rederive the Runge-Gross theorem for quantum electrodynamics.Comment: 8 page

[Viewpoint:] Inducing Multiple Reactions with a Single Photon

Using an optical cavity to couple several molecules can potentially set up a chemical chain reaction that requires just one photon to initiate

Times of arrival: Bohm beats Kijowski

We prove that the Bohmian arrival time of the 1D Schroedinger evolution violates the quadratic form structure on which Kijowski's axiomatic treatment of arrival times is based. Within Kijowski's framework, for a free right moving wave packet, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time. We derive an inequality relating the average Bohmian arrival time to the one of Kijowksi. We prove that the average Bohmian arrival time is less than Kijowski's one if and only if the wave packet leads to position probability backflow through x. Otherwise the two average arrival times coincide.Comment: 9 page

Exact Solution for A Real Polaritonic System Under Vibrational Strong Coupling in Thermodynamic Equilibrium: Absence of Zero Temperature and Loss of Light-Matter Entanglement

The first exact quantum simulation of a real molecular system (HD+) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled systems of mixed quantum statistics (Bosons and Fermions) are discussed and circumvented by the specific choice of our molecular system. Our exact simulations reveal the absence of a zero temperature for the strongly coupled matter and light subsystems, due to cavity induced non-equilibrium conditions. Furthermore, we explore the temperature dependency of light-matter quantum entanglement, which emerges for the groundstate, but is quickly lost already in the deep cryogenic regime, opposing predictions from phenomenological models (Jaynes-Cummings). Distillable molecular light-matter entanglement of ro-vibrational states may open interesting perspectives for quantum technological applications. Moreover, we find that the dynamics (fluctuations) of matter remains modified by the quantum nature of the thermal and vacuum field fluctuations for significant temperatures, e.g. at ambient conditions. These observations (loss of entanglement and coupling to quantum fluctuations) has far reaching consequences for the understanding and control of polaritonic chemistry and materials science, since a semi-classical theoretical description of light-matter interaction becomes feasible, but the typical canonical equilibrium assumption for the nuclear dynamics remains broken. This opens the door for quantum fluctuations induced stochastic resonance phenomena under vibrational strong coupling. A plausible theoretical mechanism to explain the experimentally observed resonance phenomena in absence of periodic driving, which have not yet been understood

Understanding polaritonic chemistry from ab initio quantum electrodynamics

In this review we present the theoretical foundations and first principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime. Having a rigorous and fully quantized description of interacting photons, electrons and nuclei/ions, from weak to strong light-matter coupling regimes, is pivotal for a detailed understanding of the emerging fields of polaritonic chemistry and cavity materials engineering. The use of rigorous first principles avoids ambiguities and problems stemming from using approximate models based on phenomenological descriptions of light, matter and their interactions. By starting from fundamental physical and mathematical principles, we first review in great detail non-relativistic QED, which allows to study polaritonic systems non-perturbatively by solving a Schrödinger-type equation. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of computational methods, such as quantum-electrodynamical density functional theory, QED coupled cluster or cavity Born-Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key-ideas behind those novel ab initio QED methods, we explain their benefits for a better understanding of photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods we identify the open theoretical questions and how a so far missing mechanistic understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first principles QED and address the open questions that need to be solved in the next years both from a theoretical as well as experimental viewpoint

Dressed-Orbital Approach to Cavity Quantum Electrodynamics and Beyond

We present a novel representation of coupled matter-photon systems that allows the application of many-body methods developed for purely fermionic systems. We do so by rewriting the original coupled light-matter problem in a higher-dimensional configuration space and then use photon-dressed orbitals as a basis to expand the thus "fermionized" coupled system. As an application we present a dressed time-dependent density-functional theory approach. The resulting dressed Kohn-Sham scheme allows for straightforward non-adiabatic approximations to the unknown exchange-correlation potential that explicitly includes correlations. We illustrate this for simple model systems placed inside a high-Q optical cavity, and show also results for observables such as the photon-field fluctuations that are hard to capture in standard matter-photon Kohn-Sham. We finally highlight that the dressed-orbital approach extends beyond the context of cavity quantum electrodynamics and can be applied to, e.g., van-der-Waals problems