Heiko Appel

Excitations in Time-Dependent Density-Functional Theory

An approximate solution to the time-dependent density-functional theory response equations for finite systems is developed, yielding corrections to the single-pole approximation. These explain why allowed Kohn-Sham transition frequencies and oscillator strengths are usually good approximations to the true values, and why sometimes they are not. The approximation yields simple expressions for Görling-Levy perturbation theory results, and a method for estimating expectation values of the unknown exchange-correlation kernel.

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

Significance Traditionally, quantum chemistry investigates molecular systems assuming that the photon field, which leads to the interaction of charged particles, is well approximated by the Coulomb interaction. On the other hand, quantum optics describe the photon field in detail while approximating the matter systems via few levels. Recent experiments at the interface between these two areas of research have uncovered situations where both the molecular system and the photon field have to be treated in detail. In this work, we show how theoretical approaches have to be adapted to treat such coupled matter–photon problems and which effects can be anticipated. Our quantum electrodynamics density-functional formalism provides the theoretical framework to open a field of research able to deal with emergent properties of matter. 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.

Ab-initio angle and energy resolved photoelectron spectroscopy with time-dependent density-functional theory

We present a time-dependent density-functional method able to describe the photoelectron spectrum of atoms and molecules when excited by laser pulses. This computationally feasible scheme is based on a geometrical partitioning that efficiently gives access to photoelectron spectroscopy in time-dependent density-functional calculations. By using a geometrical approach, we provide a simple description of momentum-resolved photoemission including multiphoton effects. The approach is validated by comparison with results in the literature and exact calculations. Furthermore, we present numerical photoelectron angular distributions for randomly oriented nitrogen molecules in a short near-infrared intense laser pulse and helium-(I) angular spectra for aligned carbon monoxide and benzene.

Time-dependent natural orbitals and occupation numbers

Using the equations of motion for the occupation numbers of natural spin orbitals we show that adiabatic extensions of common functionals employed in ground-state reduced-density-matrix-functional theory have the shortcoming of leading to occupation numbers independent of time. We illustrate the exact time-dependence of the natural spin orbitals and occupation numbers for two strongly nonlinear cases, namely electron-ion scattering and atoms in strong laser fields. In the latter case, we observe strong variations of the occupation numbers in time.

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the densityfunctional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photonfield. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.

Förster-Induced Energy Transfer in Functionalized Graphene

Carbon nanostructures are ideal substrates for functionalization with molecules since they consist of a single atomic layer giving rise to an extraordinary sensitivity to changes in their surrounding. The functionalization opens a new research field of hybrid nanostructures with tailored properties. Here, we present a microscopic view on the substrate–molecule interaction in the exemplary hybrid material consisting of graphene functionalized with perylene molecules. First experiments on similar systems have been recently realized illustrating an extremely efficient transfer of excitation energy from adsorbed molecules to the carbon substrate, a process with a large application potential for high-efficiency photovoltaic devices and biomedical imaging and sensing. So far, there has been no microscopically founded explanation for the observed energy transfer. Based on first-principle calculations, we have explicitly investigated the different transfer mechanisms revealing the crucial importance of Förster coupling. Due to the efficient Coulomb interaction in graphene, we obtain strong Förster rates in the range of 1/fs. We investigate its dependence on the substrate–molecule distance R and describe the impact of the momentum transfer q for an efficient energy transfer. Furthermore, we find that the Dexter transfer mechanism is negligibly small due to the vanishing overlap between the involved strongly localized orbital functions. The gained insights are applicable to a variety of carbon-based hybrid nanostructures.

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

Significance Density-functional theory (DFT) is a well-established method to study many-electron systems. Over the past decades advanced algorithms have been designed that allow even large systems to be solved computationally very efficiently. Only recently, DFT has been generalized to correctly incorporate the quantum nature of light, which becomes important, e.g., in cavity quantum electrodynamics (QED). In general, the accuracy in density-functional theory depends crucially on the capability to construct good approximations that reflect the features of the exact effective potential for the Kohn–Sham system. In this work, we introduce a fixed-point scheme to construct these exact effective potentials for a cavity QED system and demonstrate their features for the ground-state and time-dependent situations. 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.

Time-dependent density-functional and reduced density-matrix methods for few electrons: Exact versus adiabatic approximations

To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem is solved exactly by exploiting the mapping of the 1D N-electron problem onto an N-dimensional single electron problem. We analyze the performance of the recently derived 1D local density approximation as well as the exact-exchange orbital functional for those systems. We show that the interaction with an external resonant laser field shows Rabi oscillations which are detuned due to the lack of memory in adiabatic approximations. To investigate situations where static correlations play a role, we consider the time-evolution of the natural occupation numbers associated to the reduced one-body density matrix. Those studies shed light on the non-locality and time-dependence of the exchange and correlation functionals in time-dependent density and density-matrix functional theories.

Cavity Born–Oppenheimer Approximation for Correlated Electron–Nuclear-Photon Systems

In this work, we illustrate the recently introduced concept of the cavity Born–Oppenheimer approximation [Flick et al. PNAS2017, 10.1073/pnas.1615509114] for correlated electron–nuclear-photon problems in detail. We demonstrate how an expansion in terms of conditional electronic and photon-nuclear wave functions accurately describes eigenstates of strongly correlated light-matter systems. For a GaAs quantum ring model in resonance with a photon mode we highlight how the ground-state electronic potential-energy surface changes the usual harmonic potential of the free photon mode to a dressed mode with a double-well structure. This change is accompanied by a splitting of the electronic ground-state density. For a model where the photon mode is in resonance with a vibrational transition, we observe in the excited-state electronic potential-energy surface a splitting from a single minimum to a double minimum. Furthermore, for a time-dependent setup, we show how the dynamics in correlated light-matter systems can be understood in terms of population transfer between potential energy surfaces. This work at the interface of quantum chemistry and quantum optics paves the way for the full ab initio description of matter-photon systems.

Time-dependent exchange-correlation functional for a Hubbard dimer: Quantifying nonadiabatic effects

We address and quantify the role of nonadiabaticity (“memory effects”) in the exchange-correlation (xc) functional of time-dependent density functional theory (TDDFT) for describing nonlinear dynamics of many-body systems. Time-dependent resonant processes are particularly challenging for available TDDFT approximations, due to their strong nonlinear and nonadiabatic character. None of the known approximate density functionals are able to cope with this class of problems in a satisfactory manner. In this work we look at the prototypical example of the resonant processes by considering Rabi oscillations within the exactly soluble two-site Hubbard model. We construct the exact adiabatic xc functional and show that (i) it does not reproduce correctly resonant Rabi dynamics, and (ii) there is a sizable nonadiabatic contribution to the exact xc potential, which turns out to be small only at the beginning and at the end of the Rabi cycle when the ground-state population is dominant. We then propose a “two-level” approximation for the time-dependent xc potential which can capture Rabi dynamics in the two-site problem. It works well both for resonant and for detuned Rabi oscillations and becomes essentially exact in the linear response regime.