Fast Green's Function Method for Ultrafast Electron-Boson Dynamics

Electroluminescence Rectification and High Harmonic Generation in Molecular Junctions

The field of molecular electronics has emerged from efforts to understand electron propagation through single molecules and to use them in electronic circuits. Serving as a testbed for advanced theoretical methods, it reveals a significant discrepancy between the operational time scales of experiments (static to GHz frequencies) and theoretical models (femtoseconds). Utilizing a recently developed time-linear nonequilibrium Green function formalism, we model molecular junctions on experimentally accessible time scales. Our study focuses on the quantum pump effect in a benzenedithiol molecule connected to two copper electrodes and coupled with cavity photons. By calculating both electric and photonic current responses to an ac bias voltage, we observe pronounced electroluminescence and high harmonic generation in this setup. The mechanism of the latter effect is more analogous to that from solids than from isolated molecules, with even harmonics being suppressed or enhanced depending on the symmetry of the driving field.

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, with a focus on polaritonic chemistry. By starting from fundamental physical and mathematical principles, we first review in great detail ab initio nonrelativistic QED. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of (in principle exact but in practice) approximate 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, at the same time, 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 ab initio QED methods, we highlight their benefits for understanding photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods, we identify open theoretical questions and how a so far missing detailed understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first-principles QED.

Real-Time GW-Ehrenfest-Fan-Migdal Method for Nonequilibrium 2D Materials

Quantum simulations of photoexcited low-dimensional systems are pivotal for understanding how to functionalize and integrate novel two-dimensional (2D) materials in next-generation optoelectronic devices. First-principles predictions are extremely challenging due to the simultaneous interplay of light-matter, electron-electron, and electron-nuclear interactions. We here present an advanced ab initio many-body method that accounts for quantum coherence and non-Markovian effects while treating electrons and nuclei on equal footing, thereby preserving fundamental conservation laws like the total energy. The impact of this advancement is demonstrated through real-time simulations of the complex multivalley dynamics in a molybdenum disulfide (MoS2) monolayer pumped above gap. Within a single framework, we provide a parameter-free description of the coherent-to-incoherent crossover, elucidating the role of microscopic and collective excitations in the dephasing and thermalization processes.

Time-Linear Quantum Transport Simulations with Correlated Nonequilibrium Green's Functions

We present a time-linear scaling method to simulate open and correlated quantum systems out of equilibrium. The method inherits from many-body perturbation theory the possibility to choose selectively the most relevant scattering processes in the dynamics, thereby paving the way to the real-time characterization of correlated ultrafast phenomena in quantum transport. The open system dynamics is described in terms of an "embedding correlator" from which the time-dependent current can be calculated using the Meir-Wingreen formula. We show how to efficiently implement our approach through a simple grafting into recently proposed time-linear Green's function methods for closed systems. Electron-electron and electron-phonon interactions can be treated on equal footing while preserving all fundamental conservation laws.

Calibrating Out-of-Equilibrium Electron-Phonon Couplings in Photoexcited MoS2

Nonequilibrium electron-phonon coupling (EPC) serves as a dominant interaction in a multitude of transient processes, including photoinduced phase transitions, coherent phonon generation, and possible light-induced superconductivity. Here we use monolayer MoS₂ as a prototype to investigate the variation in electron-phonon couplings under laser excitation, on the basis of real-time time-dependent density functional theory simulations. Phonon softening, anisotropic modification of the deformation potential, and enhancement of EPC are observed, which are attributed to the reduced electronic screening and modulated potential energy surfaces by photoexcitation. Furthermore, by tracking the transient deformation potential and nonthermal electronic population, we can monitor the ultrafast time evolution of the energy exchange rate between electrons and phonons upon laser excitation. This work provides an effective strategy to investigate the nonequilibrium EPC and constructs a scaffold for understanding nonequilibrium states beyond the multitemperature models.

A perspective on ab initio modeling of polaritonic chemistry: The role of non-equilibrium effects and quantum collectivity

This Perspective provides a brief introduction into the theoretical complexity of polaritonic chemistry, which emerges from the hybrid nature of strongly coupled light-matter states. To tackle this complexity, the importance of ab initio methods is highlighted. Based on those, novel ideas and research avenues are developed with respect to quantum collectivity, as well as for resonance phenomena immanent in reaction rates under vibrational strong coupling. Indeed, fundamental theoretical questions arise about the mesoscopic scale of quantum-collectively coupled molecules when considering the depolarization shift in the interpretation of experimental data. Furthermore, to rationalize recent findings based on quantum electrodynamical density-functional theory (QEDFT), a simple, but computationally efficient, Langevin framework is proposed based on well-established methods from molecular dynamics. It suggests the emergence of cavity-induced non-equilibrium nuclear dynamics, where thermal (stochastic) resonance phenomena could emerge in the absence of external periodic driving. Overall, we believe that the latest ab initio results indeed suggest a paradigmatic shift for ground-state chemical reactions under vibrational strong coupling from the collective quantum interpretation toward a more local, (semi)-classically and non-equilibrium dominated perspective. Finally, various extensions toward a refined description of cavity-modified chemistry are introduced in the context of QEDFT, and future directions of the field are sketched.

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

Quantum electronics has significantly evolved over the last decades. Where initially the clear focus was on light-matter interactions, nowadays approaches based on the electron's wave nature have solidified themselves as additional focus areas. This development is largely driven by continuous advances in electron quantum optics, electron based quantum information processing, electronic materials, and nanoelectronic devices and systems. The pace of research in all of these areas is astonishing and is accompanied by substantial theoretical and experimental advancements. What is particularly exciting is the fact that the computational methods, together with broadly available large-scale computing resources, have matured to such a degree so as to be essential enabling technologies themselves. These methods allow to predict, analyze, and design not only individual physical processes but also entire devices and systems, which would otherwise be very challenging or sometimes even out of reach with conventional experimental capabilities. This review is thus a testament to the increasingly towering importance of computational methods for advancing the expanding field of quantum electronics. To that end, computational aspects of a representative selection of recent research in quantum electronics are highlighted where a major focus is on the electron's wave nature. By categorizing the research into concrete technological applications, researchers and engineers will be able to use this review as a source for inspiration regarding problem-specific computational methods.

Real-Time GW: Toward an Ab Initio Description of the Ultrafast Carrier and Exciton Dynamics in Two-Dimensional Materials

We demonstrate the feasibility of the time-linear scaling formulation of the GW method [Phys. Rev. Lett. 124, 076601 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.076601] for ab initio simulations of optically driven two-dimensional materials. The time-dependent GW equations are derived and solved numerically in the basis of Bloch states. We address carrier multiplication and relaxation in photoexcited graphene and find deviations from the typical exponential behavior predicted by the Markovian Boltzmann approach. For a resonantly pumped semiconductor we discover a self-sustained screening cascade leading to the Mott transition of coherent excitons. Our results draw attention to the importance of non-Markovian and dynamical screening effects in out-of-equilibrium phenomena.