Coupled forward-backward trajectory approach for non-equilibrium electron-ion dynamics

We introduce a simple ansatz for the wavefunction of a many-body system based on coupled forward and backward-propagating semiclassical trajectories. This method is primarily aimed at, but not limited to, treating nonequilibrium dynamics in electron-phonon systems. The time-evolution of the system is obtained from the Euler-Lagrange variational principle, and we show that this ansatz yields Ehrenfest mean field theory in the limit that the forward and backward trajectories are orthogonal, and in the limit that they coalesce. We investigate accuracy and performance of this method by simulating electronic relaxation in the spin-boson model and the Holstein model. Although this method involves only pairs of semiclassical trajectories, it shows a substantial improvement over mean field theory, capturing quantum coherence of nuclear dynamics as well as electron-nuclear correlations. This improvement is particularly evident in nonadiabatic systems, where the accuracy of this coupled trajectory method extends well beyond the perturbative electron-phonon coupling regime. This approach thus provides an attractive route forward to the ab-initio description of relaxation processes, such as thermalization, in condensed phase systems

Photovoltaic Effect from the Viewpoint of Time-reversal Symmetry

We theoretically investigate field-induced charge-transport processes from the viewpoint of time-reversal symmetry. We analytically demonstrate that breaking of the time-reversal symmetry is a necessary condition to induce charge-transport and direct-current by external fields. This finding provides microscopic insights into photovoltaic effects and optical-control of currents

Frequency-resolved microscopic current density analysis of linear and nonlinear optical phenomena in solids

We perform a frequency-resolved analysis of electron dynamics in solids to obtain microscopic insight into linear and nonlinear optical phenomena. For the analysis, we first compute the electron dynamics under optical electric fields and evaluate the microscopic current density as a function of time and space. Subsequently, we perform the Fourier transformation on the microscopic current density and obtain the corresponding quantity in the frequency domain. The frequency-resolved microscopic current density provides insight into the microscopic electron dynamics in real-space at the frequency of linear and nonlinear optical responses. We apply frequency-resolved microscopic current density analysis to light-induced electron dynamics in aluminum, silicon, and diamond based on the first-principles electron dynamics simulation according to the time-dependent density functional theory. Consequently, the nature of delocalized electrons in metals and bound electrons in semiconductors and insulators is suitably captured by the developed scheme

Nonlinear polarization evolution using time-dependent density functional theory

We propose a theoretical and computational approach to investigate temporal behavior of a nonlinear polarization in perturbative regime induced by an intense and ultrashort pulsed electric field. First-principles time-dependent density functional theory is employed to describe the electron dynamics. Temporal evolution of third-order nonlinear polarization is extracted from a few calculations of electron dynamics induced by pulsed electric fields with the same time profile but different amplitudes. We discuss characteristic features of the nonlinear polarization evolution as well as an extraction of nonlinear susceptibilities and time delays by fitting the polarization. We also carry out a decomposition of temporal and spatial changes of the electron density in power series with respect to the field amplitude. It helps to get insight into the origin of the nonlinear polarization in atomic scale.Comment: 11 pages, 9 figure

Nonlinear electric conductivity and THz-induced charge transport in graphene

Based on the quantum master equation approach, the nonlinear electric conductivity of graphene is investigated under static electric fields for various chemical potential shifts. The simulation results show that, as the field strength increases, the effective conductivity is firstly suppressed, reflecting the depletion of effective carriers due to the large displacement in the Brillouin zone caused by the strong field. Then, as the field strength exceeds $1$~MV/m, the effective conductivity increases, overcoming the carrier depletion via the Landau--Zener tunneling process. Based on the nonlinear behavior of the conductivity, the charge transport induced by few-cycle THz pulses is studied to elucidate the ultrafast control of electric current in matter

Limitations of mean-field approximations in describing shift-current and injection-current in materials

We theoretically investigate bulk photovoltaic effects, with a specific focus on shift-current and injection-current. Initially, we perform a numerical analysis of the direct current (dc) induced by a laser pulse with a one-dimensional model, utilizing mean-field theories such as time-dependent Hartree--Fock and time-dependent Hartree methods. Our numerical results, obtained with mean-field theories, reveal that the dc component of the current exists even after irradiation with linearly polarized light as a second-order nonlinear effect, indicating the generation of injection current. Conversely, when we employ the independent particle approximation, no injection current is generated by linearly polarized light. To develop the microscopic understanding of injection current within the mean-field approximation, we further analyze the dc component of the current with the perturbation theory, employing the mean-field approximations, the independent-particle approximation, and the exact solution of the many-body Schr\"odinger equation. The perturbation analysis clarifies that the injection current induced by linearly polarized light under the mean-field approximations is an artifact caused by population imbalance, created through quantum interference from unphysical self-excitation pathways. Therefore, investigation of many-body effects on the bulk photovoltaic effects have to be carefully conducted in mean-field schemes due to potential contamination by unphysical dc current. Additionally, we perform the first-principles electron dynamics calculation for BaTiO$_3$ based on the time-dependent density functional theory, and we confirm that the above findings from the one-dimensional model calculation and the perturbation analysis apply to realistic systems

Floquet engineering non-equilibrium steady states: on the optimization of system properties with gradient-based methods

Non-equilibrium steady states are created when a periodically driven quantum system is also incoherently interacting with an environment -- as it is the case in most realistic situations. The notion of Floquet engineering refers to the manipulation of the properties of systems under periodic perturbations. Although it more frequently refers to the coherent states of isolated systems (or to the transient phase for states that are weakly coupled to the environment), it may sometimes be of more interest to consider the final steady states that are reached after decoherence and dissipation take place. In this work, we propose a computational method to find the multicolor periodic perturbations that lead to the final steady states that are optimal with respect to a given predefined metric, such as for example the maximization of the temporal average value of some observable. We exemplify the concept using a simple model for the nitrogen-vacancy center in diamond: the goal in this case is to find the driving periodic magnetic field that maximizes a time-averaged spin component. We show that, for example, this technique permits to prepare states whose spin values are forbidden in thermal equilibrium at any temperature.Comment: 14 pages, 3 figures. Added a few more paragraphs commenting on the relationship of this work with other methods, computational issues and other minor detail

Terahertz-induced high-order harmonic generation and nonlinear charge transport in graphene

We theoretically study the THz-induced high-order harmonic generation (HHG) and nonlinear electric transport in graphene based on the quantum master equation with the relaxation time approximation. To obtain microscopic insight into the phenomena, we compare the results of the fully dynamical calculations with those under a quasi-static approximation, where the electronic system is approximated as a nonequilibrium steady state. As a result, we find that the THz-induced electron dynamics in graphene can be accurately modeled with the nonequilibrium steady-state at each instance. The population distribution analysis further clarifies that the THz-induced HHG in graphene originates from the reduction of effective conductivity due to a large displacement of electrons in the Brillouin zone. By comparing the present nonequilibrium picture with a thermodynamic picture, we explore the role of the nonequilibrium nature of electron dynamics on the extremely nonlinear optical and transport phenomena in graphene