Understanding detailed balance for an electron-radiation system through mixed quantum-classical electrodynamics

Abstract

We investigate detailed balance for a quantum system interacting with thermal radiation within mixed quantum-classical theory. For a two-level system coupled to classical radiation fields, three semiclassical methods are benchmarked: (1) Ehrenfest dynamics over-estimate the excited state population at equilibrium due to the failure of capturing vacuum fluctuations. (2) The coupled Maxwell-Bloch equations, which supplement Ehrenfest dynamics by damping at the full golden rule rate, under-estimate the excited state population due to double-counting of the self-interaction effect.(3) Ehrenfest+R dynamics recover detailed balance and the correct thermal equilibrium by enforcing the correct balance between the optical excitation and spontaneous emission of the quantum system. These results highlight the fact that, when properly designed, mixed quantum-classical electrodynamics can simulate thermal equilibrium in the field of nanoplasmonics.

Dissipative Equation of Motion for Electromagnetic Radiation in Quantum Dynamics

“…Most implementations of these methods have been limited to just a few-often just two-level systems. An overview and comparative analysis of these approaches have been recently contributed by Nitzan, Subotnik, and co-authors [34][35][36]. In particular, these researchers have proposed a correction to Ehrenfest dynamics that, by construction, reproduces spontaneous emission according to the radiative decay rate deduced from Fermi's golden rule (FGR) [37].…”

Radiative thermalization in semiclassical simulations of light-matter interaction

“…The ability of an electrodynamics approach to capture the equilibrium quantum populations of electrons subject to a radiation bath, in accordance with Planck's law of black-body radiation, is a fundamental feature that can be regarded as a key test to assess the overall quality of a given theoretical model of light-matter interaction [1]. A number of such models have been proposed in the framework of quantum electrodynamics, with a quantized description of both the electron and the photon degrees of freedom [2][3][4][5][6].…”

Incorporating Lindblad Decay Dynamics into Mixed Quantum-Classical Simulations

“…We want to emphasize the connections and differences between the current L-MFE method and previous approaches that try to accomplish Lindblad dynamics through stochastic wavefunction approaches, such as Monte Carlo wave-function methods [35][36][37][38] and the Ehren-fest+R approach. [10][11][12]39,40 The Monte Carlo wavefunction method 35,36 expresses the stochastic time evolution of the system's wavefunction as follows 34,56 d|ψ…”

“…At the same time, the quantum subsystem, in principle, can also interact with other environmental DOFs. Example of these interacting environmental DOFs include the interaction of the electromagnetic field with molecules that causes spontaneous emission [10][11][12] and farfield electromagnetic modes that couple to a quantized radiation mode inside an optical cavity that causes phoa) Electronic mail: ekoessle@ur.rochester.edu b) Electronic mail: pengfei.huo@rochester.edu ton leakage. [13][14][15][16][17] It is often desirable to implicitly capture the environmental influence on the dynamics and avoid simulating these environmental DOFs explicitly.…”

“…In particular, we give the derivation of a method to propagate the coefficients of the MFE method that fully agrees with Lindblad dynamics. The coefficient-propagation method derived using this framework is inspired by the Ehrenfest+R method; [10][11][12]39,40 however, our approach exactly recovers Lindblad dynamics whereas the Ehren-fest+R approach does not. Additionally, we derive a simple fix to the approximations present in the Ehren-fest+R method and give rigorous justifications for particular algorithmic choices.…”