Quasiclassical modeling of cavity quantum electrodynamics

Abstract

We model a collection of N two-level systems (TLSs) coupled to a multimode cavity via Meyer-Miller-Stock-Thoss (MMST) dynamics, sampling both electronic and photonic zero-point energies (ZPEs) and propagating independent trajectories in Wigner phase space. By investigating the ground state stability of a single TLS, we use MMST dynamics to separately study both electronic ZPE effects (which would naively lead to the breakdown of the electronic ground state) as well as photonic ZPE effects (which would naively lead to spontaneous absorption). By contrast, including both effects (i.e., sampling both electronic and photonic ZPEs) leads to the dynamical stability of the electronic ground state. Therefore, MMST dynamics provide a practical way to identify the contributions of self-interaction and vacuum fluctuations. More importantly, we find that MMST dynamics can predict accurate quantum dynamics for both electronic populations and electromagnetic field intensity in the high saturation limit. For a single TLS in a cavity, MMST dynamics correctly predict the initial exponential decay of spontaneous emission, Poincaré recurrences, and the positional dependence of a spontaneous emission rate. For an array of N equally spaced TLSs with only one TLS excited initially, MMST dynamics correctly predict the modification of spontaneous emission rate as a function of the spacing between TLSs. Finally, MMST dynamics also correctly model Dicke's superradiance and subradiance (i.e., the dynamics when all TLSs are excited initially) including the correct quantum statistics for the delay time (as found by counting trajectories, for which a full quantum simulation is hard to achieve). Therefore, this work raises the possibility of simulating large-scale collective light-matter interactions with methods beyond mean-field theory.

Ring-Polymer Quantization of Photon Field in Polariton Chemistry

“…It can be clearly seen that treating the radiation mode with a classical initial distribution (green dashed line) does not account the quantum effects associated with the high frequency photon modes and thus, fails to predict accurate PMET rate constant throughout the entire range of driving force. Further, in contrast to the previous results of cavity QED, [25][26][27][28] treating the photon mode with initial Wigner distribution (orange dashed line) also fails to provide the quantitative results of the rate constants. The breakdown of the classical Wigner model is likely due to the fact that the classical equation of motion for the photon field in this calculation does not preserve the Wigner distribution, 29,31,74 a well-known limitation of the classical Wigner model leading to the incorrect flow of the photonic energy to the electronic subsystem.…”

“…23,24 Recent example of the quasi-classical description of the radiation mode in cavity QED includes the classical Wigner model [25][26][27] as well as the symmetric quasi-classical window approach. 27,28 These quasi-classical approaches can significantly reduce the computational cost due to the quasi-classical treatment of the field. However, the classical Wigner model 25,26 is not expected to preserve the quantum distribution associated with the photon field, 28 which often leads to the incorrect quantum dynamics due to the leakage of the zero-point energy (ZPE).…”

“…27,28 These quasi-classical approaches can significantly reduce the computational cost due to the quasi-classical treatment of the field. However, the classical Wigner model 25,26 is not expected to preserve the quantum distribution associated with the photon field, 28 which often leads to the incorrect quantum dynamics due to the leakage of the zero-point energy (ZPE). [29][30][31] These shortcomings of the quasi-classical treatment can be readily addressed with the recently developed state-dependent ring polymer molecular dynamics (RPMD) approaches.…”

Dissipative Equation of Motion for Electromagnetic Radiation in Quantum Dynamics

“…Strategies that do not fit exactly in these groups have been explored very recently [38,39]. Furthermore, we draw attention to Rashkovskiy's work on the non-linear Schrödinger equation, where thermal radiation and spontaneous emission are described without energy quantization in a classical field framework [40,41].…”

Cavity molecular dynamics simulations of liquid water under vibrational ultrastrong coupling

“…In order to investigate whether such modification occurs, below we will model VSC and V-USC using cavity molecular dynamics (MD) simulation, where the nuclei are evolved under a realistic electronic ground-state potential surface. Such an approach is an extension of the usual simplified 1D models where the matter side is evolved as two-level systems (24)(25)(26) or coupled harmonic oscillators (16,17,27,28). Although such simplified models are adequate enough for studying Rabi splitting qualitatively by fitting experimental parameters, these models usually ignore translation, rotation, and collision, as well as the intricate structure of molecular motion, all of which are crucial for determining the dynamic properties of molecules.…”