Benchmarking semiclassical and perturbative methods for real-time simulations of cavity-bound emission and interference

Abstract

We benchmark a selection of semiclassical and perturbative dynamics techniques by investigating the correlated evolution of a cavity-bound atomic system to assess their applicability to study problems involving strong light-matter interactions in quantum cavities. The model system of interest features spontaneous emission, interference, and strong coupling behaviour, and necessitates the consideration of vacuum fluctuations and correlated light-matter dynamics. We compare a selection of approximate dynamics approaches including fewest switches surface hopping, multi-trajectory Ehrenfest dynamics, linearized semiclasical dynamics, and partially linearized semiclassical dynamics. Furthermore, investigating self-consistent perturbative methods, we apply the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the second Born approximation. With the exception of fewest switches surface hopping, all methods provide a reasonable level of accuracy for the correlated light-matter dynamics, with most methods lacking the capacity to fully capture interference effects.Here we broaden our scope by investigating the performance of a comprehensive class of approximate quantum dynamics methods for simulating spontaneous emission in an optical cavity, including Ehrenfest meanfield theory 33,34 , Tully's surface hopping algorithm 35 , fully linearized 36 and partially linearized 37,38 semilclassical dynamics techniques, and a selection of approximate closures for the quantum mechanical Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Through benchmark comparisons with exact numerical results, we assess the accuracy and efficiency of each method and highlight the possibilities and theoretical challenges involved with extending these approaches towards realistic systems.The remainder of this work is divided into four sections: Sec. II gives a short overview of general quantum mechanical arXiv:1909.07177v2 [quant-ph]

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.…”

Cumulant expansion for the treatment of light–matter interactions in arbitrary material structures

“…Truncating this description by neglecting operator correlations above some order leads to a closed set of equations. This method was already applied in the context of cavity QED [56][57][58][59] , but a systematic study of the importance of the different terms appearing in the expansion has not been provided yet. We here present an extensive study of how different truncations of the cumulant expansion perform in the computation of the dynamics of the quantum emitter and EM modes.…”

Ring-Polymer Quantization of Photon Field in Polariton Chemistry

“…In fact, quasi-classical quantization (in the actionangle quasi-classical description) of the photon field has been historically used to treat molecule-laser field interaction by Miller and co-workers. 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.…”

“…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.…”

“…(ii) Wigner: using the Wigner initial distribution of the photon field [25][26][27] and Ehrenfest dynamics to propagate the non-adiabatic dynamics.…”