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.

arXiv comment18 pages, 13 figures

References in corpus (25)

• On the Integrability of the Rabi Model
• Cavity-controlled chemistry in molecular ensembles
• Atoms and Molecules in Cavities: From Weak to Strong Coupling in QED Chemistry
• Realizing strong light-matter interactions between single nanoparticle plasmons and molecular excitons at ambient conditions
• Broadband Purcell effect: Radiative decay engineering with metamaterials
• Subradiance in a Large Cloud of Cold Atoms
• Resonant catalysis of thermally-activated chemical reactions via vibrational polaritons
• Cavity Casimir-Polder forces and their effects in ground state chemical reactivity
• Optimized Effective Potential for Quantum Electrodynamical Time-Dependent Density Functional Theory
• Quantum-Classical Liouville Dynamics in the Mapping Basis
• Subradiant states of quantum bits coupled to a one-dimensional waveguide
• Mapping quantum-classical Liouville equation: projectors and trajectories
• Numerical studies of the interaction of an atomic sample with the electromagnetic field in two dimensions
• Light-Matter Interactions via the Exact Factorization Approach
• Capturing Vacuum Fluctuations and Photon Correlations in Cavity Quantum Electrodynamics with Multi-Trajectory Ehrenfest Dynamics
• Analysis of the quantum-classical Liouville equation in the mapping basis
• Benchmarking Semiclassical and Perturbative Methods for Real-time Simulations of Cavity-Bound Emission and Interference
• Mixed Quantum-Classical Electrodynamics: Understanding Spontaneous Decay and Zero Point Energy
• Ehrenfest+R Dynamics I: A Mixed Quantum-Classical Electrodynamics Simulation of Spontaneous Emission
• Robustness of Dicke subradiance against thermal decoherence
• A Comparison of Different Classical, Semiclassical and Quantum Treatments of Light-Matter Interactions: Understanding Energy Conservation
• Ehrenfest+R Dynamics II: A Semiclassical QED Framework for Raman Scattering
• A Necessary Trade-off for Semiclassical Electrodynamics: Accurate Short-Range Coulomb Interactions versus the Enforcement of Causality?
• Predictive Semiclassical Model for Coherent and Incoherent Emission in the Strong Field Regime: The Mollow Triplet Revisited
• Understanding the Nature of Mean-Field Semiclassical Light-Matter Dynamics: An Investigation of Energy Transfer, Electron-Electron Correlations, External Driving and Long-Time Detailed Balance

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• Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics
• Coupling and Decoupling of Polaritonic States in Multimode Cavities
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• A Mean-Field Treatment of Vacuum Fluctuations in Strong Light-Matter Coupling
• Exploring the Nature of High-Order Cavity Polaritons under the Coupling-Decoupling Transition
• Practical guide to the statistical mechanics of molecular polaritons
• Ehrenfest Modeling of Cavity Vacuum Fluctuations and How to Achieve Emission from a Three-Level Atom
• Focused Sampling for Low-Cost and Accurate Ehrenfest Modeling of Cavity Quantum Electrodynamics