Mixed Quantum-Classical Electrodynamics: Understanding Spontaneous Decay and Zero Point Energy

TL;DR

This paper compares different semiclassical methods for simulating spontaneous emission in quantum-electrodynamics, highlighting the strengths and limitations of Ehrenfest and SQC dynamics in capturing light-matter interactions.

Contribution

It demonstrates that SQC dynamics reliably reproduce spontaneous emission, while Ehrenfest dynamics can do so under specific initial conditions, offering insights into semiclassical modeling of quantum optical phenomena.

Findings

Ehrenfest dynamics can describe spontaneous emission if starting in a superposition state.

SQC dynamics consistently reproduce spontaneous emission.

Different semiclassical methods yield varying results for transient excited state decay.

Abstract

The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one and three dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. We consider three flavors of mixed quantum-classical dynamics: the classical path approximation (CPA), Ehrenfest dynamics, and symmetrical quantum-classical (SQC) dynamics. The CPA fails to recover a consistent description of spontaneous emission. A consistent "spontaneous" emission can be obtained from Ehrenfest dynamics--provided that one starts in an electronic superposition state. Spontaneous emission is always obtained using SQC dynamics. Using the SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by W. Miller [J. Chem. Phys. 69, 2188-2195, 1978] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights new possibilities for studying light-matter interactions with semiclassical mechanics.