A Mean-Field Treatment of Vacuum Fluctuations in Strong Light-Matter Coupling

Mean-field mixed quantum-classical dynamics could provide a much-needed means to inexpensively model quantum electrodynamical phenomena by describing the optical field and its vacuum fluctuations classically. However, this approach is known to suffer from an unphysical transfer of energy out of the vacuum fluctuations when the light-matter coupling becomes strong. We highlight this issue for the case of an atom in an optical cavity and resolve it by introducing an additional set of classical coordinates to specifically represent vacuum fluctuations whose light-matter interaction is scaled by the instantaneous ground-state population of the atom. This not only rigorously prevents the aforementioned unphysical energy transfer but is also shown to yield a radically improved accuracy in terms of the atomic population and the optical field dynamics, generating results in excellent agreement with full quantum calculations. As such, the resulting method emerges as an attractive solution for the affordable modeling of strong light-matter coupling phenomena involving macroscopic numbers of optical modes.

Automated summary

Mean-field mixed quantum-classical dynamics offers an affordable way to model quantum electrodynamical phenomena by treating the optical field and its vacuum fluctuations classically. However, when the light-matter coupling becomes strong, it suffers from an unphysical transfer of energy out of the vacuum. We resolve this issue by introducing an additional set of classical coordinates that represent vacuum fluctuations scaled by the instantaneous ground-state population of the atom, which not only prevents the energy transfer but also improves the accuracy of atomic population and optical field dynamics.