  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.
