  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, Poincar\'e 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.
