  A quantum simulation of vibrational strong coupling (VSC) in the collective
regime via thermostatted ring-polymer molecular dynamics (TRPMD) is reported.
For a collection of liquid-phase water molecules resonantly coupled to a single
lossless cavity mode, the simulation shows that, as compared with a fully
classical calculation, the inclusion of nuclear and photonic quantum effects
does not lead to a change in the Rabi splitting but does broaden polaritonic
linewidths roughly by a factor of two. Moreover, under thermal equilibrium,
both quantum and classical simulations predict that the static dielectric
constant of liquid water is largely unchanged inside versus outside the cavity.
This result disagrees with a recent experiment demonstrating that the static
dielectric constant of liquid water can be resonantly enhanced under VSC,
suggesting either limitations of our approach or perhaps other experimental
factors that have not yet been explored.
