  Strong cavity coupling of gas-phase molecules will enable studies of
benchmark chemical processes under strong light-matter interactions with a high
level of experimental control and no solvent effects. We recently demonstrated
the formation of gas-phase molecular polaritons by strongly coupling the bright
$\nu_3$, $J=3 \rightarrow 4$ rovibrational transitions of methane (CH$_4$) to a
Fabry-P\'{e}rot optical cavity mode inside a cryogenic buffer gas cell. Here,
we further explore the flexible capabilities of this infrastructure. We show
that we can greatly increase the collective coupling strength of the molecular
ensemble to the cavity by increasing the intracavity CH$_4$ number density. In
doing so, we can tune from the single-mode coupling regime to the multimode
coupling regime in which many nested polaritonic states arise as the Rabi
splitting approaches the cavity mode spacing. We explore polariton formation
for cavity geometries of varying length, finesse, and mirror radius of
curvature. We also report a proof-of-principle demonstration of rovibrational
gas-phase polariton formation at room temperature. This experimental
flexibility affords a great degree of control over the properties of molecular
polaritons and opens up a wider range of simple molecular processes to future
interrogation under strong cavity-coupling. We anticipate that ongoing work in
gas-phase polaritonics will facilitate convergence between experimental results
and theoretical models of cavity-altered chemistry and physics.
