  When the interaction between a molecular system and confined light modes in
an optical or plasmonic cavity is strong enough to overcome the dissipative
process, hybrid light-matter states (polaritons) become the fundamental
excitations in the system. The mixing between the light and matter characters
modifies the photophysical and photochemical properties. Especially, it was
reported that these polaritons can be employed to control photochemical
reactions, charge and energy transfer, and other processes. In addition,
according to recent studies, vibrational strong coupling can be employed to
resonantly enhance the thermally-activated chemical reactions. In this work, a
theoretical model and an efficient numerical method for studying the dynamics
of molecules strongly interacting with quantum light are developed based on
non-adiabatic excited-state molecular dynamics. The methodology was employed to
study the \textit{cis-trans} photoisomerization of a realistic molecule in a
cavity. Numerical simulations demonstrate that the photochemical reactions can
be controlled by tuning the properties of the cavity. In the calculated
example, the isomerization is suppressed when polaritonic states develop a
local minimum on the lower polaritonic state. Moreover, the observed reduction
of isomerization is tunable via the photon energy and light-molecule coupling
strength. But the fluctuation in transition dipole screens the effect of
light-matter, which makes it harder to tune the photochemical properties via
the coupling strength. These insights suggest quantum control of photochemical
reactions is possible by specially designed photonic or plasmonic cavities.
