  With technological advancements to achieve strong single-photon
optomechanical coupling it becomes necessary to explore the effect of such a
strongly coupled system interacting with the environment. In this limit the
standard Lindblad master equation for the quantum optical case does not hold
because it does not take into account the correct eigenstates. Hence another
type of master equation which is the Dressed-state master equation is used. In
order to emphasize its use we report on the effect of squeezed vacuum/squeezed
thermal reservoir on the decoherence of cavity photon Fock states in an
optomechanical system in the strong single-photon coupling regime. We not only
demonstrate that this decoherence can be effectively controlled by changing the
parameters of the reservoir but that such a control can occur via a cavity
dephasing term at high enough reservoir temperatures. The presence of cavity
dephasing term is an outcome of using correct eigenstates in the strong
single-photon optomechanical coupling regime. This study is also different from
previous studies of system interacting with phase-sensitive reservoirs where
such a dephasing term is absent. Our study might be important in understanding
information processing in strongly coupled photonic systems and quantum
memories.
