  We study the dynamics of strongly coupled nanophotonic systems with
time-variable parameters. The approximate analytic solutions are obtained for a
broad class of open quantum systems including a two-level fermion emitter
strongly coupled to a multimode quantized electromagnetic field in a cavity
with time-varying cavity resonances or the electron transition energy. The
coupling of the fermion and photon subsystems to their dissipative reservoirs
is included within the stochastic equation of evolution approach, which is
equivalent to the Lindblad approximation in the master equation formalism. The
analytic solutions for the quantum states and the observables are obtained
under the approximation that the rate of parameter modulation and the amplitude
of the frequency modulation are much smaller than the optical transition
frequencies. At the same time, they can be arbitrary with respect to the
generalized Rabi oscillations frequency which determines the coherent dynamics.
Therefore, our analytic theory can be applied to an arbitrary modulation of the
parameters, both slower and faster than the Rabi frequency, for complete
control of the quantum state. In particular, we demonstrate protocols for
switching on and off the entanglement between the fermionic and photonic
degrees of freedom, swapping between the quantum states, and the decoupling of
the fermionic qubit from the cavity field due to modulation-induced
transparency.
