  Based on a Liouville-space formulation of open systems, we present a solution
to the quantum master equation of two coupled optical waveguides with varying
loss. The periodic modulation of the Markovian loss of one of them yields a
passive $\mathcal{PT}$-symmetric Floquet system that, at resonance, shows a
strong reduction of the required loss for the $\mathcal{PT}$ symmetry to be
broken. We showcase this transition for a multi-photon state, and we show how
to physically implement the modulated loss with reservoir engineering of a set
of bath modes.
