A Passive $\mathcal{P}\mathcal{T}$-Symmetric Floquet-Coupler

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 $\mathcal{P}\mathcal{T}$-symmetric Floquet system that, at resonance, shows a strong reduction of the required loss for the $\mathcal{P}\mathcal{T}$ 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.