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We use a non-Lindbladian master equation of the Scully-Lamb laser model forthe analysis of light propagation in a parity-time symmetric photonic systemcomposed of coupled active and passive whispering-gallery microresonators.Performing the semiclassical approximation, we obtain a set of two nonlinearcoupled differential equations describing the time evolution of intracavityfields. These coupled equations are able to explain the experimentally-observedlight non-reciprocity [Peng {\em et al.}, Nature Physics {\bf 10}, 394 (2014),Chang {\em et al.}, Nature Photonics {\bf 8}, 524 (2014)]. We show that thiseffect arises from the interplay between gain saturation in the activemicrocavity, intercavity coupling, and losses in the cavities. Additionally,using this approach, we study the effect of the gain saturation on exceptionalpoints, i.e., exotic degeneracies in non-Hermitian systems. Namely, wedemonstrate that the inclusion of gain saturation leads to a modification ofthe exceptional points in the presence of intense intracavity fields. TheScully-Lamb master equation for systems of coupled optical structures, asproposed and applied here, constitutes a promising tool for the study ofquantum optical effects in coupled systems with losses, gain, and gainsaturation.

Scully-Lamb quantum laser model for parity-time-symmetric whispering-gallery microcavities: Gain saturation effects and non-reciprocity