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

## TL;DR

This paper models light propagation in parity-time symmetric whispering-gallery microcavities using a Scully-Lamb laser approach, revealing how gain saturation influences non-reciprocity and exceptional points in non-Hermitian systems.

## Contribution

It introduces a non-Lindbladian Scully-Lamb laser model for analyzing gain saturation effects and non-reciprocity in parity-time symmetric microcavities, extending understanding of exceptional points.

## Key findings

- Gain saturation causes non-reciprocal light propagation.
- Gain saturation modifies the position of exceptional points.
- The model explains experimentally observed non-reciprocity.

## Abstract

We use a non-Lindbladian master equation of the Scully-Lamb laser model for the analysis of light propagation in a parity-time symmetric photonic system composed of coupled active and passive whispering-gallery microresonators. Performing the semiclassical approximation, we obtain a set of two nonlinear coupled differential equations describing the time evolution of intracavity fields. These coupled equations are able to explain the experimentally-observed light 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 this effect arises from the interplay between gain saturation in the active microcavity, intercavity coupling, and losses in the cavities. Additionally, using this approach, we study the effect of the gain saturation on exceptional points, i.e., exotic degeneracies in non-Hermitian systems. Namely, we demonstrate that the inclusion of gain saturation leads to a modification of the exceptional points in the presence of intense intracavity fields. The Scully-Lamb master equation for systems of coupled optical structures, as proposed and applied here, constitutes a promising tool for the study of quantum optical effects in coupled systems with losses, gain, and gain saturation.