Dissipative Two-Mode Tavis-Cummings Model with Time-Delayed Feedback Control

TL;DR

This paper analyzes a two-mode laser system using an extended Tavis-Cummings model with feedback control, identifying steady states and phase diagrams, and demonstrating stabilization and mode selection via time-delayed feedback schemes.

Contribution

It introduces a comprehensive analysis of a dissipative two-mode laser with feedback control, deriving multiple steady states and phase diagrams, and shows how feedback can stabilize or select modes.

Findings

Multiple non-equilibrium steady states identified

Feedback can stabilize unstable fixed points

Mode selection achieved through time delay control

Abstract

We investigate the dynamics of a two-mode laser system by extending the two-mode Tavis-Cummings model with dissipative channels and incoherent pumping and by applying the mean-field approximation in the thermodynamic limit. To this end we analytically calculate up to four possible non-equilibrium steady states (fixed points) and determine the corresponding complex phase diagram. Various possible phases are distinguished by the actual number of fixed points and their stability. In addition, we apply three time-delayed Pyragas feedback control schemes. Depending on the time delay and the strength of the control term this can lead to the stabilization of unstable fixed points or to the selection of a particular cavity mode that is macroscopically occupied.