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

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• Unraveling coherent quantum feedback for Pyragas control
• Intensified antibunching via feedback-induced quantum interference
• Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers
• Collective enhancements in many-emitter phonon lasing
• Solid state based analog of optomechanics
• Self-trapping phenomenon, multistability and chaos in open anisotropic Dicke dimer
• Matrix diagonalization and exact solution of the k-photon Jaynes-Cummings model
• Nonequilibrium dynamics of the Jaynes-Cummings dimer
• Intertwining of lasing and superradiance under spintronic pumping
• Algebraic approach to the Tavis-Cummings model with three modes of oscillation
• Emergence of a quasi-ergodic steady state in a dissipative Tavis-Cummings array
• Wiseman-Milburn Control for the Lipkin-Meshkov-Glick Model
• $Sp(4,R)$ algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry
• Algebraic approach and Berry phase of a Hamiltonian with a general $SU(1,1)$ symmetry
• Dissipative chaos and steady state of open Tavis-Cummings dimer
• Berry phase of the Tavis-Cummings model with three modes of oscillation