Feedback-induced instabilities and dynamics in the Jaynes-Cummings model

TL;DR

This paper explores how time-delayed coherent feedback influences the dynamics and steady states of the Jaynes-Cummings model, revealing non-Markovian effects, revival phenomena, and robust non-equilibrium states observable in experimental setups.

Contribution

It introduces a novel analysis of feedback-induced non-Markovian effects in the Jaynes-Cummings model, highlighting new steady-state behaviors and spectral properties.

Findings

Feedback induces non-Markovian dynamics and revivals.

Steady states exhibit narrowed spectral linewidth.

Effects are observable in standard photon detection experiments.

Abstract

We investigate the coherence and steady-state properties of the Jaynes-Cummings model subjected to time-delayed coherent feedback in the regime of multiple excitations. The introduced feedback qualitatively modifies the dynamical response and steady-state quantum properties of the system by enforcing a non-Markovian evolution. This leads to recovered collapses and revivals as well as non-equilibrium steady states when the two-level system (TLS) is directly driven by a laser. The latter are characterized by narrowed spectral linewidth and diverging correlation functions that are robust against the time delay and feedback phase choices. These effects are also demonstrated in experimentally accessible quantities such as the power spectrum and the second-order correlation function $g^{(2)}(\tau)$ in standard and widely available photon-detection setups.