Non-Markovian Light-Matter Dynamics in the Time Fractional Jaynes-Cummings Model with Modulated Coupling

TL;DR

This paper explores how fractional time derivatives in a generalized Jaynes-Cummings model affect light-matter interactions, revealing memory effects, damping, and controllable non-periodic dynamics influenced by coupling types and fractional order.

Contribution

It introduces a fractional time approach to the Jaynes-Cummings model with various coupling modulations, analyzing their effects on population inversion and entanglement.

Findings

Fractional order induces memory effects like damping and decay.

Time-dependent couplings influence entanglement and dynamics.

Fractional order can control non-periodic evolution under sinusoidal coupling.

Abstract

We investigate the fractional time description of a generalized quantum light-matter system modeled by a time-dependent Jaynes-Cummings (JC) interaction, with different coupling types: constant, linear, exponential, and sinusoidal. Two formulations of the time fractional Schr\"odinger equation (TFSE) are examined, with a focus on their impact on population inversion and entanglement. Our findings highlight that the introduction of fractional order introduces memory effects, associated with damped oscillations and asymptotic decay. Furthermore, we find that the time-dependent couplings, combined with distinct fractional formulations, influence how these effects occur, ultimately resulting in high or low entanglement. A key finding of our work is that, under sinusoidal coupling, non-periodic dynamics is preserved for both formulations of the TFSE; however, within a certain range, the fractional order can act as a control mechanism for the non-periodic evolution.