Analytic approach to dynamics of the resonant and off-resonant Jaynes-Cummings systems with cavity losses

TL;DR

This paper introduces an analytic method to study the dynamics of Jaynes-Cummings systems with cavity losses, providing explicit solutions for resonant and off-resonant cases, enabling detailed analysis of quantum states under dissipation.

Contribution

The paper develops a new analytic approach for the Jaynes-Cummings system with cavity losses, including explicit solutions for both resonant and off-resonant cases, and examines various initial states.

Findings

Explicit analytic solutions for resonant Jaynes-Cummings dynamics.

Systematic analysis of off-resonant cases and detuning effects.

Insights into photon coherence, collapses, and revivals under dissipation.

Abstract

A new analytic approach to investigate the zero-temperature time evolution of the Jaynes-Cummings system with cavity losses is developed. With the realistic coupling between the cavity and the environment assumed, a simple master equation is derived, leading to the explicit analytic solution for the resonant case. This solution is suitable for the analyses not only on the single excitation states but also on many excitation states, which enables us to investigate the photon coherent state and to observe sharp collapses and revivals under dissipation. For the off-resonant case, on the other hand, the present study presents an analytic, systematic method instead. We examine the small and large detuning limits and discuss the condition where the widely-used phenomenological treatment is justified. Explicit evaluations of the time evolutions for various initial states with finite detuning are also presented.