An Approximate Solution of the Jaynes-Cummings Model with Dissipation II : Another Approach

TL;DR

This paper presents a new method to derive a more compact approximate solution for the dissipative Jaynes-Cummings model's master equation, improving upon previous approaches by simplifying the solution form.

Contribution

The authors develop an alternative approach that yields a more manageable approximate solution for the Jaynes-Cummings model with dissipation under specific initial conditions.

Findings

Achieved a compact approximate solution for the master equation

Simplified the form of the solution compared to previous methods

Enhanced the practicality of solving the model with initial conditions

Abstract

In the preceding paper (arXiv:1103.0329 [math-ph]) we treated the Jaynes-Cummings model with dissipation and gave an approximate solution to the master equation for the density operator under the general setting by making use of the Zassenhaus expansion. However, to obtain a compact form of the approximate solution (which is in general complicated infinite series) is very hard when an initial condition is given. To overcome this difficulty we develop another approach and obtain a compact approximate solution when some initial condition is given.