Collapse and revivals for the binomial field distribution

TL;DR

This paper derives approximate analytical expressions for collapse and revival phenomena in the atomic inversion of the Jaynes-Cummings model when the field is in a binomial state, using complex integral methods.

Contribution

It introduces a novel analytical approach to evaluate collapse and revivals for binomial field states in the Jaynes-Cummings model.

Findings

Derived simple approximate formulas for collapse and revival times.

Validated the analytical expressions with numerical comparisons.

Provided insights into the dynamics of binomial states in quantum optics.

Abstract

The exact representation of the atomic inversion in the Jaynes-Cummings model as an integral over the Hankel contour is used. For a field in a binomial state, the integral is evaluated using the saddle point method. Simple approximate analytical expressions for collapse and revivals are obtained.