A characteristic function approach to the Jaynes-Cummings model revivals

TL;DR

This paper introduces a characteristic function approach to analyze the revival phenomena in the Jaynes-Cummings model, revealing how atomic population dynamics relate to photon-number distributions and enabling quantum-state reconstruction.

Contribution

It presents a novel spectral decomposition method using the characteristic function to understand and interpret revival structures in the Jaynes-Cummings model.

Findings

Revival structures correspond to interference of quantum wave packet snapshots.

Photon-number distribution can be retrieved when revival structures do not overlap.

The approach links atomic population dynamics to the field's quantum state.

Abstract

A two-level atom interacting with an electromagnetic mode in a cavity experiences population collapses and revivals. They are an indirect signature of the field quantization, and also hold information about the mode. Thus, they may be harnessed for quantum-state reconstruction. In this work, we study the revival structures with the characteristic function approach. The characteristic function is essentially a spectral decomposition of the photon-number probability distribution. Exploiting the characteristic function periodicity, we find that the atomic population inversion can be understood as the result of interference between a set of structures akin to a free quantum-mechanical wave packet, each structure corresponding to snapshots of this packet for different degrees of dispersion. When these structures do not overlap, each of which can be identified to one of the inversion revivals, in which case we may also retrieve the photon-number distribution.