Relationship between the atomic inversion and Wigner function for multiphoton multimode Jaynes-Cummings model

TL;DR

This paper establishes a direct link between atomic inversion and the Wigner function at the phase space origin in a multimode multiphoton Jaynes-Cummings model, enabling potential atomic state detection via phase space methods.

Contribution

It demonstrates that the evolution of the Wigner function at the origin reflects atomic inversion under various conditions, including nonlinearities and different initial states.

Findings

Wigner function at the origin indicates atomic inversion.

Relation holds even with Kerr nonlinearity and Stark shifts.

Potential for atomic state detection through phase space techniques.

Abstract

In this paper we consider multimode multiphoton Jaynes-Cummings model, which consists of a two-level atom, initially prepared in an excited atomic state, interacting with $N$ modes of electromagnetic field prepared in general pure quantum states. For this system we show that under certain conditions the evolution of the Wigner function at the phase space origin provides direct information on the corresponding atomic inversion. This relation is also valid even if the system includes Kerr-like nonlinearity, Stark shift effect, different types of the initial atomic state as well as moving atom. Furthermore, based on this fact we discuss for the single-mode case the possibility of detecting the atomic inversion by means of techniques similar to those used for Wigner function.