The Jaynes-Cummings model in Phase Space Quantum Mechanics

TL;DR

This paper develops a phase space approach to the Jaynes-Cummings model, deriving a full Wigner function for a hybrid atom-field system to analyze quantum phenomena like Rabi oscillations and entanglement.

Contribution

It introduces an explicit construction of the Wigner function for the Jaynes-Cummings model using the Stratonovich-Weyl correspondence and coadjoint orbit method, providing new insights into quantum dynamics.

Findings

Derived a complete Wigner function for the system

Analyzed quantum phenomena such as Rabi oscillations and entanglement

Measured purity to study entanglement dynamics

Abstract

In this paper, we address the phase space formulation of the Jaynes-Cummings model through the explicit construction of the full Wigner function for a hybrid bipartite quantum system composed of a two-level atom and a quantized coherent field. By employing the Stratonovich-Weyl correspondence and the coadjoint orbit method, we derive an informationally complete quasi-probability distribution that captures the full dynamics of light-matter interaction. This approach provides a detailed phase space perspective of fundamental quantum phenomena such as Rabi oscillations, atomic population inversion, and entanglement generation. We further measure the purity of the reduced quantized field state by means of an appropriate Wigner function corresponding to the bosonic field part in order to investigate the entanglement dynamics of the system.