Exploring Supersymmetry: Interchangeability Between Jaynes-Cummings and Anti-Jaynes-Cummings Models

TL;DR

This paper uncovers a supersymmetric link between the Jaynes-Cummings and anti-Jaynes-Cummings models, introducing a new method to analyze their dynamics and quantum properties for photonic quantum technologies.

Contribution

It presents a novel supersymmetric approach to derive the dynamics of the AJC model and explores how initial states influence quantum behavior, expanding analytical tools in quantum optics.

Findings

Supersymmetric techniques can determine the evolution of the AJC model.

Control of initial states influences collapse-revival phenomena.

Method extends to high-order photon counting statistics.

Abstract

The supersymmetric connection that exists between the Jaynes-Cummings (JC) and anti-Jaynes Cummings (AJC) models in quantum optics is unraveled entirely. A new method is proposed to obtain the temporal evolution of observables in the AJC model using supersymmetric techniques, providing an overview of its dynamics and extending the calculation to full photon counting statistics. The approach is general and can be applied to determine the high-order cumulants given an initial state. The analysis reveals that engineering the collapse-revival behavior and the quantum properties of the interacting field is possible by controlling the initial state of the atomic subsystem and the corresponding atomic frequency in the AJC model. The substantial potential for applications of supersymmetric techniques in the context of photonic quantum technologies is thus demonstrated.