An approach to exact solutions of the time-dependent supersymmetric two-level three-photon Jaynes-Cummings model

TL;DR

This paper derives exact solutions for the time-dependent supersymmetric two-level three-photon Jaynes-Cummings model using invariant theory, highlighting the model's supersymmetric structure and discussing adiabatic approximations.

Contribution

It introduces a method to obtain exact solutions of the time-dependent supersymmetric Jaynes-Cummings model via invariant-related unitary transformations, leveraging supersymmetric generators.

Findings

Exact solutions for the time-dependent model are obtained.

The supersymmetric structure facilitates the solution process.

Adiabatic approximation case is analyzed.

Abstract

By utilizing the property of the supersymmetric structure in the two-level multiphoton Jaynes-Cummings model, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators. We obtain the exact solutions of the time-dependent Schr\"{o}dinger equation which describes the time-dependent supersymmetric two-level three-photon Jaynes-Cummings model (TLTJCM) by using the invariant-related unitary transformation formulation. The case under the adiabatic approximation is also discussed. Keywords: Supersymmetric Jaynes-Cummings model; exact solutions; invariant theory; geometric phase factor; adiabatic approximation