Underlying SUSY in a generalized Jaynes-Cummings model

TL;DR

This paper introduces a generalized Jaynes-Cummings model with supersymmetric algebraic structure, enabling analytic solutions for complex quantum dynamics involving nonlinear and multi-boson interactions.

Contribution

It presents a new generalized model with underlying supersymmetric algebra, providing a diagonalization scheme and analytic time evolution for complex quantum systems.

Findings

Derived closed-form expressions for observables.

Analyzed dynamics of population inversion and boson quadratures.

Included various interaction types like Kerr and multi-boson exchange.

Abstract

We propose a generalized Jaynes-Cummings model that includes but is not limited to an extensive collection of experimental and theoretical proposals from the literature. It covers nonlinear boson terms, nonlinear dispersive and multi-boson exchange interaction. Our model features an underlying Lie graded algebra symmetry reminiscent to supersymmetric quantum mechanics. This allows us to propose a diagonalization scheme and calculate its analytic time evolution. In consequence, we are able to construct closed forms for relevant observables and explore the dynamics of particular realizations of our model independent of their complexity. As an practical example, we show the evolution of the population inversion and the boson quadratures for an initial state consisting of the qubit in the ground state interacting with a coherent field for a selection of cases including the standard JC model with Stark shift, Kerr-like terms, intensity dependent coupling, multi-boson exchange and algebraic deformations.