Expected values for SUSY hierarchies of Jaynes-Cummings Hamiltonian

TL;DR

This paper investigates how supersymmetric (SUSY) partner Hamiltonians of the Jaynes-Cummings model influence the evolution of expected quantum optical values, including field operators and atomic inversion, and their classical and revival times.

Contribution

It provides a detailed analysis of the expected values' evolution under SUSY partner Hamiltonians with finite spectral differences in the Jaynes-Cummings framework.

Findings

Expected values are affected by SUSY partner structures.

Classical and revival times are influenced by SUSY transformations.

Spectral differences in SUSY partners modify quantum evolution characteristics.

Abstract

The aim of this letter is to compute the evolution of some expected values, such as the field operators $a^\pm$, quadratures and atomic inversion, under supersymmetric (SUSY) partner Hamiltonians associated to the Jaynes-Cummings Hamiltonian of quantum optics. This kind of SUSY partners are characterized by having spectra which differ in a finite number of energy levels. We wish to elucidate if the partner connection has any influence on these expected values. In particular, we want also to know in which way the classical and revival times are affected by such SUSY partners.