Underlying SUSY in a generalized Jaynes-Cummings model

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.

Entangling operations in nonlinear two-atom Tavis-Cummings models

“…We identify constants of motion that lead to an exact solvability. Similar general models have already been considered in the past and their exact solution is known [36][37][38][39][40][41][42][43]. However, here we are interested in presenting a general approximate solution for initial coherent states with large mean number of quanta that is especially convenient to analyze the entanglement in the system as it is expressed in terms of material Bell states and coherent states of the field.…”