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.

20 pages, 8 figures

References in corpus (2)

• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• A photonic crystal realization of a phase driven two-level atom

Cited by in corpus (6)

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• Spectral response of a nonlinear Jaynes-Cummings model
• A supersymmetry journey from the Jaynes-Cummings to the anisotropic Rabi model
• Tripartite multiphoton Jaynes-Cummings model: Analytical solution and Wigner nonclassicalities
• SUSY hierarchies of Jaynes-Cummings Hamiltonians with different detuning parameters