Supersymmetric gauge potentials in multiphoton transition of atoms and squeezed-vacuum-state driven supersymmetric “isospin” evolution

Abstract

Energy spectrum of a multiphoton-transition Jaynes-Cummings model with supersymmetry breaking and some relevant topics such as multiphoton dark state (photon-atom dark-state polariton) and multiphoton coherent population trapping are considered in this paper. We show that for a moving atom, because of Doppler effect and the relativistic electromagnetic induction for the incident optical field, there appears supersymmetric gauge potentials induced by the multiphoton transition and then this can lead to some interesting physical effects such as supersymmetric “spin” Hall effect and supersymmetric Aharonov-Bohm effect of atoms. Both supersymmetric vectorial gauge potential and scalar gauge potential can drive the population transition in the supersymmetric “isospin” doublet states in this Jaynes-Cummings model. As an illustrative example, we address the quantum collapse and revival in atomic population inversion driven by squeezed vacuum states and displaced squeezed vacuum states in such a multiphoton-transition Jaynes-Cummings model. It can be found that different from a coherent state that drives the Jaynes-Cummings model, where quantum collapse-revival effect in atomic level population inversion can be exhibited, a squeezed vacuum state, which excites the Jaynes-Cummings model, cannot give rise to the quantum collapse and revival because there is no Fock-state probability peak in the distribution function in the squeezed vacuum state. If, however, the Jaynes-Cummings model with multiphoton transition is driven by a displaced squeezed vacuum state, it can exhibit the effect of collapse and revival in the energy-level population inversion. In addition, we shall consider the interaction among atom paths (spatial wavefunctions), atomic internal levels and the photon field. Such a coupling leads to an atomic path-level-photon entangled state, and the traditional atomic-level quantum Rabi oscillation and quantum collapse-revival effect that occurred in time domain would be exhibited in the atom spatial wavefunctions (or in atomic paths).