A Generalized Multiphoton Jaynes–cummings Model for Two Collectively Radiating Atoms Solved via Supersymmetric Unitary Transformation

Abstract

The multiphoton Jaynes-Cummings model is theoretically generalized to the simplest case of collectively radiating atoms. For this Jaynes-Cummings model, we find its supersymmetric structure. Based on this, we introduce a supersymmetric unitary transformation to diagonalize the Hamiltonian, and in so doing, its eigenvalues and eigenfunctions are obtained. Some transition processes are calculated.

Quantum collapse-revival effect in a supersymmetric Jaynes–Cummings model and its possible application in supersymmetric qubits

“…Inspired by the above work [28][29][30]44], it seems that the scenario of Dirac-like dynamics mimicked by a single trapped ion [30] can be generalized to a supersymmetric one: specifically, the quantum operators of the interaction terms in the supersymmetric Hamiltonian of Jaynes-Cummings model [35][36][37][38][39] can be chosen as…”

“…The Jaynes-Cummings model [6,7] is an ideal one for analyzing the light-matter interaction, where many new interesting characteristics have been found [27][28][29][30]. A light-atom interacting Jaynes-Cummings model, where multiphoton transition in one ñ g | -ñ e | process is involved, has been studied by some researchers from the various aspects such as field statistics, coherent atomic preparation and high-order squeezing [31][32][33][34] and relevant characteristics indicated by using some supersymmetry-transformation solvable models [35][36][37][38][39]. Such a kind of multiphoton-transition Jaynes-Cummings processes would have some possible applications such as quantum filters and multiphoton quantum interference [40].…”

“…Such a kind of multiphoton-transition Jaynes-Cummings processes would have some possible applications such as quantum filters and multiphoton quantum interference [40]. The full-quantum Hamiltonian of such a Jaynes-Cummings model that can have supersymmetric Lie algebra structure (because of multiphoton transition between two atomic levels) is given by [35][36][37][38][39]…”

“…This is a characteristic of fermion-boson supersymmetry. The two photon-atom polariton states ñ F | , ñ B | can be transformed to one another under the supersymmetry transformation, of which the supersymmetric operators (Lie algebra generators) [35][36][37][38][39]…”

“…dynamical Stark effect [27] as well as Jaynes-Cummings analog of Dirac Hamiltonian dynamics [28][29][30]. In section 6 we conclude with some remarks on the quantum collapse-revival effect and some potential applications in a multiphoton Jaynes-Cummings model [31][32][33][34] that is of supersymmetry in Lie algebra structure [35][36][37][38][39].…”