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Chinese Physics

Exact solution for Super-Jaynes-Cummings model

Huai-Xin Lu, Wang Xiao-qing, Zhang Yong-de

Published May 1, 2000• 13 citations
Publisher

Abstract

Based on the linear quantum transformation theory, we further propose a supersymmetric unitary transformation, whose operator can be constructed by the supersymmetric generators of Lie superalgebra. Therefore, by making use of the supersymmetric unitary transformation, we can obtain the eigenspectrum, the eigenstates and the super-partition function for the Super-Jaynes-Cummings model when the coupling constants are Grassmann valued.

DOI
10.1088/1009-1963/9/5/002

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Based on the linear quantum transformation theory, we further propose a supersymmetric unitary transformation, whose operator can be constructed by the supersymmetric generators of Lie superalgebra. Therefore, by making use of the supersymmetric unitary transformation, we can obtain the eigenspectrum, the eigenstates and the super-partition function for the Super-Jaynes-Cummings model when the coupling constants are Grassmann valued.
The super-algebraic structure of a generalized version of the Jaynes–Cummings model is investigated. We find that a Z 2 graded extension of the so (2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the four-dimensional super-algebra u (1/1) with two odd and two even elements. Differential matrix operators are taken as realization of the elements of the superalgebra to which the model Hamiltonian belongs. Several examples with various choices of superpotentials are presented. The energy spectrum and corresponding wavefunctions are obtained analytically.