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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Two-level Jaynes-Cummings Hamiltonian as a supersymmetric quantum-mechanical system

H. A. Schmitt, A. Mufti

Published Apr 15, 1991• 8 citations
Publisher

Abstract

Using a realization of the noncompact orthosymplectic superalgebra $\mathrm{Osp}(\frac{2}{2}, R)$, the two-level Jaynes-Cummings Hamiltonian is shown to be a supersymmetric quantum-mechanical system in the sense of Witten. The existence of the supersymmetry is shown to place a restriction on the physical parameters of the Hamiltonian.

DOI
10.1103/physrevd.43.2743

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Spin-1/2 particle and hole as supersymmetry partners

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Using supersymmetry quantum mechanics, we explain the covariance of the eigenvalue equation for the Jaynes-Cummings (JC) Hamiltonian under the particle-hole transformation. The JC Hamiltonians for the original spin-1/2 ``particle'' and the transformed partner (the ``hole'') are shown to be the fermionic and the bosonic parts of a supersymmetric Hamiltonian. The Hamiltonian, unlike ordinary one-dimensional supersymmetric quantum-mechanical models, can have a degenerate zero-energy ground state despite exact supersymmetry. The degeneracy is shown to arise from the hidden particle-hole exchange symmetry as well as supersymmetry in the Hamiltonian.

Physical Review A•Jul 1, 1994•10 citations
Using a realization of the noncompact orthosymplectic superalgebra Osp(22,R)\mathrm{Osp}(\frac{2}{2}, R)Osp(22​,R), the two-level Jaynes-Cummings Hamiltonian is shown to be a supersymmetric quantum-mechanical system in the sense of Witten. The existence of the supersymmetry is shown to place a restriction on the physical parameters of the Hamiltonian.
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.
Using supersymmetry quantum mechanics, we explain the covariance of the eigenvalue equation for the Jaynes-Cummings (JC) Hamiltonian under the particle-hole transformation. The JC Hamiltonians for the original spin-1/2 ``particle'' and the transformed partner (the ``hole'') are shown to be the fermionic and the bosonic parts of a supersymmetric Hamiltonian. The Hamiltonian, unlike ordinary one-dimensional supersymmetric quantum-mechanical models, can have a degenerate zero-energy ground state despite exact supersymmetry. The degeneracy is shown to arise from the hidden particle-hole exchange symmetry as well as supersymmetry in the Hamiltonian.