On the Jaynes-Cummings hamiltonian supersymmetric characteristics

Christine Geron

Published Jan 1, 1999• 0 citations

Abstract

We study some degeneracies of the Jaynes-Cummings Hamiltonian eigen-states. More precisely, we underscore operators connecting the degenerated eigenstates or explaining their non-degeneracy. These operators actually are supercharges and the supersymmetry underlying the Jaynes-Cummings model is thus exhibited. We also consider two extensions of the Hamiltonian to show the unicity of their supercharges.

Related papers

Spin-1/2 particle and hole as supersymmetry partners

Chang Jae Lee

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 AJul 1, 199410 citations

Supersymmetric Unitary Operator for Some Generalized Jaynes–Cummings Models

Hong-Yi Fan, Liang‐shi Li

We introduce supersymmetric unitary operators to directly diagonalize some generalized Jaynes–Cummings (J–C) Hamiltonians; which more deeply shows that supersymmetry is a natural language to depict the J–C model.

Communications in Theoretical PhysicsFeb 14, 199641 citations

Pseudo-invariant Eigen-operator for Deriving Energy-Level Gap for Jaynes–Cummings Model

Fan Hong-Yi, Cheng Da

We extend the concept of invariant eigen-operator to pseudo-invariant eigen-operator case through analyzing the standard Jaynes–Cummings model. We find the pseudo-invariant eigen-operator in terms of supersymmetric generators of this model, which diretly leads to the energy-level gap for Jaynes–Cummings Hamiltonian.

Communications in Theoretical PhysicsFeb 1, 20069 citations

Exactly solvable non-Hermitian Jaynes–Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry

Pijush K Ghosh

It is shown that for a given Hermitian Hamiltonian possessing supersymmetry, there is always a non-Hermitian Jaynes–Cummings-type Hamiltonian (JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the corresponding non-Hermitian JCTH are simultaneously diagonalizable. The exact eigenstates of these non-Hermitian Hamiltonians are constructed algebraically for certain shape-invariant potentials, including a non-Hermitian version of the standard Jaynes–Cummings (JC) model for which the parent supersymmetric Hamiltonian is the superoscillator. It is also shown that a non-Hermitian version of the several physically motivated generalizations of the JC model admits entirely real spectra. The positive-definite metric operator in the Hilbert space is constructed explicitly along with the introduction of a new inner product structure, so that the eigenstates form a complete set of orthonormal vectors and the time evolution is unitary.

arXiv:quant-ph/0501087Journal of Physics A Mathematical and GeneralAug 3, 200529 citations

Supersymmetry in the Jaynes-Cummings model

Octavio Castaños

A review is presented of the Darboux method and its relation to the supersymmetric quantum mechanics, together with the embedding of a n-dimensional scalar Hamiltonian into a supersymmetric matrix. It is also shown that the Jaynes-Cummings model, with or without rotating wave approximation, admit a supersymmetric quantum mechanics description.

AIP conference proceedingsJan 1, 20132 citations

Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry

Ghosh, P K

It is shown that for a given Hermitian Hamiltonian possessing supersymmetry, there is alwayas a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the corresponding non-hermitian JCTH are simultaneously diagonalizable. The exact eigenstates of these non-hermitian Hamiltonians are constructed algebraically for certain shape-invariant potentials, including a non-hermitian version of the standard Jaynes-Cummings model for which the parent supersymmetric Hamiltonian is the superoscillator. The positive-definite metric operator in the Hilbert space is constructed explicitly along with the introduction of a new inner product structure, so that the eigenstates form a complete set of orthonormal vectors and the time-evolution is unitary.

Jan 17, 200515 citations