Darboux transformations of the Jaynes-Cummings Hamiltonian

Abstract

A detailed analysis of matrix Darboux transformations under the condition that the derivative of the superpotential be self-adjoint is given. As a onsequence, a class of the symmetries associated to Schrödinger matrix Hamiltonians is characterized. The applications are oriented towards the Jaynes-Cummings eigenvalue problem, so that exactly solvable $2\times 2$ matrix Hamiltonians of the Jaynes-Cummings type are obtained. It is also established that the Jaynes-Cummings Hamiltonian is a quadratic function of a Dirac-type Hamiltonian.

15 pages

References in corpus (3)

• Intertwining technique for the one-dimensional stationary Dirac equation
• Matrix Hamiltonians: SUSY approach to hidden symmetries
• Chains of Darboux transformations for the matrix Schroedinger equation

Cited by in corpus (5)

• SUSY approach to Pauli Hamiltonians with an axial symmetry
• PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras
• Exploring Supersymmetry: Interchangeability Between Jaynes-Cummings and Anti-Jaynes-Cummings Models
• Correlation of Dirac potentials and atomic inversion in cavity quantum electrodynamics
• SUSY hierarchies of Jaynes-Cummings Hamiltonians with different detuning parameters