Extended Jaynes-Cummings models and (quasi)-exact solvability

Abstract

The original Jaynes-Cummings model is described by a Hamiltonian which is exactly solvable. Here we extend this model by several types of interactions leading to a nonhermitian operator which doesn't satisfy the physical condition of space-time reflection symmetry (PT symmetry). However the new Hamiltonians are either exactly solvable admitting an entirely real spectrum or quasi exactly solvable with a real algebraic part of their spectrum.

16 pages, 3 figures, discussion extended, one section added

References in corpus (12)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Quasi-Exactly Solvable Systems and Orthogonal Polynomials
• Pseudo-hermitian interaction between an oscillator and a spin half particle in the external magnetic field
• Quasi Exactly Solvable 2$\times$2 Matrix Equations
• Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry
• Quasi exactly solvable operators and Lie superalgebras
• Realizations of the Lie superalgebra q(2) and applications

Cited by in corpus (3)

• Ultracold atoms in U(2) non-Abelian gauge potentials preserving the Landau levels
• Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians
• PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras