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 (3)

• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Pseudo-hermitian interaction between an oscillator and a spin half particle in the external magnetic field
• Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry

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