Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry

Abstract

We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic $n${-}excitation subspace obey the same equations of motion that can be obtained from a \emph{static} non-Hermitian Jaynes-Cummings Hamiltonian with $\mathcal{P}T$ symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of $\mathcal{P}T$ symmetric non-Hermitian Hamiltonians. We also generalize the well-known diagonalization of the Jaynes-Cummings Hamiltonian to the non-Hermitian case in terms of pseudo-bosons and pseudo-fermions, and discuss relevant mathematical and physical aspects.

arXiv comment9 pages

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• Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians
• A description of pseudo-bosons in terms of nilpotent Lie algebras
• Resonance dipole-dipole interaction between two accelerated atoms in the presence of a reflecting plane boundary
• Weak pseudo-bosons
• A concise review on pseudo-bosons, pseudo-fermions and their relatives
• A spin chain with non-Hermitian $\mathcal{PT}-$symmetric boundary couplings: exact solution, dissipative Kondo effect, and phase transitions on the edge
• $\mathcal{P}\mathcal{T}$ symmetry of a square-wave modulated two-level system
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• Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip
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