Dynamical Superalgebra of the "Dressed" Jaynes-Cummings Model

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Abstract
We show how, by resorting to a one-fermion realization of the Pauli operators, the Hamiltonian of the Jaynes-Cummings (JC) model can be identified as an element of the superalgebra u(1|1), which plays the role of a dynamical algebra. The extension of this notion to osp(2|2) allows adding both virtual and real two-photon processes to the JC Hamiltonian. The exact diagonalization problem is tackled here in the special case when the coupling constants of the fermionic terms of the "dressed" JC Hamiltonian are assumed to nilpotent Grassman-Banach numbers.