Generation and dynamics of crystallised-type states of light within the Tavis-Cummings model

Abstract

A generation of superpositions of photon number operator states within the generalized Tavis-Cummings model (GTC) is proposed, which is independent of the dipolar strengths and of the considered number of atoms. These are obtained by considering a linear combination of states, with total number of excitations M₁ and M₂, whose corresponding Husimi function for the electromagnetic field exhibits a cyclic point group symmetry Cn, with n = |M₂ –M₁|, that is, describes a crystallised-type state. Finally we establish that these superpositions under evolution with respect to the GTC Hamiltonian yields a Husimi function that preserves the cyclic point group symmetry.