Entangled coherent states for the description of the interaction of matter and radiation

In this expression ↠and â denote the creation and annihilation operators of the one-mode radiation field of frequency Ω, ωA the separation between the atomic levels, Ĵz denotes a collective atomic operator which counts the difference of population between the two atomic levels, Ĵ+ a collective atomic operator which promotes atoms from the lower level to the upper level, Ĵ− = Ĵ † +, and μ stands for the dipolar intensity in the interaction between matter and radiation. A variational description of the ground state of Ĥ2 can be achieved using as a trial state the tensorial product of HW (1) coherent states for radiation field and SU(2) coherent states for the atoms. Minimizing with respect to the parameters of the coherent states we obtain a good approximation of the ground state of the system. [2] However the Dicke Hamiltonian is invariant under the transformation by the unitary operator Û = exp iπ M̂ , where we have introduced the excitation number operator