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Phase space information in a non-linear quantum system containing a Kerr-like medium through Su(1, 1)-algebraic treatment

Abstract Analytical description for a Su(2)-quantum system interacting with a damped Su(1, 1)-cavity, which is filled with a non-linear Kerr medium, is presented. The dynamics of non-classicality of Su(1, 1)-state is investigated via the negative part of the Wigner function. We show that the negative part depends on the unitary interaction and the Kerr-like medium and it can be disappeared by increasing the dissipation rate and the detuning parameter. The phase space information of the Husimi function and its Wehrl density is very sensitive not only to the coupling to the environment and the unitary interaction but also to the detuning as well as to the Kerr-like medium. The phase space information may be completely erased by increasing the coupling to the environment. The coherence loss of the Su(2)-state is investigated via the Husimi Wehrl entropy. If the effects of the detuning parameter or/and of the Kerr-like medium are combined with the damping effect, the damping effect of the coupling to the environment may be weaken, and the Wehrl entropy is delayed to reach its steady-state value. At the steady-state value, the phase space information and the coherence are quickly lost.