Husimi distribution and phase space analysis of Dicke model quantum phase transition

The Husimi distribution is proposed for a phase space analysis of quantum phase transitions in the Dicke model of spin-boson interactions. We show that the inverse participation ratio and Wehrl entropy of the Husimi distribution give sharp signatures of the quantum phase transition. The analysis has been done using two frameworks: a numerical treatment and an analytical variational approximation. Additionally we have proposed a new characterization of the Dicke model quantum phase transition by means of the zeros of the Husimi distribution in the variational approach.