Narrow Results

In this paper, we employ the energy surface method to study a system of a two-level atom Bose–Einstein condensate coupled to a high-finesse optical cavity interacting with a single-mode electromagnetic field in the presence of the Stark-shift. The energy surface, the Phase transitions and the Berry phase of the two-level atom in Dicke model are obtained. Employing the Holstein–Primakoff representation of the angular momentum Lie algebra, the coupling line separation of the normal phase and the superradiant phase which occurs in a collection of fluorescent emitters (such as atoms), between a state containing few electromagnetic excitations are studied and a mean field description of the Dicke model is presented. We notice that in the thermodynamic limit, the energy surface takes a simple form for a direct description of the phase transition. Moreover, we show that the Stark-shift parameters and the atom–atom interactions can strongly affect the phase transition point. The results in the absence of the Stark-shift agree precisely with those obtained by Li, Liu and Zhou, who studied the same model using a different method.

In this paper, we have analyzed the critical behavior of even–even Ru and Pd isotopes between U(5) and SO(6) limits of interacting boson model via Catastrophe Theory in combination with a coherent state formalism to generate energy surfaces. The parameters of the Hamiltonian are determined via least-square fitting to the experimental data for different Ru and Pd isotopes. Our results suggest a second-order phase transition in these isotopic chains and propose the best candidates for E(5) critical symmetry. Also, the analogy between the critical exponents of ground state quantum phase transition and Landau values for the critical exponents of thermodynamic phase transitions are described.