Symmetry adapted states and the quantum phase transition in the Dicke model

Abstract

We study the phase transition properties of the ground state of the Dicke model by means of a variational procedure together with the catastrophe formalism. The proposed variational state is the tensorial product of the SU(2) and Weyl coherent states, and the expectation value of the Dicke Hamiltonian with respect this state is calculated. The stability properties of the energy surface exhibit a phase transition from the normal to the super-radiant behavior of the two-level atoms, when ΩaΩF = ±4γ2. At the same time, the analytic form of the ground state in terms of the minimum critical points of the system is obtained. The Dicke Hamiltonian is invariant under transformations of the point groupC 2 = {I, exp(iπ Λ)}, with Λ the excitation number operator. To restore this parity symmetry, we separate the variational proposed states into orthogonal even and odd components, which give rise to analytic expressions for the ground and first excited states. The fidelity of these projected variational states is verified by studying their overlap with the exact quantum results. © 2010 American Institute of physics.