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Physics Letters A

A new phase transition in the Dicke hamiltonian

G. Compagno, A. Panzarella, Franco Persico

Published Nov 1, 1980• 6 citations
Publisher
DOI
10.1016/0375-9601(80)90201-7

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The thermodynamic equilibrium properties of the Dicke Hamiltonian for a collection of spin- 1 / 2 particles interacting via magnetic dipole interaction with a single mode of the radiation field and with each other by spin-spin interaction are analysed and the conditions for the existence of a super-radiant phase transition are derived. It is shown, using the approximate long-range spin-spin interaction (MI), in the Dicke Hamiltonian, that the conditions for the existence of the super-radiant phase transition are invariant with respect to isotropic MI whether or not the A 2 term is included.
A system of N two-level atoms, Tavis-Cummings Dicke (TC-Dicke) model, interacting with a one-mode electromagnetic radiation field in the presence of the Stark shifts is studied, which is expected to predict new phenomena that are not explored in the original TC-Dicke model. We obtained the potential energy surface of the system using a trial state the direct product of coherent states in each subspace. In the frame of mean-field approaches, the variational energy is evaluated as the expectation value of the Hamiltonian for this state. The order of the quantum phase transitions is determined explicitly and numerically. We estimate the ground-state energy and the macroscopic excitations in the superradiant phase. Moreover, we investigated the critical properties of the TC-Dicke model in the classical spin limit and coherent state. We observed that in the thermodynamic limit, the energy surface takes a simple form a direct description of the phase transition. Moreover, it is found that when the microwave amplitude changes the new phase transition occurs with the Stark shift. The analytical solutions and numerical results, which appear in this paper are agreement with our paper which published recently in Int. J. Mod. Phys. B when we studied the same model using a different coherent state.