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arXiv:1011.3075 · Physica A Statistical Mechanics and its Applications

Path integral approach to the full Dicke model

M. Aparicio Alcalde, B. M. Pimentel

Published May 23, 2011• 12 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2011.05.018

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We consider the full Dicke spin-boson model composed by a single bosonic mode and an ensemble of N identical two-level atoms with different couplings for the resonant and anti-resonant interaction terms, and incorporate a dipole–dipole interaction between the atoms. Assuming that the system is in thermal equilibrium with a reservoir at temperature β −1 , we compute the free energy in the thermodynamic limit N → ∞ in the saddle-point approximation to the path integral and determine the critical temperature for the super-radiant phase transition. In the zero temperature limit, we recover the critical coupling of the quantum phase transition, presented in the literature.
The Dicke model is derived in the contraction limit of a pseudo-deformation of the quasispin algebra in the su (2)-based Richardson-Gaudin models. Likewise, the integrability of the Dicke model is established by constructing the full set of conserved charges, the form of the Bethe Ansatz state, and the associated Richardson-Gaudin equations. Thanks to the formulation in terms of the pseudo-deformation, the connection from the su (2)-based Richardson-Gaudin model towards the Dicke model can be performed adiabatically.
In this paper we predict a topological quantum interference effect in an extended Dicke model with controllable long-range atom-atom interactions by means of coherent-state path integral. Due to the intrinsic competition between the atom-atom interactions and atom-field coupling, an interesting topological interference of the instanton and anti-instanton tunneling paths could occur. As a consequence, this model only with a few odd-number atoms has a twofold absolute degenerate ground-state subspace with a large energy gap, which becomes larger with the increasing of the system size. Therefore, the collective decoherence arising from noise in the external control parameters could be effectively suppressed in terms of adiabatic process between this absolute degenerate ground-state subspace associated with a finite energy gap.