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Journal Article

#### Path integral approach to the full Dicke model with dipole-dipole interaction

##### Fulltext (public)

1107.2945

(Preprint), 124KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Alcalde, M. A., Stephany, J., & Svaiter, N. F. (2011). Path integral approach to
the full Dicke model with dipole-dipole interaction.* Journal of Physics A: Mathematical and General,*
*44*: 505301. Retrieved from http://arxiv.org/abs/1107.2945.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-1E8F-7

##### Abstract

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 $\beta^{-1}$, we compute
the free energy in the thermodynamic limit $N\rightarrow\infty$ in the
saddle-point approximation to the path integral and determine the critical
temperature for the superradiant phase transition. In the zero temperature
limit, we recover the critical coupling of the quantum phase transition,
presented in the literature.