2010/11/12 by M. Aparicio Alcalde, B. M. Pimentel, Alcalde, M. Aparicio +1 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Optical properties and cooling technologies in crystalline materials #Strong Light-Matter Interactions #quant-ph
paper · pdf · doi:10.48550/arxiv.1011.3075
arxiv created 2010/11/12 · arxiv updated 2010/11/16
The full Dicke model describes a system of N identical two level-atoms coupled to a single-mode quantized bosonic field. The model considers rotating and counter-rotating coupling terms between the atoms and the bosonic field, with coupling constants g1 and g2, for each one of the coupling terms, respectively. We study finite temperature properties of the model using the path integral approach and functional methods. In the thermodynamic limit, N→∞, the system exhibits phase transition from normal to superradiant phase, at some critical values of temperature and coupling constants. We distinguish between three particular cases, the first one corresponds to the case of rotating wave approximation, which g1≠ 0 and g2=0, the second one corresponds to the case of g1=0 and g2≠ 0, in these two cases the model has a continuous symmetry. The last one, corresponds to the case of g1≠ 0 and g2≠ 0, which the model has a discrete symmetry. The phase transition in each case is related to the spontaneous breaking of its respective symmetry. For each one of these three particular cases, we find the asymptotic behaviour of the partition function in the thermodynamic limit, and the collective spectrum of the system in the normal and the superradiat phase. For the case of rotating wave approximation, and also the case of g1=0 and g2≠ 0, in the superradiant phase, the collective spectrum has a zero energy value, corresponding to the Goldstone mode associated to the continuous symmetry breaking of the model. Our analyse and results are valid in the limit of zero temperature, β→∞, in which, the model exhibits a quantum phase transition.