Macroscopic Quantum States and Quantum Phase Transition in Dicke Models of Arbitrary Atom-Number

• Main Authors: Lian, Jinling, Zhang, Yuanwei, Liang, J. -Q.
• Format: Text
• Language: unknown
• Published: arXiv 2011
• Subjects: Quantum Physics quant-ph; Other Condensed Matter cond-mat.other; FOS Physical sciences; North Pole
• Online Access: https://dx.doi.org/10.48550/arxiv.1110.3862; https://arxiv.org/abs/1110.3862

The energy spectrum of Dicke Hamiltonians with and without the rotating wave approximation for arbitrary atom-number is obtained analytically with the variational method, in which the effective pseudo-spin Hamiltonian resulted from the expectation value in the boson-field coherent state is diagonalized by the spin-coherent-state transformation. In addition to the ground-state energy an excited macroscopic quantum-state is found corresponding to the south-and-north-pole gauges of the spin-coherent states respectively. Our results of ground-state energies in exact agreement with various approaches show that these models exhibit a zero-temperature quantum phase transition of second-order for any number of atoms, which however was commonly considered as a phenomenon of the thermodynamic limit with the atom-number tending to infinite. The critical behavior of geometric phase is analyzed, which displays no singularity at the critical point. : 5 pages, 2 figures