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arXiv · 1110.3862

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

Jinling Lian·Yuanwei Zhang·J. -Q. Liang
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Abstract

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.

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Jinling Lian, Yuanwei Zhang, J. -Q. Liang. 2011-11-22. Macroscopic Quantum States and Quantum Phase Transition in Dicke Models of Arbitrary Atom-Number. https://doi.org/10.1088/0256-307x%2F29%2F6%2F060302

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