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Macroscopic Quantum States and Quantum Phase Transition in the Dicke Model |
| LIAN Jin-Ling, ZHANG Yuan-Wei, LIANG Jiu-Qing** |
| Institute of Theoretical Physics and Department of Physics, Shanxi University, Taiyuan 030006 |
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| Cite this article: |
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LIAN Jin-Ling, ZHANG Yuan-Wei, LIANG Jiu-Qing 2012 Chin. Phys. Lett. 29 060302 |
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Abstract The energy spectrum of Dicke Hamiltonians with and without the rotating wave approximation for an arbitrary atom number is obtained analytically by means of the variational method, in which the effective pseudo-spin Hamiltonian resulting 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 the second order for any number of atoms, which was commonly considered as a phenomenon of the thermodynamic limit with the atom number tending to infinity. The critical behavior of the geometric phase is analyzed.
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Received: 20 February 2012
Published: 31 May 2012
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| PACS: |
03.65.Fd
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(Algebraic methods)
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64.70.Tg
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(Quantum phase transitions)
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42.50.Ct
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(Quantum description of interaction of light and matter; related experiments)
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03.65.Vf
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(Phases: geometric; dynamic or topological)
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