Quantum rotor theory of spinor condensates in tight traps
arXiv:1011.3517 · doi:10.1103/PhysRevA.83.023613
Abstract
In this work, we theoretically construct exact mappings of many-particle bosonic systems onto quantum rotor models. In particular, we analyze the rotor representation of spinor Bose-Einstein condensates. In a previous work it was shown that there is an exact mapping of a spin-one condensate of fixed particle number with quadratic Zeeman interaction onto a quantum rotor model. Since the rotor model has an unbounded spectrum from above, it has many more eigenstates than the original bosonic model. Here we show that for each subset of states with fixed spin F_z, the physical rotor eigenstates are always those with lowest energy. We classify three distinct physical limits of the rotor model: the Rabi, Josephson, and Fock regimes. The last regime corresponds to a fragmented condensate and is thus not captured by the Bogoliubov theory. We next consider the semiclassical limit of the rotor problem and make connections with the quantum wave functions through use of the Husimi distribution function. Finally, we describe how to extend the analysis to higher-spin systems and derive a rotor model for the spin-two condensate. Theoretical details of the rotor mapping are also provided here.
10 pages, 2 figures
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Cited by in corpus (9)
- Quantum optomechanics of a Bose-Einstein Antiferromagnet
- Spin fragmentation of Bose-Einstein condensates with antiferromagnetic interactions
- Goldstone-mode Instability leading to Fragmentation in a Spinor Bose-Einstein Condensate
- Fluctuation-induced and symmetry-prohibited metastabilities in spinor Bose-Einstein condensates
- Spin 1 microcondensate in a magnetic field: semiclassics and exact solution
- Optical Control of a Quantum Rotor
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- Probing mechanical quantum coherence with an ultracold-atom probe
- Quantum Rotor Theory of Systems of Spin-2 Bosons