An algebraic approach to the study of weakly excited states for a condensate in a ring geometry
arXiv:cond-mat/0508687 · doi:10.1088/0305-4470/38/39/007
Abstract
We determine the low-energy spectrum and the eigenstates for a two-bosonic mode nonlinear model by applying the Inönü-Wigner contraction method to the Hamiltonian algebra. This model is known to well represent a Bose-Einstein condensate rotating in a thin torus endowed with two angular-momentum modes as well as a condensate in a double-well potential characterized by two space modes. We consider such a model in the presence of both an attractive and a repulsive boson interaction and investigate regimes corresponding to different values of the inter-mode tunneling parameter. We show that the results ensuing from our approach are in many cases extremely satisfactory. To this end we compare our results with the ground state obtained both numerically and within a standard semiclassical approximation based on su(2) coherent states.
arXiv comment24 pages, 5 figures, accepted for publication on J. Phys. A
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- Quantum dynamics of attractive versus repulsive bosonic Josephson junctions: Bose-Hubbard and full-Hamiltonian results
- Some remarks on the coherent-state variational approach to nonlinear boson models
- Quantum signatures of self-trapping transition in attractive lattice bosons
- Dynamics and symmetries of a repulsively bound atom pair in an infinite optical lattice
- Quasi-angular momentum of Bose and Fermi gases in rotating optical lattices