Condensed Vortex Ground States of Rotating Bose–Einstein Condensate in Harmonic Atomic Trap
✍ Scribed by M.S. Hussein; O.K. Vorov
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 222 KB
- Volume
- 298
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
We study a system of N Bose atoms trapped by a symmetric harmonic potential, interacting via weak central forces. Considering the ground state of the rotating system as a function of the two conserved quantities, the total angular momentum, and its collective component, we develop an algebraic approach to derive exact wave functions and energies of these ground states. We describe a broad class of the interactions for which these results are valid. This universality class is defined by simple integral condition on the potential. Most of the potentials of practical interest which have pronounced repulsive component belong to this universality class. C 2002 Elsevier Science (USA)
where V is a typical matrix element of the interaction . The problem is therefore to find a nonperturbative solution for the highly degenerate states at a single level hωn, which is similar in spirit to the problem of the lowest Landau level for the electrons in high magnetic field, which arises in the theory of the fractional quantum Hall effect or to the problem of compound states in an atomic nucleus. The yrast states are those with minimal energy at given angular momentum, L. This is illustrated in Fig. , where the spectrum patterns are shown for the cases of zero and finite interaction.
As is usually the case for interacting many-body systems, the evaluation of the exact ground state is a prohibitive task, even with the simplification introduced by the weak coupling limit [3-5], . The yrast states in the case of attractive δ-forces have been found analytically by Wilkin et al. . Later, these results were shown to be valid for a broad class of attractive interactions in Ref. . The case of repulsive interaction is more difficult to analyze . One of the first important results obtained for the repulsive forces was that of Bertsch and Papenbrock [5]: these authors diagonalized the repulsive δ-interaction numerically and suggested analytical formulas for the wave functions and energies of the yrast states. Later, it was shown analytically by several authors using various methods [15-19] that the states of the form of Bertsch and Papenbrock are indeed eigenstates of the Hamiltonian. Only recently was it shown that these states indeed correspond to minimum energy .