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arXiv:cond-mat/0307175 · Physical Review A

Effectively attractive Bose-Einstein condensates in a rotating toroidal trap

G. M. Kavoulakis

Published Feb 19, 2004• 22 citations
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Abstract

We examine an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a rotating toroidal trap, as the magnitude of the coupling constant and the rotational frequency are varied. Using both a variational mean-field approach, as well as a diagonalization technique, we identify the phase diagram between a uniform and a localized state and we describe the system in the two phases.

DOI
10.1103/physreva.69.023613

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We examine an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a rotating toroidal trap, as the magnitude of the coupling constant and the rotational frequency are varied. Using both a variational mean-field approach, as well as a diagonalization technique, we identify the phase diagram between a uniform and a localized state and we describe the system in the two phases.
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We study the quantum and the mean-field Gross-Pitaevskii (GP) dynamics of a Bose-Einstein condensate gas confined in a toroidal trap. According to GP, if the interatomic interaction is attractive, the rotational states of the system can be dynamically stable or unstable depending on the strength of the mean-field energy. The full quantum analysis, however, reveals that the condensate is always unstable. Quantum fluctuations are particularly important close to the GP stability borderline, even for systems with a relatively large number of condensate atoms.
We examine an effectively repulsive Bose-Einstein condensate of atoms that rotates in a quadratic-plus-quartic trapping potential. We investigate the phase diagram of the system as a function of the angular frequency of rotation and of the coupling constant, demonstrating that there are phase transitions between multiply and singly quantized vortex states. We also show that states of different circulation can be metastable and, as a result, the gas can exhibit hysteresis as the angular frequency of rotation of the trap is varied. The simplicity of the picture that emerges for small coupling strengths suggests that this system may be attractive for studies of phase transitions.
We consider Bose-Einstein-condensed atoms confined in a toroidal trap. Under conditions of one-dimensional behavior, the density distribution of the atoms may be exponentially localized or delocalized, even for very small variations in the trapping potential along the torus. For similar reasons, small irregularities of the trap may also have a very pronounced effect on the density of the cloud. The excitation spectrum is also affected by the presence of some spatially varying potential and/or irregularities in the trap.