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arXiv:cond-mat/9812362 · Physical Review Letters

Phase Diagram of Quantized Vortices in a Trapped Bose-Einstein Condensed Gas

S. Stringari

Published May 31, 1999• 77 citations
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Abstract

We investigate the thermodynamic stability of quantized vortices in a dilute Bose gas confined by a rotating harmonic trap at finite temperature. Interatomic forces play a crucial role in characterizing the resulting phase diagram, especially in the large $N$ Thomas-Fermi regime. We show that the critical temperature for the creation of stable vortices exhibits a maximum as a function of the frequency of the rotating trap, and that the corresponding transition is associated with a discontinuity in the number of atoms in the condensate. Possible strategies for approaching the vortical region are discussed.

DOI
10.1103/physrevlett.82.4371

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We investigate the thermodynamic stability of quantized vortices in a dilute Bose gas confined by a rotating harmonic trap at finite temperature. Interatomic forces play a crucial role in characterizing the resulting phase diagram, especially in the large NNN Thomas-Fermi regime. We show that the critical temperature for the creation of stable vortices exhibits a maximum as a function of the frequency of the rotating trap, and that the corresponding transition is associated with a discontinuity in the number of atoms in the condensate. Possible strategies for approaching the vortical region are discussed.
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We compute the structure of a quantized vortex line in a harmonically trapped dilute atomic Bose-Einstein condensate using the Popov version of the Hartree-Fock-Bogoliubov mean-field theory. The vortex is shown to be (meta)stable in a nonrotating trap even in the zero-temperature limit, thus confirming that weak particle interactions induce for the condensed gas a fundamental property characterizing "classical" superfluids. We present the structure of the vortex at ultralow temperatures and discuss the crucial effect of the thermal gas component to its energetic stability.
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Multiply quantized vortices in trapped Bose-Einstein condensates are studied using the Bogoliubov theory. Suitable combinations of a localized pinning potential and an external rotation of the system are found to energetically stabilize, both locally and globally, vortices with multiple circulation quanta. We present a phase diagram for stable multiply quantized vortices in terms of the angular rotation frequency of the system and the width of the pinning potential. We argue that multiquantum vortices could be experimentally created using a suitable choice of these two parameters.
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.