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arXiv:1301.3251 · Physical Review A

Phase diagram of a rapidly rotating two-component Bose gas

Elife Öznur Karabulut, Francesc Malet, G. M. Kavoulakis, S. M. Reimann

Published Apr 9, 2013• 9 citations
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Abstract

We derive analytically the phase diagram of a two-component Bose gas confined in an anharmonic potential, which becomes exact and universal in the limit of weak interactions and small anharmonicity of the trapping potential. The transitions between the different phases, which consist of vortex states of single and multiple quantization, are all continuous because of the addition of the second component.

DOI
10.1103/physreva.87.043609

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We derive analytically the phase diagram of a two-component Bose gas confined in an anharmonic potential, which becomes exact and universal in the limit of weak interactions and small anharmonicity of the trapping potential. The transitions between the different phases, which consist of vortex states of single and multiple quantization, are all continuous because of the addition of the second component.
Rapidly rotating Bose-Einstein condensates confined in anharmonic traps can exhibit a rich variety of vortex phases, including a vortex lattice, a vortex lattice with a hole, and a giant vortex. Using an augmented Thomas-Fermi variational approach to determine the ground state of the condensate in the rotating frame -- valid for sufficiently strongly interacting condensates -- we determine the transitions between these three phases for a quadratic-plus-quartic confining potential. Combining the present results with previous numerical simulations of small rotating condensates in such anharmonic potentials, we delineate the general structure of the zero temperature phase diagram.
We examine the phase diagram of an effectively repulsive Bose-Einstein condensate of atoms that rotates in a quadratic-plus-quartic potential. With use of a variational method we identify the three possible phases of the system as a function of the rotational frequency of the trap and of the coupling constant. The derived phase diagram is shown to be universal and partly exact in the limit of weak interactions and small anharmonicity. The variational results are found to be consistent with numerical solutions of the Gross-Pitaevskii equation.
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 investigate the rotational phase diagram of a quasi-two-dimensional, weakly-interacting Bose-Einstein condensate confined in power-law and in hard-wall trapping potentials. For weak interactions, the system undergoes discontinuous transitions between multiply-quantized vortex states as the rotation frequency of the trap increases. In contrast, stronger interactions induce continuous phase transitions toward mixed states involving both singly and multiply-quantized vortex states. A central result is the qualitative (and experimentally observable) difference between power-law and hard-wall confinement: In hard-wall traps, the leading instability always involves states with nonzero density at the trap center, whereas in power-law traps the density vanishes as the rotation frequency increases. The two different types of confinement give rise to scaling properties in the derived phase diagrams.