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arXiv:cond-mat/0311066 · Physical Review A

Vortices and hysteresis in a rotating Bose-Einstein condensate with anharmonic confinement

Andrew David Jackson, G. M. Kavoulakis

Published Aug 4, 2004• 37 citations
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Abstract

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.

DOI
10.1103/physreva.70.023601

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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 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 investigate the rotational properties of a zero-temperature Bose-Einstein condensed gas, which is confined in a hard-wall potential. For weak interactions the gas carries its angular momentum via vortices of multiple quantization. As the coupling increases and for sufficiently slow rotational frequencies of the trap, the multiply-quantized vortex states become unstable against a mixed state. For stronger couplings, as the angular frequency of the trap increases, there is a transition from a vortex lattice, to a vortex lattice with a hole at the trap center, and finally to a giant vortex. For weak effective attractive interactions we still have vortices of multiple quantization. These states become unstable towards states which break the axial symmetry of the problem and resemble center-of-mass excitation, as the coupling becomes more negative. Finally, for even more attractive forces, the system becomes unstable against collapse.
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 study rotational motion of an interacting atomic Bose-Einstein condensate confined in a quadratic-plus-quartic potential. We calculate the lowest energy surface mode frequency and show that a symmetric trapped (harmonic and quartic) Bose-Einstein condensate breaks the rotational symmetry of the Hamiltonian when rotational frequency is greater than one-half of the lowest energy surface mode frequency. We argue that the formation of a vortex is not possible in a non-interacting as well as in an attractive Bose-Einstein condensate confined in a harmonic trap due to the absence of the spontaneous shape deformation, but it can occur which leads to the vortex formation if we add an additional quartic potential. Moreover, the spontaneous shape deformation and consequently the formation of a vortex in an attractive system depends on the strengths of the two-body interaction and the quartic potential.
We study rotational motion of an interacting atomic Bose-Einstein condensate confined in a quadratic-plus-quartic potential. We calculate the lowest energy surface mode frequency and show that a symmetric trapped (harmonic and quartic) Bose-Einstein condensate breaks the rotational symmetry of the Hamiltonian when rotational frequency is greater than one-half of the lowest energy surface mode frequency. We argue that the formation of a vortex is not possible in a non-interacting as well as in an attractive Bose-Einstein condensate confined in a harmonic trap due to the absence of the spontaneous shape deformation, but it can occur which leads to the vortex formation if we add an additional quartic potential. Moreover, the spontaneous shape deformation and consequently the formation of a vortex in an attractive system depends on the strengths of the two-body interaction and the quartic potential.