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arXiv:cond-mat/0409501 · Acta Physica Slovaca Reviews and Tutorials

Quantum theory of vortex lattice state in a rotating Bose-Einstein condensate

Aranya B. Bhattacherjee

Published Sep 20, 2004• 0 citations
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Abstract

We study system of large number of singly quantized vortices in a rotating Bose-Einstein condensate. Analogous to the Meissner effect in superconductors, we show that the vector potential due to the external rotational field can be tuned to cancel the vector potential due to the Magnus field, resulting in a zero average angular momentum and a shear modulus of the vortex lattice. The vortex lattice state exhibits two states, namely, an elastic state and a plastic state. A clear distinction between these states is controlled by the filling fraction, which is the ratio of the number of bosons to the average number of vortices.

DOI
10.48550/arxiv.cond-mat/0409501

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We study system of large number of singly quantized vortices in a rotating Bose-Einstein condensate. Analogous to the Meissner effect in superconductors, we show that the vector potential due to the external rotational field can be tuned to cancel the vector potential due to the Magnus field, resulting in a zero average angular momentum and a shear modulus of the vortex lattice. The vortex lattice state exhibits two states, namely, an elastic state and a plastic state. A clear distinction between these states is controlled by the filling fraction, which is the ratio of the number of bosons to the average number of vortices.
We study a harmonically confined Bose-Einstein condensate under rotation. Vortex lattice configurations are investigated through a variational approach. Vortices with more than a unit of angular momentum are not stable. We explicitly show that the critical rotational frequency is quite small, as was reported in a recent experiment, with an asymmetric harmonic confining potential. The width of the condensate along the z direction (the anisotropy direction) and in the xy plane and the vortex density are determined as functions of the rotational frequency. The aspect ratio becomes small for large rotational frequencies, making the condensate an effectively two-dimensional system.
We investigate the ground states of weakly interacting bosons in a rotating trap as a function of the number of bosons, N, and the average number of vortices, N(V). We identify the filling fraction nu identical with N/N(V) as the parameter controlling the nature of these states. We present results indicating that, as a function of nu, there is a zero temperature phase transition between a triangular vortex lattice phase, and strongly correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states.
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.
Bose gases in rotating optical lattices combine two important topics in quantum physics: superfluid rotation and strong correlations. In this paper, we examine square two-dimensional systems at zero temperature comprised of strongly repulsive bosons with filling factors of up to one atom per lattice site. The entry of vortices into the system is characterized by jumps of $2\ensuremath{\pi}$ in the phase winding of the condensate wave function. A lattice of size $L\ifmmode\times\else\texttimes\fi{}L$ can have at most $L\ensuremath{-}1$ quantized vortices in the lowest Bloch band. In contrast to homogeneous systems, angular momentum is not a good quantum number since the continuous rotational symmetry is broken by the lattice. Instead, a quasiangular momentum captures the discrete rotational symmetry of the system. Energy level crossings indicative of quantum phase transitions are observed when the quasiangular momentum of the ground state changes.
We study the vortex lattices in a Bose-Einstein condensate in a rotating anisotropic harmonic trap. We first investigate the single-particle wave functions obtained by the exact solution of the problem and give simple expressions for these wave functions in the small anisotropy limit. Depending on the strength of the interactions, a few or a large number of vortices can be formed. In the limit of many vortices, we calculate the density profile of the cloud and show that the vortex lattice stays triangular. We also find that the vortex lattice planes align themselves with the weak axis of the external potential. For a small number of vortices, we numerically solve the Gross-Pitaevskii equation and find vortex configurations that are very different from the vortex configurations in an axisymmetric rotating trap.