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arXiv:0806.2323 · Europhysics Letters (EPL)

Spin structure and critical nucleation frequency of fractionalized vortices in 2D topologically ordered superfluids of cold atoms

Jun Liang Song, Fei Zhou

Published Jan 1, 2009• 2 citations
arXivHTMLPDF

Abstract

We have studied spin structures of fluctuation-driven fractionalized vortices and topological spin order in 2D nematic superfluids of cold sodium atoms. Our Monte Carlo simulations suggest a softened π-spin disclination structure in a half-quantum vortex when spin correlations are short ranged; in addition, calculations indicate that a unique non-local topological spin order emerges simultaneously as cold atoms become a superfluid below a critical temperature. We have also estimated fluctuation-dependent critical frequencies for half-quantum vortex nucleation in rotating optical traps and discussed probing these excitations in experiments.

DOI
10.1209/0295-5075/85/20002

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We have studied spin structures of fluctuation-driven fractionalized vortices and topological spin order in 2D nematic superfluids of cold sodium atoms. Our Monte Carlo simulations suggest a softened π-spin disclination structure in a half-quantum vortex when spin correlations are short ranged; in addition, calculations indicate that a unique non-local topological spin order emerges simultaneously as cold atoms become a superfluid below a critical temperature. We have also estimated fluctuation-dependent critical frequencies for half-quantum vortex nucleation in rotating optical traps and discussed probing these excitations in experiments.
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In this paper we suggest a convenient quantum statistical approach to calculate the critical rotation frequency for vortex nucleation in a rotating condensate boson atoms. We extende the quantum mecanices approach for achieving the critical rotation rate to enclode the effect of finite temperature. Dependence of the critical rotation on the interatomic interaction, atoms number and temperature is considered. A simple semiclassical approach is suggested. The calculated results showed that the critical rotation rate α depending crucially on the above mensioned parameters, its change very rapidly at very low temperature. Which means that the vortical configuration is achieved for an accurate rotation rate value α, depends on temperature, interatomic interaction and number of condensate atoms. The obtained results provide useful qualitative theoretical results for future Bose Einstein condensation experiments in rotating traps. Motivated by our work, it will be interesting to study the critical rotation for vortex nucleation of rotating condensate boson atoms in optical lattice.
We analyze the thermodynamics of the atomic and (nematic) pair superfluids appearing in the attractive two-dimensional Bose-Hubbard model with a three-body hard-core constraint that has been derived as an effective model for cold atoms subject to strong three-body losses in optical lattices. We show that the thermal disintegration of the pair superfluidity is governed by the proliferation of fractional half vortices leading to a Berezinskii-Kosterlitz-Thouless transition with an unusual jump in the helicity modulus. In addition to the (conventional) Berezinskii-Kosterlitz-Thouless transition out of the atomic superfluid, we furthermore identify a direct thermal phase transition separating the pair and the atomic superfluid phases and show that this transition is continuous with critical scaling exponents consistent with those of the two-dimensional Ising universality class. We exhibit a direct connection between the partial loss of quasi-long-range order at the Ising transition between the two superfluids and the parity selection in the atomic winding number fluctuations that distinguish the atomic from the pair superfluid.
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We review some recent developments in the theory of rotating atomic gases. These studies have thrown light on the process of nucleation of vortices in regimes where mean-field methods are inadequate. In our review, we shall describe and compare quantum vortex nucleation of a dilute ultracold bosonic gas trapped in three different configurations: a one-dimensional ring lattice, a one-dimensional ring superlattice and a two-dimensional asymmetric harmonic trap. In all of them, there is a critical rotation frequency, at which the particles in the ground state exhibit strong quantum correlations. However, the entanglement properties vary significantly from case to case. We explain these differences by characterizing the intermediate states that participate in the vortex nucleation process. Finally, we show that noise correlations are sensitive to these differences. These new studies have, therefore, shown how novel quantum states may be produced and probed in future experiments with rotating neutral atom systems.