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arXiv:1112.1264 · Physical Review A

Berezinskii-Kosterlitz-Thouless transition of two-dimensional Bose gases in a synthetic magnetic field

Junjun Xu, Qiang Gu

Published Apr 11, 2012• 3 citations
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Abstract

We study the field dependency of the Berezinskii-Kosterlitz-Thouless transition temperature ${T}_{c}(H)$ of Bose gases in a two-dimensional optical lattice in the synthetic magnetic field using the Metropolis Monte Carlo method. The system is described by the frustrated $XY$ model and the critical temperature is determined through observing the disappearance of the central peak of the momentum distribution of the gas, which can be directly measured by the time-of-flight absorbing imaging in cold-atom experiments. ${T}_{c}(H)$ is found to exhibit a largest peak at the fraction of a flux quantum $f=\ensuremath{\varphi}/{\ensuremath{\varphi}}_{0}=1/2$ and a second-largest one at $f=1/3$, in agreement with former studies on superconducting Josephson arrays. We also indicate that the synthetic magnetic field experiment can produce strong enough frustration for exploring the physics of the frustrated $XY$ model.

DOI
10.1103/physreva.85.043608

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We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed with respect to the parameter driving the transition, have extrema that are located off the critical point even in the thermodynamic limit. We discuss whether such extrema provide solid evidence of the quantum Berezinskii-Kosterlitz-Thouless transition taking place in this system. The calculations are done for systems with the mean number of atoms per lattice site equal to either one or two. They also characterize the nearest-neighbor correlation function, which is typically discussed in the context of time-of-flight images of cold atoms.