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The European Physical Journal B

First principle explanation of phase transition for Bose-Einstein condensates in optical lattices

Andrea Sacchetti

Published Oct 1, 2014• 1 citation
Publisher
DOI
10.1140/epjb/e2014-50404-x

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We discuss several possible experimental signatures of the Bose-Einstein condensation (BEC) transition for an ultracold Bose gas in an inhomogeneous optical lattice. Based on the commonly used time-of-flight imaging technique, we show that the momentum-space density profile in the first Brillouin zone, supplemented by the visibility of interference patterns, provides valuable information about the system. In particular, by crossing the BEC transition temperature, the appearance of a clear bimodal structure sets a qualitative and universal signature of this phase transition. Furthermore, the momentum distribution can also be applied to extract the condensate fraction, which may serve as a promising thermometer in such a system.
Similarities between alkali-metal gases in optical lattices with noninteger occupation of the lattice sites and quantum crystals are explored. The analogy with the vacancy liquid (VL) provides an alternative explanation to the Mott transition for the recent experiment on the phase transition in the lattice. The VL can undergo Bose-Einstein condensation (BEC) with Tc{T}_{c}Tc​ within experimental reach. Direct and vacancy-assisted mechanisms of the band motion for hyperfine impurities are discussed. A large concentration of vacancies can result in the spatial decomposition of the system into pure hyperfine components. Below the vacancy condensation the impurity component resembles 3He{}^{3}\mathrm{He}3He in 3He−−He{}^{3}\mathrm{He}--\mathrm{He}3He−−He II mixtures.