Attractive gases in 1D: thermal phase transition

Posted on 12th December 2016

An international collaboration led by Dr. Christoph Weiss, Durham University, UK, currently investigates the influence of temperature on one-dimensional (1D) attractive gases [1-3]. Trains or narrow rivers are examples of effectively one-dimensional motion in our three-dimensional world. In winter rivers are less likely to freeze than, say, lakes. Scientists had expected that this also is true for quantum systems. Surprisingly, attractively interacting Bose gases in a very elongated, thus effectively one-dimensional "tube", display a low-temperature behaviour similar to water turning into ice [2].

Processes like water freezing / ice melting are called "phase transitions". For thermally isolated ultracold attractive Bose gases, the low-temperature phase (a large bright soliton) and the high-temperature phase (free gas) contrary to previous predictions [1,5] co-exist [2]. As the relative distance between attractive bosons cannot become large, this phase transition does not violate the Mermin-Wagner theorem [4]. Dr. Weiss says "surprisingly, the new findings [2] also differ considerably from the assumption that all particles form the bright soliton." The assumption that all particles form the bright soliton is made by the mean-field theory (Gross-Piteavskii equation). State-of-the-art experiments with bright solitons in Bose-Einstein condensates often are modelled with mean-field theory. The quasi-1D geometry prevents attractive Bose-Einstein condensates from collapsing.

[1] C. Weiss, "Finite-temperature phase transition in a homogeneous one-dimensional gas of attractive bosons",
[2] C. Weiss, S. A. Gardiner and B.  Gertjerenken "Temperatures are not useful to characterise bright-soliton experiments for ultra-cold atoms",
[3] C. Weiss, S. A. Gardiner, J. Tempere and B.  Gertjerenken, manuscript in preparation.
Further reading:
[4] Mermin-Wagner Theorem
[5] C. Herzog, M. Olshanii, Y. Castin, Comptes Rendus Physique 15 (2014) 285,

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