ROTBEC · Rotating Bose-Einstein condensates in optical lattices

Final Activity Report Summary - ROTBEC (Rotating Bose-Einstein condensates in optical lattices)

How would our life be if we were leaving in a world with a different number of dimensions? Say for example that it had only two dimensions of space instead of three, like the FlatLand imagined by Abbott. How would the relevant physical objects look like? It is actually known, since the seminal work of Peierls in the 1930s that no system with long range order, like a perfect crystal, could exist at finite temperature. The main achievement of this project was the investigation of such two-dimensional systems made of quantum matter, i.e. ultracold atomic gases in which one degree of freedom was frozen because of a very strongly confining potential. In our three-dimensional world, a sufficiently cold gas of atoms undergoes a well known phase transition, the Bose-Einstein condensation, which consists of the apparition of a macroscopic phase which extends over the whole sample, at least if the atoms are integer spin particles, the so-called bosons, which was the case that we examined. Even though a true Bose-Einstein condensate could not exist in a two-dimensional world because of Peierls argument, such systems could still undergo a phase transition associated with the appearance of superfluidity. This phase transition, which was predicted by Berezinski, Kosterlitz and Thouless (BKT) at the beginning of the 1970s, is very peculiar in the sense that it does not involve any true long range order. Its microscopic mechanism is based on quantised vortices. Above the transition temperature, these vortices proliferate, with each vortex corresponding to the fluid rotating clockwise or counterclockwise. Below the transition temperature vortices only exist as bound pairs, formed by a clockwise vortex and a counterclockwise vortex. The superfluid transition in two-dimensional systems was observed in several physical systems since its prediction by BKT. However, the underlying mechanism, i.e. the quantised vortices, remained inaccessible. The main result of this project was the provision of direct evidence for their proliferation at the transition temperature and the parallel study of the quasi-long range order that could appear in our quantum gas when the temperature was lowered. This study was possible through the development of a new investigation technique, based on the interference between two independent gases. By studying some statistical properties of the interference patterns we could gain access to the physics of the transition predicted by BKT and obtain some novel results on two-dimensional physics. Our results were published in major scientific journals, namely Nature and Physical Review Letters, and were presented in several invited talks in international conferences. Our work was also featured in several editorials and news’ articles in journals such as Nature, Pour la Science and Physics Today.

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