The dimensionality of a system can drastically influence its physical properties. This is in particular apparent in order phenomena which can occur by spontaneous symmetry breaking only in three dimensions. In lower dimensions fluctuations inhibit the emergence of true long-range order such as the macroscopic magnetization in a ferromagnet. In two dimensions (2D), the situation is special as the effect is marginal, and a quasi long range ordered superfluid low temperature phase can be established without symmetry breaking. This very different type of phase transition is associated with the Berezinskii-Kosterlitz-Thouless (BKT) paradigm where topological order is reached through pairing of thermally activated vortices of opposite circulations.
We experimentally study the low temperature physics of a trapped 2D Bose gas of rubidium-87 atoms. Unlike in the homogeneous system, Bose-Einstein condensation (BEC) of an ideal 2D gas is possible in a trap. By measuring the transition point as a function of atom number and temperature, we find that this seems to be no longer true for the interacting gas and that BKT theory provides a quantitatively correct prediction for our system. Furthermore, we study the emergence of quasi long range order in the low temperature phase in interference experiments. We observe that the loss of order parameter correlations coincides with the appearance of free vortices, again in agreement with BKT theory.
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