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Advances in Solid State Physics

Criticality and Correlations in Cold Atomic Gases

Michael Köhl, Tobias Donner, Stephan Ritter, Thomas Bourdel, Anton Öttl, Ferdinand Brennecke, Tilman Esslinger

Published Jan 22, 2008• 3 citations
Publisher
DOI
10.1007/978-3-540-74325-5_7

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The transition from a thermal cloud to a Bose–Einstein condensate (BEC) in an interacting ultra-cold Bose gas is a prototype in a universality class of diverse phase transitions. For a trapped ultra-cold Bose gas, we were able to study the critical regime both above and below the critical temperature with a Talbot–Lau interferometer, observing a peak in the correlation length. From this peak, we managed to determine the universal critical exponents for this phase transition as well as the finite-size and interaction corrections to the critical temperature. The results are all in quantitative agreement with theory. This work demonstrates the potential application of the Talbot–Lau interferometer to a wide range of critical phase transitions in ultra-cold atomic gases.
Summary form only given. Phase transitions are among the most dramatic phenomena in nature. Minute variations in the conditions controlling a system trigger a fundamental change of its properties. In the critical regime near a second-order phase transition point the fluctuations of the order parameter are so dominant that they completely govern the behaviour of the system on all length scales. The correlation length of the ultracold gas measures the characteristic length scale of these fluctuations and diverges at the critical temperature. Using cold atomic gases, we have directly observed critical fluctuations of the order parameter near the phase transition of Bose-Einstein condensation. From the divergence of the correlation length of the order parameter versus temperature we have determined its critical exponent v. Despite our densities being ten orders of magnitude smaller and our interactions considerably weaker, we find a remarkable similarity to case of the lambda-transition of helium-4.