Final Activity Report Summary - BEC COHERENCE (Onset of coherence in Bose-Einstein condensates) The Bose-Einstein condensate, the atomic counterpart of the laser in optics, is usually considered to be fully phase coherent. However, this is true for systems of moderate anisotropy only. For highly elongated condensates, phase fluctuations appear along the long axis of the condensate and lead to a reduction of the coherence length. Such a phase-fluctuating condensate is called a quasi-condensate.The two main research objectives of this Fellowship concerned the coherence of highly elongated cylindrical-shaped condensates. The first study involved the development of a matter-wave interferometer: by superposing two copies of the same condensate and measuring the contrast of the resulting interference fringes, we were able to measure the coherence length of the condensate, via its correlation function. This technique complements that of Bragg Spectroscopy by extending the measurement range to coherence lengths close to the length of the condensate. Our measurements show the cross-over from a fully phase-coherent condensate to a quasi-condensate as the amplitude of the phase fluctuations increases. We also observed that the shape of the condensate correlation function changes from a Gaussian-like shape, for nearly-coherent condensates, to an exponential-like shape, as predicted phase-fluctuating condensates.The second study focused on the kinetics of condensate growth. After 'shock-cooling' a thermal cloud of atoms to a temperature below the critical temperature for condensation, we observed the growth of the condensate over a time-scale of a few hundred milliseconds. We measured both the condensed fraction and the phase coherence length of the growing condensate as a function of time. For our experimental parameters, we found that the growing condensate rapidly reaches its equilibrium coherence length, that is to say, the coherence length we would expect for the same condensate, under the same condition, but at equilibrium. This occurs on a time-scale faster than the growth of the condensed fraction. In addition, we found that the presence of phase fluctuations slowed the growth of the condensate compared to that of a fully-coherent condensate. This was possible by comparing our experimental results with detailed theoretical calculations, performed by our collaborator M.J.Davis.A new direction of research was launched in the second year of the Fellowship, leading to a third study. This concerned the effects of disorder on the transport properties of the condensate. Whereas many studies have been carried out on the behaviour of condensates in optical lattices (i.e. 'ordered' potentials), the effects of disorder present a new challenge, with strong links to research in condensed matter, optics, acoustics, etc, where disorder has been observed to lead to surprising effects such as Anderson localisation. We designed and implemented an optical setup to create a one-dimensional random potential for cold atoms using laser speckle. The expansion of the condensate along a magnetic waveguide was then observed in the presence or absence of this random potential. Whereas condensates can travel through an optical lattice unperturbed, we found that the random potential inhibited the transport of the atoms, leading to an effect we have termed 'disorder-induced' trapping.
