Quasi-1d Bose-einstein Condensates in the Dimensional Crossover Regime
نویسنده
چکیده
– We study theoretically the dimensional crossover from a three-dimensional elongated condensate to a one-dimensional condensate as the transverse degrees of freedom get frozen by tight confinement, in the limit of small density fluctuations, i.e. for a strongly degenerate gas. We compute analytically the radially integrated density profile at low temperatures using a local density approximation, and study the behavior of phase fluctuations with the transverse confinement. Previous studies of phase fluctuations in trapped gases have either focused on the 3D elongated regimes or on the 1D regime. The present approach recovers these previous results and is able to interpolate between them. We show in particular that in this strongly degenerate limit the shape of the spatial correlation function is insensitive to the transverse regime of confinement, pointing out to an almost universal behavior of phase fluctuations in elongated traps. In the recent years, one-dimensional (1D) ultracold atomic gases have been produced in very elongated magnetic [1, 2] or optical traps [3, 4], with such tight confinement in two transverse directions that the atomic motion " freezes " to radial zero-point oscillations. The equilibrium phase diagram of these trapped 1D gases shows a rich behavior [5]: at low densities the cloud behaves as a gas of impenetrable bosons (" Tonks-Girardeau gas " [6]), and for higher densities (corresponding to most current experimental setups), the cloud is a " quasi-condensate [5, 7], characterized by suppressed density fluctuations and the same kind of local correlations as in a true condensate, but also by the lack of long-range phase coherence due to significant phase fluctuations. The latter die out continuously around a characteristic temperature T φ , below which the quasicondensate turns into a true condensate. It was realized in [8] that such quasicondensates could also exist in very elongated, but three-dimensional (3D) traps: although atomic motion is possible in all directions, the lowest-lying excitations of these systems, which dominate the long range decay of the phase correlations, are 1D in character [9]. These 3D quasicondensates were observed in equilibrium [10] and non-equilibrium samples [11], and their coherence properties studied through Bragg spectroscopy [12, 13] or matter-wave interferometry [14].
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