Density ripples in expanding low-dimensional gases as a probe of correlations

A. Imambekov 1, 2, I. E. Mazets 3, 4, D. S. Petrov 5, 6, V. Gritsev 7, S. Manz 3, S. Hofferberth 8, T. Schumm 3, 9, E. Demler 8, J. Schmiedmayer 3

Physical Review A: Atomic, Molecular and Optical Physics 80 (2009) 033604

We investigate theoretically the evolution of the two-point density correlation function of a low-dimensional ultracold Bose gas after release from a tight transverse confinement. In the course of expansion thermal and quantum fluctuations present in the trapped systems transform into density fluctuations. For the case of free ballistic expansion relevant to current experiments, we present simple analytical relations between the spectrum of ``density ripples'' and the correlation functions of the original confined systems. We analyze several physical regimes, including weakly and strongly interacting one-dimensional (1D) Bose gases and two-dimensional (2D) Bose gases below the Berezinskii-Kosterlitz-Thouless (BKT) transition. For weakly interacting 1D Bose gases, we obtain an explicit analytical expression for the spectrum of density ripples which can be used for thermometry. For 2D Bose gases below the BKT transition, we show that for sufficiently long expansion times the spectrum of the density ripples has a self-similar shape controlled only by the exponent of the first-order correlation function. This exponent can be extracted by analyzing the evolution of the spectrum of density ripples as a function of the expansion time.

  • 1. Department of Physics,
    Yale University
  • 2. Department of Physics and Astronomy,
    Rice University
  • 3. Atominstitut,
    Fakiltat fur Physik
  • 4. Ioffe Physico-Technical Institute,
    Ioffe Physico-Technical Institute
  • 5. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 6. National Research Centre "Kurchatov Institute" (NRC KI),
    University of Moscow
  • 7. Physics Department,
    University of Fribourg
  • 8. Department of Physics,
    University of Harvard
  • 9. Wolfgang Pauli Institute (WPI),
    University of Vienna