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A. Imambekov, I. Mazets, D. Petrov, V. Gritsev, S. Manz, S. Hofferberth, Thorsten Schumm, E. Demler, H.-J. Schmiedmayer:
"Density ripples in expanding low-dimensional gases as a probe of correlations";
Physical Review A, 80 (2009), 1 - 14.

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 twodimensional
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.

http://publik.tuwien.ac.at/files/PubDat_181251.pdf