  We propose to utilize density distributions from a series of time-of-flight
images of an expanding cloud to reconstruct single-particle correlation
functions of trapped ultra-cold atoms. In particular, we show how this
technique can be used to detect off-diagonal correlations of atoms in a
quasi-one-dimensional trap, where both real- and momentum- space correlations
are extracted at a quantitative level. The feasibility of this method is
analyzed with specific examples, taking into account finite temporal and
spatial resolutions in experiments.

Quantum Gases;Statistical Mechanics