Two-point correlation function of a one-dimensional Bose gas in free expansion

We theoretically investigate the evolution of the two-point correlation function of an ultra cold gas of bosonic atoms after the release from a tight waveguide. The correlation function rapidly attains the values characteristic for a non-degenerate gas: it reaches 2 for vanishing interparticle distance, and is 1 for distances much larger than the typical correlation length $\lambda _c$. The associated timescale is on the order of $m\lambda_c^2/\hbar $. In the strongly interacting gas regime $\lambda_c$ is the mean interatomic distance, in the opposite (weakly interacting) limit it is determined by both the mean interparticle distance and the temperature of the gas. In the latter limit, the correlation function, which is initially very close to 1 everywhere, locally (at distances of about the correlation length) decreases to values significantly below 1 in the course of evolution.