Interference of two Bose-Einstein condensates

The visibility of the density interference pattern of two Bose-Einstein condensates, which are produced in traps and overlap after the trapping potential is switched off, is investigated. Coherent wave packets are used to describe the order parameter in a second-quantization formalism. This results in a decrease of the visibility of the interference fringes with increasing time delay between the formation of the condensates and the observation of interference. In the two limiting cases of ideal and very dense gases the correlation time increases, τ →∞, and the result is identical to that obtained using an approach based on the Gross-Pitaevskii equation. Under the conditions of the experiment performed by M. R. Andrews, C. G. Townsend, H. J. Miesner et al. , Science 275 , 6367 (1997), the computed correlation time τ ≈0.2 s is much longer than the confinement time of the condensate, and it is possible to observe the predicted decrease of visibility of the interference fringes of the density of the atoms.