Interference of a variable number of coherent atomic sources

We have studied the interference of a variable number of independently created $m_F=0$ microcondensates in a CO$_{2}$-laser optical lattice. The observed average interference contrast decreases with condensate number N. Our experimental results agree well with the predictions of a random walk model. While the exact result can be given in terms of Kluyver's formula, for a large number of sources a $1/\sqrt{N}$ scaling of the average fringe contrast is obtained. This scaling law is found to be of more general applicability when quantifying the decay of coherence of an ensemble with N independently phased sources.