Spatial correlation diagnostics for atoms in optical lattices

We explore the use of first and second order same-time atomic spatial corre lation functions as a diagnostic for probing the small scale spatial struct ure of atomic samples trapped in optical lattices. Assuming an ensemble of equivalent atoms, properties of the local wave function at a given lattice site can be measured using same-position first-order correlations. Statisti cs of atomic distributions over the lattice can be measured via two-point c orrelations, generally requiring the averaging of multiple realizations of statistically similar but distinct realizations in order to obtain sufficie nt signal to noise. Whereas two-point first order correlations are fragile due to phase fluctuations from shot-to-shot in the ensemble, second order c orrelations are robust. We perform numerical simulations to demonstrate the se diagnostic tools. (C) 1999 Optical Society of America.