Revealing the superfluid–Mott-insulator transition in an optical lattice

We study (by an exact numerical scheme) the single-particle density matrix of $\sim {10}^3$ ultracold atoms in an optical lattice with a parabolic confining potential. Our simulation is directly relevant to the interpretation and further development of the recent pioneering experiment by Greiner et al., Nature, (London) $415,$ 39 (2002). In particular, we show that restructuring of the spatial distribution of the superfluid component when a domain of Mott-insulator phase appears in the system, results in a fine structure of the particle momentum distribution. This feature may be used to locate the point of the superfluid–Mott-insulator transition.