Interference Pattern of Density-Density Correlation for Incoherent Atoms with Vortices Released from an Optical Lattice

For a series of incoherent condensate atomic clouds with vortices （an orbital angular momentum） released from an optical lattice, the density-density correlation function of this freely expanding ultracold gases is theoretically investigated. It is shown that the nonzero angular momentum of the atoms has an important effect on the fringe pattern of density-density correlation. Particularly, for a short expansion time, even the rotation direction of the atoms could have an observable effect on the fringe pattern. Observation of this specific fringe pattern would constitute experimental evidence for the presence of a vortex in an atomic condensate.