Atom Counting in Expanding Ultracold Clouds

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S. Braungardt, M. Rodríguez, A. Sen De, U. Sen, M. Lewenstein


DOI: 10.1103/PhysRevA.84.043635
PACS: 67.85.-d, 37.10.Jk, 05.30.Jp

We study the counting statistics of ultracold bosonic atoms that are released from an optical lattice. We show that the counting probability distribution of the atoms collected at a detector located far away from the optical lattice can be used to characterize the initially trapped states. We consider trapped superfluid and insulating states with different occupation patterns. We analyze how the correlations between the modes that develop during the expansion in the gravitational field appear in the counting distribution and find that the ratio of the detector size with respect to the expanded wave function determines whether short-range or long-range correlations of the initial state are reflected in the counting statistics. We find that detectors which are large compared to the size of the expanded wave function distinguish insulating and superfluid phases irrespective of the occupation pattern. We show that using detectors that are small compared to the size of the expanded wave function, occupation patterns in insulating and supersolid states can be distinguished. Finally, we show how the magnetic phase patterns are dramatically reflected in the number distribution.