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Physical Review A

Density-density correlation of incoherent atoms with angular momentum released from an optical lattice

Shujuan Liu, Hongwei Xiong, Baolong Lü

Published Jun 19, 2008• 4 citations
Publisher

Abstract

For a series of incoherent and ultracold atoms with an orbital angular momentum (or vortices) released from an optical lattice, we consider the density-density correlation of this freely expanding ultracold gases. Because of the unique phase structure originating from the quantized angular momentum, it is shown that the phase structure plays an important role in the distribution of the density-density correlation through the appearance of crescent-shaped peaks accompanying the ordinary round-shaped peaks. In particular, it is found that the orientation of the crescent-shaped peaks corresponds with the rotation direction of the atoms prepared in the optical lattices.

DOI
10.1103/physreva.77.063619

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For a series of incoherent and ultracold atoms with an orbital angular momentum (or vortices) released from an optical lattice, we consider the density-density correlation of this freely expanding ultracold gases. Because of the unique phase structure originating from the quantized angular momentum, it is shown that the phase structure plays an important role in the distribution of the density-density correlation through the appearance of crescent-shaped peaks accompanying the ordinary round-shaped peaks. In particular, it is found that the orientation of the crescent-shaped peaks corresponds with the rotation direction of the atoms prepared in the optical lattices.
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.
Atoms in the Mott insulator state trapped in an optical lattice are incoherence matter wave source. It is not the first-order, but the second-order interference effect (density correlation) that will appear for this incoherence wave source after being released. A density correlation function of the freely expanding ultracold gases is obtained theoretically, which presents sharp peaks of interference, and the stripes structure is similar to the diffraction gratings. It is further pointed out that the peak structure of the density correlation function depends on the relative position between two detectors. The phenomenon of subwavelength interference of matter waves is also proposed in this paper.
Density-density correlation analysis is a convenient diagnostic tool to reveal the hidden order in the strongly correlated phases of ultracold atoms. We report on a study of the density-density correlations of ultracold bosonic atoms which were initially prepared in a Mott insulator (MI) state in one-dimensional optical lattices. For the atomic gases released from the deep optical lattice, we extracted the normalized density-density correlation function from the atomic density distributions of freely expanded atomic clouds. Periodic bunching peaks were observed in the density-density correlation spectra, as in the case of higher-dimensional lattices. Treating the bosonic gas within each lattice well as a subcondensate without quantum tunneling, we simulated the post-expansion density distribution along the direction of the 1D lattice, and the calculated density-density correlation spectra agreed with our experimental observations.
The density-density correlations of ultracold Bosons released from a two-dimensional square optical lattice are investigated based on the quantum phase field U (1) rotor field. With the effects of the particle number fluctuations and the phase degrees of freedom taken into consideration, the theory can be used to describe the cold atom system with strong interaction. Using this theory, the characteristics of ultracold atom gas in the process in which the superfluid state of optical lattice transits to insulating state, are well described. The results show that in the patterns of the density-density correlations, the continuous diagonal lines gradually transit to scattered peaks. The results match the experimental ones. In addition, the effects of the quantum depletion on the density-density correlation are also included in the result, and the relevant conclusions are also consistent with the existing theoretical and experimental results.
The time-correlation function of ultracold atomic gas is theoretically investigated. Atoms are initially confined in an optical lattice and in a Mott insulator regime. We consider the effect of gravity on the time correlation among atomic wave functions when the atomic cloud is released from the optical lattice. The time-correlation function in this process displays sharp peaks, a feature that is analogous to the spatial-normalized correlation observed in recent experiments. The origin and properties of the interference pattern are theoretically investigated in detail. Similar to the spatial correlation, the time correlation in expanding atomic clouds reveals the ordering of indistinguishable particles in an optical lattice. Experimental detection scheme and its potential use in the measurement of gravitational acceleration are briefly discussed.
Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the Gross-Pitaevskii mean-field approximation. However, the true dynamics of angular momentum in finite, interacting many-body systems like trapped Bose-Einstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full many-body dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the phantom vortex. Contrary to the conventional mean-field vortex, can be detected as a topological defect of spatial coherence, but not of the density. We describe previously unknown many-body mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortices modes which so far seem to have evaded experimental detection. This phenomenon is likely important in the formation of the Abrikosov lattice and the onset of turbulence in superfluids.