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Chinese Physics Letters

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

Xu Zhi-Jun, Dongmei Zhang, Xiayin Liu

Published Jan 1, 2011• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/28/1/010305

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•May 22, 2009•0 citations
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.
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.
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.
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.
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 structure of vortices in Bose-Einstein condensed atomic gases is studied taking into account many-body correlation effects. It is shown that for excited vortices the particle density in the vortex core increases as the angular momentum of the system increases. The core density can increase by several times with only a few percent change in the angular momentum. This result provides an explanation for the observations in which the measured angular momentum is higher than the estimation based on counting the number of vortices and the visibility of the vortex cores is simultaneously reduced. The calculated density profiles for the excited vortices are in good agreement with experimental measurements of a single vortex.
Atomic clouds in a rotating optical lattice are at the intellectual intersection of several major paradigms of condensed matter physics. An optical lattice simulates the periodic potential ubiquitous in solid state physics, while rotation probes the superfluid character of these cold atomic gases by driving the formation of quantized vortices. Here we explore the theory of vortices in an optical lattice. We first provide a detailed introduction section aimed at providing the reader with the information necessary to understand and appreciate the research presented in later chapters. Next we study an infinite square lattice configuration of vortices in a rotating optical lattice near the superfluid-Mott-insulator transition. We find a series of abrupt structural phase transitions where vortices are pinned with their cores only on plaquettes or only on sites. We discuss connections between these vortex structures and the Hofstadter-butterfly spectrum of free particles on a rotating lattice. We then investigate vortex configurations within a harmonically trapped Bose-Einstein condensate in a rotating optical lattice. We find that proximity to the Mott insulating state dramatically affects the vortex structures. To illustrate we give examples in which the vortices: (i) all sit at a fixed distance from the center of the trap, forming a ring, or (ii) coalesce at the center of the trap, forming a giant vortex. We model time-of-flight expansion to demonstrate the experimental observability of our predictions. Finally for a trapped gas far from the Mott regime, the competition between vortex-vortex interactions and pinning to the optical lattice results in a complicated energy landscape, which leads to hysteretic evolution. The qualitative structure of the vortex configurations depends on the commensurability between the vortex density and the site density - with regular lattices when these are commensurate, and concentric rings when they are not. Again we model the imaging of these structures by calculating time-of-flight column densities. As in the absence of the optical lattice, the vortices are much more easily observed in a time-of-flight image than in-situ.