Article

# Correlation functions of cold bosons in an optical lattice

Cardinal Stefan Wyszynski University in Warsaw, Warszawa, Masovian Voivodeship, Poland
(Impact Factor: 2.81). 07/2004; 70(6). DOI: 10.1103/PhysRevA.70.063622
Source: arXiv

ABSTRACT

Motivated by the experimental observation of collapses and revivals of Bose matter wave field, we investigate correlation functions of cold bosons in an optical lattice. Within a simple model we examine two kinds of states: one that employs the commonly used notion of coherent states, and one that obeys the total number of atoms conservation. We identify rare situations at which these states behave differently. Typically, however, their predictions coincide and so: As a function of "interaction time" the interference pattern in the density undergoes collapse and revival. Exactly at revival times the system mimics the ideal gas case, in which all correlation functions factorize, while in the collapsed phase of the evolution the system effectively behaves as if initially there was no long-range coherence. Even in the latter case though, an interference pattern should be seen in a single experiment. We stress the role of column averaging, which in fact corresponds to an averaged observation of an ensemble of two-dimensional realizations. We also note that, contrary to the common belief, an interference pattern should also be seen in a single observation of a Mott state.

### Full-text preview

Available from: ArXiv
• Source
##### Article: Interference of an Array of Independent Bose-Einstein Condensates
[Hide abstract]
ABSTRACT: A 1D periodical array of independent condensates prepared in a deep optical lattice was studied. It was shown that most single-shot realizations of the system shows high-contrast interference patterns in a time of-flight expansion. This effect was explained with a simple model which naturally extended to 3D lattices. It was shown that the initial result should be taken into account in the ongoing studies of atomic superfluidity and coherence in optical lattices, where the contrast of the interference patterns is used as a diagnostic.
Full-text · Article · Nov 2004 · Physical Review Letters
• Source
##### Article: Fölling, S. et al. Spatial quantum noise interferometry in expanding ultracold atom clouds. Nature 434, 481-484
[Hide abstract]
ABSTRACT: In a pioneering experiment, Hanbury Brown and Twiss (HBT) demonstrated that noise correlations could be used to probe the properties of a (bosonic) particle source through quantum statistics; the effect relies on quantum interference between possible detection paths for two indistinguishable particles. HBT correlations--together with their fermionic counterparts--find numerous applications, ranging from quantum optics to nuclear and elementary particle physics. Spatial HBT interferometry has been suggested as a means to probe hidden order in strongly correlated phases of ultracold atoms. Here we report such a measurement on the Mott insulator phase of a rubidium Bose gas as it is released from an optical lattice trap. We show that strong periodic quantum correlations exist between density fluctuations in the expanding atom cloud. These spatial correlations reflect the underlying ordering in the lattice, and find a natural interpretation in terms of a multiple-wave HBT interference effect. The method should provide a useful tool for identifying complex quantum phases of ultracold bosonic and fermionic atoms.
Full-text · Article · Apr 2005 · Nature
• Source
##### Article: Interference of a variable number of coherent atomic sources
[Hide abstract]
ABSTRACT: We have studied the interference of a variable number of independently created $m_F=0$ microcondensates in a CO$_{2}$-laser optical lattice. The observed average interference contrast decreases with condensate number N. Our experimental results agree well with the predictions of a random walk model. While the exact result can be given in terms of Kluyver's formula, for a large number of sources a $1/\sqrt{N}$ scaling of the average fringe contrast is obtained. This scaling law is found to be of more general applicability when quantifying the decay of coherence of an ensemble with N independently phased sources.
Full-text · Article · May 2005 · Physical Review A