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arXiv:cond-mat/0601032 · Physical Review A

Imaging of critical correlations in optical lattices and atomic traps

Qian Niu, Iacopo Carusotto, Anatoly B. Kuklov

Published May 10, 2006• 23 citations
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Abstract

We consider critical space-time correlations in trapped utracold atoms and propose a method for their detection by the interference with a reference Bose-Einstein condensate. Important information about universal properties can be obtained despite nonuniformity and small sizes of atomic clouds. The advantage of this method is that the correlation properties of the interference pattern are robust with respect to expansion and are not, practically, affected by the microscopic structure of the underlying lattice including structural disorder. The nondestructive scheme allows measuring the space-time correlators of arbitrary order.

DOI
10.1103/physreva.73.053604

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We consider critical space-time correlations in trapped utracold atoms and propose a method for their detection by the interference with a reference Bose-Einstein condensate. Important information about universal properties can be obtained despite nonuniformity and small sizes of atomic clouds. The advantage of this method is that the correlation properties of the interference pattern are robust with respect to expansion and are not, practically, affected by the microscopic structure of the underlying lattice including structural disorder. The nondestructive scheme allows measuring the space-time correlators of arbitrary order.
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We show that the phase of a Bose-Einstein condensate wave function of ultracold atoms in an optical lattice potential in two dimensions can be detected. The time-of-flight images, obtained in a free expansion of initially trapped atoms, are related to the initial distribution of atomic momenta but the information on the phase is lost. However, the initial atomic cloud is bounded and this information, in addition to the time-of-flight images, is sufficient in order to employ the phase retrieval algorithms. We analyze the phase retrieval methods for model wave functions in a case of a Bose-Einstein condensate in a triangular optical lattice in the presence of artificial gauge fields.
We investigate the properties of a coherent array containing about 200 Bose-Einstein condensates produced in a far detuned 1D optical lattice. The density profile of the gas, imaged after releasing the trap, provides information about the coherence of the ground-state wave function. The measured atomic distribution is characterized by interference peaks. The time evolution of the peaks, their relative population, as well as the radial size of the expanding cloud are in good agreement with the predictions of theory. The 2D nature of the trapped condensates and the conditions required to observe the effects of coherence are also discussed.
In this Letter we report the investigation of transport and static properties of a Bose-Einstein condensate in a large-spaced optical lattice. The lattice spacing can be easily tuned starting from few micrometers by adjusting the relative angle of two partially reflective mirrors. We have performed in-situ imaging of the atoms trapped in the potential wells of a 20 microm spaced lattice. For a lattice spacing of 10 microm we have studied the transport properties of the system and the interference pattern after expansion, evidencing quite different results with respect to the physics of BECs in ordinary near-infrared standing wave lattices, owing to the different length and energy scales.
We discuss the experimental signal for the Bose-Einstein condensation of cold atoms in an optical lattice at finite temperature. Instead of using the visibility of the interference pattern via time-of-flight imaging, we show that the momentum-space density profile in the first Brillouin zone, in particular its bimodal distribution, provides an unambiguous signal for the Bose-Einstein condensation. We confirm this point with detailed calculations of the change in the atomic momentum distribution across the condensation phase transition, taking into account both the global trapping potential and the atomic interaction effects.
We discuss several possible experimental signatures of the Bose-Einstein condensation (BEC) transition for an ultracold Bose gas in an inhomogeneous optical lattice. Based on the commonly used time-of-flight imaging technique, we show that the momentum-space density profile in the first Brillouin zone, supplemented by the visibility of interference patterns, provides valuable information about the system. In particular, by crossing the BEC transition temperature, the appearance of a clear bimodal structure sets a qualitative and universal signature of this phase transition. Furthermore, the momentum distribution can also be applied to extract the condensate fraction, which may serve as a promising thermometer in such a system.