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arXiv:1105.0030 · New Journal of Physics

Extracting density–density correlations fromin situimages of atomic quantum gases

Chen-Lung Hung, Xibo Zhang, Li-Chung Ha, Shih-Kuang Tung, Nathan Gemelke, Cheng Chin

Published Jul 29, 2011• 98 citations
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Abstract

We present a complete recipe to extract the density–density correlations and the static structure factor of a two-dimensional (2D) atomic quantum gas from in situ imaging. Using images of non-interacting thermal gases, we characterize and remove the systematic contributions of imaging aberrations to the measured density–density correlations of atomic samples. We determine the static structure factor and report the results on weakly interacting 2D Bose gases, as well as strongly interacting gases in a 2D optical lattice. In the strongly interacting regime, we observe a strong suppression of the static structure factor at long wavelengths.

DOI
10.1088/1367-2630/13/7/075019

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We present a complete recipe to extract the density–density correlations and the static structure factor of a two-dimensional (2D) atomic quantum gas from in situ imaging. Using images of non-interacting thermal gases, we characterize and remove the systematic contributions of imaging aberrations to the measured density–density correlations of atomic samples. We determine the static structure factor and report the results on weakly interacting 2D Bose gases, as well as strongly interacting gases in a 2D optical lattice. In the strongly interacting regime, we observe a strong suppression of the static structure factor at long wavelengths.
We report the first direct in situ observation of density fluctuations on the scale of the thermal de Broglie wavelength in an ultracold gas of bosons. Bunching of ^{87}Rb atoms in a quasi-two-dimensional system is observed by single-atom imaging using a quantum gas microscope. Compared to a classical ensemble, we observe a 30% enhancement of the second-order correlation function. We show the spatial and thermal dependence of these correlations. The reported method of detecting in situ correlations can be applied to interacting many-body systems and to the study of critical phenomena near phase transitions.
We investigate the thermodynamics of one-dimensional (1D) Bose gases in the strongly correlated regime. To this end, we prepare ensembles of independent 1D Bose gases in a two-dimensional optical lattice and perform high-resolution in situ imaging of the column-integrated density distribution. Using an inverse Abel transformation we derive effective one-dimensional line-density profiles and compare them to exact theoretical models. The high resolution allows for a direct thermometry of the trapped ensembles. The knowledge about the temperature enables us to extract thermodynamic equations of state such as the phase-space density, the entropy per particle, and the local pair-correlation function.
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We perform large-scale quantum Monte Carlo (QMC) simulations for strongly interacting bosons in a two-dimensional optical lattice trap and confirm an excellent agreement with the benchmarking in situ density measurements by the Chicago group [N. Gemelke et al., Nature (London) 460, 995 (2009)]. We further present a general finite-temperature phase diagram for both the uniform and the trapped systems, demonstrating how the universal scaling properties near the superfluid-to-Mott insulator transition can be observed from the in situ density profile. The characteristic temperature to find such quantum criticality is estimated to be of the order of the single-particle bandwidth, which should be achievable in the present experiments. Finally, we examine the validity regime of the local fluctuation-dissipation theorem, which can be a used as a thermometry in the strongly interacting regime.
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Correlation functions play an important role for the theoretical and experimental characterization of many-body systems. In solid-state systems, they are usually determined through scattering experiments, whereas in cold gases systems, time-of-flight, and in situ absorption imaging are the standard observation techniques. However, none of these methods allow the in situ detection of spatially resolved correlation functions at the single-particle level. Here, we give a more detailed account of recent advances in the detection of correlation functions using in situ fluorescence imaging of ultracold bosonic atoms in an optical lattice. This method yields single-site- and single-atom-resolved images of the lattice gas in a single experimental run, thus gaining direct access to fluctuations in the many-body system. As a consequence, the detection of correlation functions between an arbitrary set of lattice sites is possible. This enables not only the detection of two-site correlation functions but also the evaluation of non-local correlations, which originate from an extended region of the system and are used for the characterization of quantum phases that do not possess (quasi-)long-range order in the traditional sense.