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arXiv:1105.4818 · Physical Review Letters

Observation of Local Temporal Correlations in Trapped Quantum Gases

Vera Guarrera, Peter Würtz, A Ewerbeck, Andreas Vogler, Giovanni Barontini, Herwig Ott

Published Oct 14, 2011• 47 citations
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Abstract

We measure the temporal pair correlation function g(2)(τ) of a trapped gas of bosons above and below the critical temperature for Bose-Einstein condensation. The measurement is performed in situ by using a local, time-resolved single-atom sensitive probing technique. Third- and fourth-order correlation functions are also extracted. We develop a theoretical model and compare it with our experimental data, finding good quantitative agreement. We discuss, finally, the role of interactions. Our results promote temporal correlations as new observables to study the dynamical evolution of ultracold quantum gases.

DOI
10.1103/physrevlett.107.160403

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We measure the temporal pair correlation function g(2)(τ) of a trapped gas of bosons above and below the critical temperature for Bose-Einstein condensation. The measurement is performed in situ by using a local, time-resolved single-atom sensitive probing technique. Third- and fourth-order correlation functions are also extracted. We develop a theoretical model and compare it with our experimental data, finding good quantitative agreement. We discuss, finally, the role of interactions. Our results promote temporal correlations as new observables to study the dynamical evolution of ultracold quantum gases.
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We study first- and second-order coherence of trapped dilute Bose gases using appropriate correlation functions. Special attention is given to the discussion of second-order or density correlations. Except for a small region around the surface of a Bose-Einstein condensate the correlations can be accurately described as those of a locally homogeneous gas with a spatially varying chemical potential. The degrees of first- and second-order coherence are therefore functions of temperature, chemical potential, and position. The second-order correlation function is governed both by the tendency of bosonic atoms to cluster and by a strong repulsion at small distances due to atomic interactions. In present experiments both effects are of comparable magnitude. Below the critical temperature the range of the bosonic correlation is affected by the presence of collective quasiparticle excitations. The results of some recent experiments on second- and third-order coherence are discussed. It is shown that the relation between the measured quantities and the correlation functions is much weaker than previously assumed.
We demonstrate atom-resolved detection of itinerant bosonic ^{23}Na and fermionic ^{6}Li quantum gases, enabling the direct in situ measurement of interparticle correlations. In contrast to prior work on lattice-trapped gases, here we realize microscopy of quantum gases in the continuum. We reveal Bose-Einstein condensation with single-atom resolution, measure the enhancement of two-particle g^{(2)} correlations of thermal bosons, and observe the suppression of g^{(2)} for fermions; the Fermi or exchange hole. For strongly interacting Fermi gases confined to two dimensions, we directly observe nonlocal fermion pairs in the BEC-BCS crossover. We obtain the pair size and the short-range contact directly from the pair correlations. In situ thermometry is enabled via the fluctuation-dissipation theorem. Our technique opens the door to the atom-resolved study of strongly correlated quantum gases of bosons, fermions, and their mixtures.
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.
Thermometry is essential for studying many-body physics with ultracold atoms. Accurately measuring low temperatures in these systems, however, remains a significant challenge due to the absence of a universal thermometer. Most widely applicable methods, such as fitting of in situ density profiles, are limited by the requirement of global thermal equilibrium and inapplicability to homogeneous systems. In this Letter, we introduce a novel in situ thermometry for quantum gases, leveraging single-atom-resolved measurements via quantum gas microscopy, and demonstrate it on an ideal Fermi gas. By analyzing number fluctuations in probe volumes containing as little as one atom on average, we extract both global and local temperatures over a broad dynamic range. Our method does not rely on the fluctuation-dissipation theorem and is based instead on the exact relationship between number fluctuations and density-density correlations. In the low-temperature regime, it allows us to observe significant deviations from fluctuation-dissipation predictions, uncovering subextensive fluctuations. Our method is applicable to systems with arbitrary trapping potentials, requiring neither precise trap calibration nor global thermal equilibrium. This thermometer for quantum gases overcomes key limitations of existing techniques, paving the way for more accurate and versatile temperature measurements in ultracold quantum systems.
The transition from a thermal cloud to a Bose–Einstein condensate (BEC) in an interacting ultra-cold Bose gas is a prototype in a universality class of diverse phase transitions. For a trapped ultra-cold Bose gas, we were able to study the critical regime both above and below the critical temperature with a Talbot–Lau interferometer, observing a peak in the correlation length. From this peak, we managed to determine the universal critical exponents for this phase transition as well as the finite-size and interaction corrections to the critical temperature. The results are all in quantitative agreement with theory. This work demonstrates the potential application of the Talbot–Lau interferometer to a wide range of critical phase transitions in ultra-cold atomic gases.