Ideal n-body correlations with massive particles

Journal name:
Nature Physics
Year published:
Published online

In 1963 Glauber introduced the modern theory of quantum coherence1, which extended the concept of first-order (one-body) correlations, describing phase coherence of classical waves, to include higher-order (n-body) quantum correlations characterizing the interference of multiple particles. Whereas the quantum coherence of photons is a mature cornerstone of quantum optics, the quantum coherence properties of massive particles remain largely unexplored. To investigate these properties, here we use a uniquely correlated 2 source of atoms that allows us to observe n-body correlations up to the sixth-order at the ideal theoretical limit (n!). Our measurements constitute a direct demonstration of the validity of one of the most widely used theorems in quantum many-body theory—Wick’s theorem3—for a thermal ensemble of massive particles. Measurements involving n-body correlations may play an important role in the understanding of thermalization of isolated quantum systems4 and the thermodynamics of exotic many-body systems, such as Efimov trimers5.

At a glance


  1. Schematic of the experiment.
    Figure 1: Schematic of the experiment.

    An ultracold cloud of atoms is confined in a tightly focused laser beam. When released, the cloud drops ~ 85cm, where its correlation properties are measured using a single-atom detector. Shown in the inset are the mean (dashed blue line) and a typical single (solid red line) longitudinal profile obtained in the experiment.

  2. Many-body correlation functions along the longitudinal direction (temporal dimension on the detector).
    Figure 2: Many-body correlation functions along the longitudinal direction (temporal dimension on the detector).

    The data is averaged over the x and y transverse directions using ~1cm×1cm spatial bins. ae, A Gaussian fit to the data yields the following peak correlation amplitudes: (a) g(2)(0)=2.05±0.09, (b) g(3)(0)=6.0±0.6, (c) g(4)(0)=23±3, (d) g(5)(0)=111±16, and (e) g(6)(0)=710±90. In f we show the n! scaling (dashed line) of the peak correlation amplitudes.

  3. Surface plot of the three-body correlation function
    Figure 3: Surface plot of the three-body correlation function g(3)z1z2).


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Author information


  1. Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory 0200, Australia

    • R. G. Dall,
    • A. G. Manning,
    • S. S. Hodgman,
    • Wu RuGway &
    • A. G. Truscott
  2. The University of Queensland, School of Mathematics and Physics, Brisbane, Queensland 4072, Australia

    • K. V. Kheruntsyan


S.S.H., R.G.D. and A.G.T. conceived the experiment. A.G.M., S.S.H. and W.R. collected the data presented in this Letter. K.V.K. developed the Bose model and provided theoretical insight into the results. All authors contributed to the conceptual formulation of the physics, the interpretation of the data and writing the manuscript.

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