Ideal n-body correlations with massive particles

Journal name:
Nature Physics
Volume:
9,
Pages:
341–344
Year published:
DOI:
doi:10.1038/nphys2632
Received
Accepted
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

Figures

  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
g(3)([Delta]z1,[Delta]z2).
    Figure 3: Surface plot of the three-body correlation function g(3)z1z2).

References

  1. Glauber, R. The quantum theory of optical coherence. Phys. Rev 130, 25292539 (1963).
  2. Van Druten, N. J. & Ketterle, W. Two-step condensation of the ideal Bose gas in highly anisotropic traps. Phys. Rev. Lett. 79, 549552 (1997).
  3. Wick, G. C. The evaluation of the collision matrix. Phys. Rev. 80, 268272 (1950).
  4. Giraud, A. & Serreau, J. Decoherence and thermalization of a pure quantum state in quantum field theory. Phys. Rev. Lett 104, 230405 (2010).
  5. Kramer, T. et al. Evidence for Efimov quantum states in an ultracold gas of caesium atoms. Nature 440, 315318 (2006).
  6. Hanbury Brown, R. & Twiss, R. Q. A test of a new type of stellar interferometer on Sirius. Nature 178, 10461048 (1956).
  7. Baym, G. The physics of Hanbury Brown–Twiss intensity interferometry: From stars to nuclear collisions. Acta Phys. Polonica B 29, 18391883 (1997).
  8. Avenhaus, M., Laiho, K., Chekhova, M. & Silberhorn, C. Accessing higher order correlations in quantum optical states by time multiplexing. Phys. Rev. Lett. 104, 063602 (2010).
  9. Yasuda, M. & Shimizu, F. Observation of two-atom correlation of an ultracold neon atomic beam. Phys. Rev. Lett. 77, 30903093 (1996).
  10. Uren, A. B., Silberhorn, C., Ball, J. L., Banaszek, K. & Walmsley, I. A. Characterization of the nonclassical nature of conditionally prepared single photons. Phys. Rev. A 72, 021802 (2005).
  11. Ivanova, O. A., Iskhakov, T. Sh., Penin, A. N. & Chekhova, M. V. Multiphoton correlations in parametric down-conversion and their measurement in the pulsed regime. Quant. Electron. 36, 951956 (2006).
  12. Schilling, U., von Zanthier, J. & Agarwal, G. Measuring arbitrary-order coherences: Tomography of single-mode multiphoton polarization-entangled states. Phys. Rev. A 81, 013826 (2010).
  13. Hodgman, S. S, Dall, R. G., Manning, A. G., Baldwin, K. G. H. & Truscott, A. G. Direct measurement of long-range higher-order coherence in Bose–Einstein condensates. Science 331, 10461049 (2011).
  14. Guarrera, V. et al. Observation of local temporal correlations in trapped quantum gases. Phys. Rev. Lett. 107, 160403 (2011).
  15. Jeltes, T. et al. Comparison of the Hanbury Brown–Twiss effect for bosons and fermions. Nature 445, 402405 (2007).
  16. Kinoshita, T., Wenger, T. & Weiss, D. S. Local pair correlations in one-dimensional Bose gases. Phys. Rev. Lett 95, 190406 (2005).
  17. Haller, E. et al. Three-body correlation functions and recombination rates for bosons in three dimensions and one dimension. Phys. Rev. Lett 107, 230404 (2011).
  18. Greiner, M., Regal, C. A., Stewart, J. T. & Jin, D. S. Probing pair-correlated fermionic atoms through correlations in atom shot noise. Phys. Rev. Lett. 94, 110401 (2005).
  19. Rom, T. et al. Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice. Nature 444, 733736 (2006).
  20. Gomes, J. V. et al. Theory for a Hanbury Brown–Twiss experiment with a ballistically expanding cloud of cold atoms. Phys. Rev. A 74, 053607 (2006).
  21. Dall, R. G. et al. Observation of atomic speckle and Hanbury Brown–Twiss correlations in guided matter waves. Nature Commun. 2, 291 (2011).
  22. Armijo, J., Jacqmin, T., Kheruntsyan, K. V. & Bouchoule, I. Mapping out the quasi-condensate transition through the dimensional crossover from one to three dimensions. Phys. Rev. A 83, 021605 (2011).
  23. Bouchoule, I., Kheruntsyan, K. V. & Shlyapnikov, G. V. Interaction-induced crossover versus finite-size condensation in a weakly interacting trapped 1D Bose gas. Phys. Rev. A 75, 031606 (2007).
  24. Bouchoule, I., Arzamasovs, M., Kheruntsyan, K. V. & Gangardt, D. M. Two-body momentum correlations in a weakly interacting one-dimensional Bose gas. Phys. Rev. A 86, 033626 (2012).
  25. Aspect, A., Dalibard, J. & Roger, G. Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 18041807 (1982).
  26. Rarity, J. G. & Tapster, P. R. Experimental violation of Bell’s inequality based on phase and momentum. Phys. Rev. Lett 64, 24952498 (1990).
  27. Ou, Z., Pereira, F., Kimble, H. & Peng, K Realization of the Einstein–Podolsky–Rosen paradox for continuous variables. Phys. Rev. Lett 68, 36633666 (1992).
  28. Perrin, A. et al. Hanbury Brown and Twiss correlations across the Bose–Einstein condensation threshold. Nature Phys. 8, 195198 (2012).
  29. Manz, S. et al. Two-point density correlations of quasicondensates in free expansion. Phys. Rev. A 81, 031610 (2010).
  30. Kitagawa, T., Aspect, A., Greiner, M. & Demler, E. Phase-sensitive measurements of order parameters for ultracold atoms through two-particle interferometry. Phys. Rev. Lett. 106, 115302 (2011).

Download references

Author information

Affiliations

  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

Contributions

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.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary Information (288KB)

    Supplementary Information

Additional data