Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Observation of pairs of atoms at opposite momenta in an equilibrium interacting Bose gas

Abstract

Quantum fluctuations play a central role in the properties of quantum matter. In non-interacting ensembles, they manifest as fluctuations of non-commuting observables, quantified by Heisenberg inequalities1. In the presence of interactions, additional quantum fluctuations appear, from which many-body correlations and entanglement arise2. Weak interactions are predicted to deplete Bose–Einstein condensates by the formation of correlated pairs of bosons with opposite momenta3,4. Here we report the observation of these atom pairs in the depletion of an equilibrium interacting Bose gas5. Our measurements of atom–atom correlations, both at opposite and close-by momenta6,7, allow us to characterize the equilibrium many-body state. We also show that the atom pairs share the properties of two-mode squeezed states8,9, including relative number squeezing10,11,12. Our results illustrate how interacting systems acquire non-trivial quantum correlations as a result of the interplay between quantum fluctuations and interactions13.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Observation of k/−k pairs in the atom–atom correlations measured after a time of flight.
Fig. 2: Atom–atom correlations in weakly interacting BECs at two different temperatures.
Fig. 3: Peak widths and amplitudes of the observed atom–atom correlations.
Fig. 4: Relative number squeezing.

Data availability

All data shown in this paper are available from the corresponding author upon reasonable request.

References

  1. Heisenberg, W. Über den anschulichen inhalt der quantentheoretischen kinematik und mechanik. Z. Phys. 43, 172–198 (1927).

    ADS  Article  Google Scholar 

  2. Amico, L., Fazio, R., Osterloh, A. & Vedral, V. Entanglement in many-body systems. Rev. Mod. Phys. 80, 517–576 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  3. Bogoliubov, N. On the theory of superfluidity. J. Phys. 11, 23 (1947).

    MathSciNet  Google Scholar 

  4. Lee, T. D., Huang, K. & Yang, C. N. Eigenvalues and eigenfunctions of a Bose system of hard spheres and its low-temperature properties. Phys. Rev. 106, 1135–1145 (1957).

    ADS  MathSciNet  Article  Google Scholar 

  5. Carcy, C., Hercé, G., Tenart, A., Roscilde, T. & Clément, D. Certifying the adiabatic preparation of ultracold lattice bosons in the vicinity of the Mott transition. Phys. Rev. Lett. 126, 045301 (2021).

    ADS  Article  Google Scholar 

  6. Carcy, C. et al. Momentum-space atom correlations in a Mott insulator. Phys. Rev. X 9, 041028 (2019).

    Google Scholar 

  7. Cayla, H. et al. Hanbury Brown and Twiss bunching of phonons and of the quantum depletion in an interacting Bose gas. Phys. Rev. Lett. 125, 165301 (2020).

    ADS  Article  Google Scholar 

  8. Loudon, R. & Knight, P. L. Squeezed light. J. Mod. Optic. 34, 709–759 (1987).

    MathSciNet  MATH  Google Scholar 

  9. Braunstein, S. L. & Van Loock, P. Quantum information with continuous variables. Rev. Mod. Phys. 77, 513–577 (2005).

    ADS  MathSciNet  Article  Google Scholar 

  10. Orzel, C., Tuchman, A. K., Fenselau, M. L., Yasuda, M. & Kasevich, M. A. Squeezed states in a Bose-Einstein condensate. Science 291, 2386–2389 (2001).

    Article  Google Scholar 

  11. Esteve, J., Gross, C., Weller, A., Giovanazzi, S. & Oberthaler, M. Squeezing and entanglement in a Bose–Einstein condensate. Nature 455, 1216–1219 (2008).

    ADS  Article  Google Scholar 

  12. Bücker, R. et al. Twin-atom beams. Nat. Phys. 7, 608–611 (2011).

    Article  Google Scholar 

  13. Pitaevskii, L. & Stringari, S. Uncertainty principle, quantum fluctuations, and broken symmetries. J. Low Temp. Phys. 85, 377–388 (1991).

    ADS  Article  Google Scholar 

  14. Miller, A., Pines, D. & Nozières, P. Elementary excitations in liquid helium. Phys. Rev. 127, 1452–1464 (1962).

    ADS  Article  Google Scholar 

  15. Ozeri, R., Katz, N., Steinhauer, J. & Davidson, N. Colloquium: bulk Bogoliubov excitations in a Bose-Einstein condensate. Rev. Mod. Phys. 77, 187–205 (2005).

    ADS  Article  Google Scholar 

  16. Fontaine, Q. et al. Observation of the Bogoliubov dispersion in a fluid of light. Phys. Rev. Lett. 121, 183604 (2018).

    ADS  Article  Google Scholar 

  17. Stepanov, P. et al. Dispersion relation of the collective excitations in a resonantly driven polariton fluid. Nat. Commun. 10, 3869 (2019).

    ADS  Article  Google Scholar 

  18. Griffin, A., Snoke, D. W. & Stringari, S. (eds) Bose-Einstein Condensation (Cambridge Univ. Press, 1995).

  19. Xu, K. et al. Observation of strong quantum depletion in a gaseous Bose-Einstein condensate. Phys. Rev. Lett. 96, 180405 (2006).

    ADS  Article  Google Scholar 

  20. Lopes, R. et al. Quantum depletion of a homogeneous Bose-Einstein condensate. Phys. Rev. Lett. 119, 190404 (2017).

    ADS  Article  Google Scholar 

  21. Burnham, D. C. & Weinberg, D. L. Observation of simultaneity in parametric production of optical photon pairs. Phys. Rev. Lett. 25, 84 (1970).

    ADS  Article  Google Scholar 

  22. 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).

    ADS  Article  Google Scholar 

  23. Arnison, G. First observation of correlations between high transverse momentum charged particles in events from the CERN proton-antiproton collider. Phys. Lett. B 118, 173–177 (1982).

    Google Scholar 

  24. Perrin, A. et al. Observation of atom pairs in spontaneous four-wave mixing of two colliding Bose-Einstein condensates. Phys. Rev. Lett. 99, 150405 (2007).

    ADS  Article  Google Scholar 

  25. Cayla, H. et al. Single-atom-resolved probing of lattice gases in momentum space. Phys. Rev. A 97, 061609 (2018).

    ADS  Article  Google Scholar 

  26. Tenart, A. et al. Two-body collisions in the time-of-flight dynamics of lattice Bose superfluids. Phys. Rev. Research 2, 013017 (2020).

    ADS  Article  Google Scholar 

  27. Butera, S., Clément, D. & Carusotto, I. Position- and momentum-space two-body correlations in a weakly interacting trapped condensate. Phys. Rev. A 103, 013302 (2021).

    ADS  MathSciNet  Article  Google Scholar 

  28. Walls, D. F. & Milburn, G. J. Quantum Optics (Springer-Verlag, 2008).

    Book  Google Scholar 

  29. Pezzè, L., Smerzi, A., Oberthaler, M. K., Schmied, R. & Treutlein, P. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys. 90, 035005 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  30. Busch, X. & Parentani, R. Quantum entanglement in analogue Hawking radiation: when is the final state nonseparable? Phys. Rev. D 89, 105024 (2014).

    ADS  Article  Google Scholar 

  31. Bergschneider, A. et al. Experimental characterization of two-particle entanglement through position and momentum correlations. Nat. Phys. 15, 640–644 (2019).

    Article  Google Scholar 

  32. Schweigler, T. et al. Experimental characterization of a quantum many-body system via higher-order correlations. Nature 545, 323–326 (2017).

    Article  Google Scholar 

Download references

Acknowledgements

We thank A. Aspect, A. Browaeys, I. Carusotto, H. Cayla and T. Roscilde for their valuable comments on the manuscript, and acknowledge fruitful discussions with the members of the Quantum Gas group at Institut d’Optique. We acknowledge financial support from the LabEx PALM (grant number ANR-10-LABX-0039), the Région Ile-de-France in the framework of the DIM SIRTEQ, the ‘Fondation d’entreprise iXcore pour la Recherche’ and the Agence Nationale pour la Recherche (grant number ANR-17-CE30-0020-01). D.C. acknowledges support from the Institut Universitaire de France.

Author information

Authors and Affiliations

Authors

Contributions

A.T. and G.H. carried out the experiments. All the authors contributed to the data analysis, progression of the project and writing of the manuscript.

Corresponding author

Correspondence to David Clément.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review informationNature Physics thanks the anonymous reviewers for their contribution to the peer review of this work

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–5 and Discussion.

Source data

Source Data Fig. 1

Graph points for Fig. 1b,c.

Source Data Fig. 2

Graph points for Fig. 2a–c.

Source Data Fig. 3

Graph points for Fig. 3a,b.

Source Data Fig. 4

Statistical source data.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tenart, A., Hercé, G., Bureik, JP. et al. Observation of pairs of atoms at opposite momenta in an equilibrium interacting Bose gas. Nat. Phys. 17, 1364–1368 (2021). https://doi.org/10.1038/s41567-021-01381-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-021-01381-2

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing