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


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.

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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.


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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.

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Authors and Affiliations



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.

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Correspondence to David Clément.

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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.

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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).

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