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Single-atom and momentum-resolved measurement of the depletion of a Bose condensate

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The interplay of quantum fluctuations and interaction is at the core of intriguing phenomena of quantum many-body physics. An emblematic example, conceptually rather simple, of such a manifestation is the quantum depletion of a Bose condensate occurring at zero temperature. The resulting many-body ground-state, a vacuum of quasi-particles, is composed of single-particle excitations on top of the condensate, for which a direct observation has been missing. I will report on the single-atom-resolved measurement of the distribution of momenta hk in a weakly-interacting Bose gas after a 330 ms time-of-flight [1]. We investigate it for various temperatures and clearly separated and identify, by their k-dependence, two distinct contributions to the depletion of the condensate. One contribution can be unambiguously associated with the thermal depletion. Thanks to a total dynamic range spanning five decades in density, we observe a second contribution consisting in high-momentum tails decaying as 1/k4, as predicted by Bogoliubov theory for the intrap Bose gas [2]. We also find that the population in the 1/k4-tails increases with the in-trap condensate density as expected for the quantum depletion but the amplitude we measure is larger than the Bogoliubov prediction by a factor of about 6. Our observations suggest to associate the 1/ k^4-tails to the quantum depletion of the trapped condensate and raise new theoretical questions [3]. [1] R. Chang, Q. Bouton, H. Cayla, C. Qu, A. Aspect, C. Westbrook and D. Clément, arXiv: 1608.04693 (2016). [2] N. N. Bogoliubov, J. Phys. (Moscow) 11, 23 (1947). [3] C. Qu, L. Pitaevskii and S. Stringari, arXiv:1608.08566 (2016).

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