Deep inelastic scattering on ultracold gases

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• Johannes Hofmann (Cambridge)
• Thursday 09 March 2017, 13:45-15:00
• Theory Library.

If you have a question about this talk, please contact Mike Gunn.

We discuss the dynamic structure factor of both Bose and Fermi gases with strong short-range interactions, focussing on the deep inelastic regime of large wave vector transfer q. Here, the dynamic structure factor is dominated by a resonance at the free-particle energy ℏω=εq=ℏ2q2/2m and is described in terms of scaling functions. We show that the high-momentum structure has a rich scaling behavior characterized by two separate scaling regions: first, for frequencies that differ from the single-particle energy by terms of order (q) (i.e., small deviations compared to the single-particle energy), the dynamic structure factor is described by the impulse approximation (IA) of Hohenberg and Platzman. Second, deviations of order (q2) (i.e., of the same order or larger than the single-particle energy) are described by the operator product expansion (OPE), with a universal cross-over connecting both regimes. We use the full asymptotic form to derive various sum rules. Furthermore, we derive an exact expression for the shift of the single-particle peak at large momentum due to interactions, which extends an old result by [S. T. Beliaev, Sov. Phys. JETP 34 , 299 (1958)] for the low-density Bose gas to arbitrary values of the scattering length a. The shift exhibits a maximum around qa≃1 which is connected with a maximum in the static structure factor due to strong short-range correlations. For Bose gases with moderate interaction strengths, the theoretically predicted shift is consistent with the value observed by [S. B. Papp et al., Phys. Rev. Lett. 101, 135301 (2008)]. Finally, we develop a diagrammatic theory for the dynamic structure factor which accounts for the correlations beyond Bogoliubov theory and which covers the full range of momenta and frequencies, showing the correct asymptotic scaling at large momentum.

This talk is part of the Theoretical Physics Seminars series.

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