Deep inelastic scattering on ultracold gases

Abstract

We discuss Bragg scattering on both Bose and Fermi gases with strong short-range interactions in the deep inelastic regime of large wave vector transfer $q$, where the dynamic structure factor is dominated by a resonance near the free-particle energy $\hslash \omega ={\epsilon }_{\mathbf{q}}={\hslash }^2{q}^2/2m$. Using a systematic short-distance expansion, the structure factor at high momentum is shown to exhibit a nontrivial dependence on frequency characterized by two separate scaling regimes. First, for frequencies that differ from the single-particle energy by terms of order $\mathcal{O}(q)$ (i.e., small deviations compared to the single-particle energy), the dynamic structure factor is described by the impulse approximation of Hohenberg and Platzman. Second, deviations of order $\mathcal{O}(q^2)$ (i.e., of the same order or larger than the single-particle energy) are described by the operator product expansion, with a universal crossover connecting both regimes. The scaling is consistent with a number of sum rules in the large momentum limit. Furthermore, we derive an exact expression for the shift and width of the single-particle peak at large momentum due to interactions, thus extending a result by Beliaev [JETP 7, 299 (1958)] for the low-density Bose gas to arbitrary values of the scattering length $a$. The shift exhibits a maximum around $qa\simeq 1$, 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 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.

arXiv comment23 pages, 11 figures

References in corpus (45)

• Feshbach Resonances in Ultracold Gases
• Universality in Few-body Systems with Large Scattering Length
• Cuba - a library for multidimensional numerical integration
• Bragg spectroscopy of a Bose-Einstein condensate
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Roton-maxon spectrum and stability of trapped dipolar condensates
• Inter-isotope determination of ultracold rubidium interactions from three high-precision experiments
• Excitation of phonons in a Bose-Einstein condensate by light scattering
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• The Excitation Spectrum of a Bose-Einstein Condensate
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Three-body recombination of ultra-cold atoms to a weakly bound $s$ level
• Spatial coherence and density correlations of trapped Bose gases
• Contact Measurements on Atomic BEC
• Universal dynamics of a degenerate unitary Bose gas
• Bragg spectroscopy of a strongly interacting 85Rb Bose-Einstein condensate
• Rotons in gaseous Bose-Einstein condensates irradiated by a laser
• Bragg spectroscopy of a strongly interacting Fermi gas
• Origin of the Three-body Parameter Universality in Efimov Physics
• Lifetime of the Bose Gas with Resonant Interactions
• Universal Relations for Identical Bosons from 3-Body Physics
• Dynamic structure factor and momentum distribution of a trapped Bose gas
• Precise determination of the structure factor and contact in a unitary Fermi gas
• Viscosity of strongly interacting quantum fluids: spectral functions and sum rules
• Stability of a unitary Bose gas
• Efimov physics beyond universality
• Anomalous fluctuations in phases with a broken continuous symmetry
• Renormalization Group Approach to the Infrared Behavior of a Zero-Temperature Bose System
• Short-distance and short-time structure of a unitary Fermi gas
• Molecular signatures in the structure factor of an interacting Fermi gas
• Dynamic spin response of a strongly interacting Fermi gas
• Renormalization Effects in a Dilute Bose Gas
• Hybrid multi-site excitations in dipolar condensates in optical lattices
• Current response, structure factor and hydrodynamic quantities of a two- and three-dimensional Fermi gas from the operator-product expansion
• Observation of local temporal correlations in trapped quantum gases
• Static structure factor of a strongly correlated Fermi gas at large momenta
• Pair correlation function of an inhomogeneous interacting Bose-Einstein condensate
• Efimov correlations in strongly interacting Bose gases
• Probing strongly interacting atomic gases with energetic atoms
• OPE convergence in non-relativistic conformal field theories
• Comparative studies of many-body corrections to an interacting Bose condensate
• Structure Function Sum rules for Systems with Large Scattering Lengths
• Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method
• Green's function formalism for a condensed Bose gas consistent with infrared-divergent longitudinal susceptibility and Nepomnyashchii-Nepomnyashchii identity

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