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arXiv:cond-mat/0512048 · Europhysics Letters (EPL)

Molecular signatures in the structure factor of an interacting Fermi gas

R. Combescot, S. Giorgini, S. Stringari

Published Jul 20, 2006• 61 citations
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Abstract

The static and dynamic structure factors of an interacting Fermi gas along the BCS-BEC crossover are calculated at momentum transfer ℏ k higher than the Fermi momentum. The spin structure factor is found to be very sensitive to the correlations associated with the formation of molecules. On the BEC side of the crossover, even close to unitarity, clear evidence is found for a molecular excitation at ℏ 2 k 2 /4 m , where m is the atomic mass. Both quantum Monte Carlo and dynamic mean-field results are presented.

DOI
10.1209/epl/i2006-10165-x

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We present a comprehensive study of the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover in fermionic 6Li using Bragg spectroscopy. A smooth transition from molecular to atomic spectra is observed with a clear signature of pairing at and above unitarity. These spectra probe the dynamic and static structure factors of the gas and provide a direct link to two-body correlations. We have characterized these correlations and measured their density dependence across the broad Feshbach resonance at 834 G.
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In recent years Quantum Monte Carlo techniques provided to be a valuable tool to study strongly interacting Fermi gases at zero temperature. We have used QMC methods to investigate several properties of the two-components Fermi gas at unitarity and in the BCS-BEC crossover, both with equal and unequal masses corresponding to the Li – K Fermi mixture. In this paper we present several recent QMC results, including the energy at zero and finite effective range, the contact parameter and the static structure factor, which, at low momentum, depends strongly on the phonons in the unitary Fermi gas.
We theoretically investigate the static structure factor of an interacting Fermi gas near the BEC-BCS crossover at large momenta. Due to short-range two-body interactions, we show that the structure factor of unlike spin correlations S ↑↓ ( q ) falls off as 1/ q in a universal scaling region with large momentum ℏ q and large scattering length. The scaling coefficient is determined by the celebrated Tan's contact parameter, which links the short-range behavior of many-body systems to their universal thermodynamic properties. By implementing this structure-factor Tan relation together with the random-phase approximation and the virial expansion theory in various limiting cases, we show how to calculate S ↑↓ ( q ) at zero and finite temperatures for arbitrary interaction strengths, at momentum transfer higher than the Fermi momentum. Our results provide a way to experimentally confirm one of the Tan relations and to accurately measure the value of contact parameter.
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We consider cigar-shaped Fermi superfluid in the Bose-Einstein condensation (BEC)-BCS crossover. Using the polytropic form of equation of state, we derive low energy multibranch bosonic excitations and the corresponding density fluctuations in three different regimes along the crossover, namely weak-coupling BCS, unitarity, and molecular BEC regimes. Bragg spectroscopy can be used to probe the multibranch nature of the low-energy bosonic excitations by measuring the dynamic structure factor. Therefore we calculate the dynamic structure factor in those three different regimes. In Bragg spectroscopy, an actual observable is momentum imparted to the superfluid due to the Bragg potential. We also present results of the momentum imparted to the superfluid due to the Bragg pulses.