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arXiv:1208.2308 · Physical Review A

Response function of a strongly interacting Fermi gas in a virial expansion

Gang Shen

Published Mar 7, 2013• 4 citations
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Abstract

The dynamic response functions of a strongly interacting fermion gas in a homogeneous space are investigated in a virial expansion to second order. The density response function exhibits transition from atomic to molecular response, as the interaction strength increases and the system undergoes BCS to Bose-Einstein condensate crossover. The qualitative features of density and spin response agree with measurements from the Bragg spectroscopy experiments. The virial response is exact at low density and high temperature, therefore providing a benchmark for many-body response.

DOI
10.1103/physreva.87.033612

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The dynamic response functions of a strongly interacting fermion gas in a homogeneous space are investigated in a virial expansion to second order. The density response function exhibits transition from atomic to molecular response, as the interaction strength increases and the system undergoes BCS to Bose-Einstein condensate crossover. The qualitative features of density and spin response agree with measurements from the Bragg spectroscopy experiments. The virial response is exact at low density and high temperature, therefore providing a benchmark for many-body response.
By developing a quantum virial expansion theory, we quantitatively calculate the dynamic density response function of a trapped strongly interacting Fermi gas at high temperatures near unitarity. A clear transition from atomic to molecular responses is identified in the spectra when crossing from the BCS to BEC regimes, in qualitative agreement with recent Bragg spectroscopy observations. Our virial expansion method provides a promising way to solve the challenging strong-coupling problems and is applicable to other dynamical properties of strongly correlated Fermi gases.
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We present an experimental investigation of the dynamic spin response of a strongly interacting Fermi gas using Bragg spectroscopy. By varying the detuning of the Bragg lasers, we show that it is possible to measure the response in the spin and density channels separately. At low Bragg energies, the spin response is suppressed due to pairing, whereas the density response is enhanced. These experiments yield the first independent measurements of the spin-parallel and spin-antiparallel dynamic and static structure factors, which provide insight into the different features of density and spin response functions. At high momentum the spin-antiparallel dynamic structure factor displays a universal high frequency tail, proportional to ω(-5/2), where ℏω is the probe energy.
Using a high temperature virial expansion, we present a controllable study of the thermodynamics of strongly correlated Fermi gases near the BEC-BCS crossover region. We propose a practical way to determine the expansion coefficients for both harmonically trapped and homogeneous cases, and calculate the third order coefficient b{3}(T) at finite temperatures T. At resonance, a T-independent coefficient b{3,infinity};{hom} approximately -0.290 952 95 is determined in free space. These results are compared with a recent thermodynamic measurement of 6Li atoms, at temperatures below the degeneracy temperature, and with Monte Carlo simulations.