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Dynamic structure function of a cold Fermi gas at unitarity

Astrakharchik, Grigori, Jordi Boronat, E. Krotscheck, T. Lichtenegger

Published Jan 1, 2014• 3 citations
OpenAlex

Abstract

We present a theoretical study of the dynamic structure function of a resonantly interacting two-component Fermi gas at zero temperature. Our approach is based on dynamic many-body theory able to describe excitations in strongly correlated Fermi systems. The fixed-node diffusion Monte Carlo method is used to produce the ground-state correlation functions which are used as an input for the excitation theory. Our approach reproduces recent Bragg scattering data in both the density and the spin channel. In the BCS regime, the response is close to that of the ideal Fermi gas. On the BEC side, the Bose peak associated with the formation of dimers dominates the density channel of the dynamic response. When the fraction of dimers is large our theory departs from the experimental data, mainly in the spin channel.

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We present a theoretical study of the dynamic structure function of a resonantly interacting two-component Fermi gas at zero temperature. Our approach is based on dynamic many-body theory able to describe excitations in strongly correlated Fermi systems. The fixed-node diffusion Monte Carlo method is used to produce the ground-state correlation functions which are used as an input for the excitation theory. Our approach reproduces recent Bragg scattering data in both the density and the spin channel. In the BCS regime, the response is close to that of the ideal Fermi gas. On the BEC side, the Bose peak associated with the formation of dimers dominates the density channel of the dynamic response. When the fraction of dimers is large our theory departs from the experimental data, mainly in the spin channel.
We present a theoretical study of the dynamic structure function of a resonantly interacting two-component Fermi gas at zero temperature. Our approach is based on dynamic many-body theory able to describe excitations in strongly correlated Fermi systems. The fixed-node diffusion Monte Carlo method is used to produce the ground-state correlation functions which are used as an input for the excitation theory. Our approach reproduces recent Bragg scattering data in both the density and the spin channel. In the BCS regime, the response is close to that of the ideal Fermi gas. On the BEC side, the Bose peak associated with the formation of dimers dominates the density channel of the dynamic response. When the fraction of dimers is large our theory departs from the experimental data, mainly in the spin channel.
Using the Landau theory of Fermi liquids, we calculate the dynamic response of both a polarized and an unpolarized normal Fermi gas at zero temperature in the strongly interacting regime of large scattering length. We show that at small excitation energies the in phase (density) response is enhanced with respect to the ideal gas prediction due to the increased compressibility. Vice versa, the out of phase (spin) response is quenched as a consequence of the tendency of the system to pair opposite spins. The long wavelength behavior of the static structure factor is explicitly calculated. The results are compared with the predictions in the collisional and superfluid regimes. The emergence of a spin zero sound solution in the unpolarized normal phase is explicitly discussed.
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.
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.
The ground-state properties of a two-component Fermi gas with attractive short-range interactions are calculated using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. We calculate the energy per particle, the one- and two-body density matrix as a function of the interaction strength. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.
We calculate the equation of state of a two-component Fermi gas with attractive short-range interspecies interactions using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. For a>0 and a smaller than the inverse Fermi wave vector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length a(m)=0.6a. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength.