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Precise Determination of the Structure Factor and Contact in a Unitary Fermi Gas

Hui Hu, Stefano Gandolfi, Joaquín E. Drut, Sascha Hoinka, Kristian Fenech, Chris J. Vale, Marcus Lingham

Published Jul 2, 2021• 0 citations
Publisher

Abstract

We present a high-precision determination of the universal contact parameter in a strongly interacting Fermi gas. In a trapped gas at unitarity, we find the contact to be 3.06±0.08 at a temperature of 0.08 of the Fermi temperature in a harmonic trap. The contact governs the high-momentum (short-range) properties of these systems, and this low-temperature measurement provides a new benchmark for the zero-temperature homogeneous contact. The experimental measurement utilizes Bragg spectroscopy to obtain the dynamic and static structure factors of ultracold Fermi gases at high momentum in the unitarity and molecular Bose-Einstein condensate regimes. We have also performed quantum Monte Carlo calculations of the static properties, extending from the weakly coupled BCS regime to the strongly coupled Bose-Einstein condensate case, that show agreement with experiment at the level of a few percent.

DOI
10.17615/wkdq-zp66

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We present a high-precision determination of the universal contact parameter in a strongly interacting Fermi gas. In a trapped gas at unitarity, we find the contact to be 3.06±0.08 at a temperature of 0.08 of the Fermi temperature in a harmonic trap. The contact governs the high-momentum (short-range) properties of these systems, and this low-temperature measurement provides a new benchmark for the zero-temperature homogeneous contact. The experimental measurement utilizes Bragg spectroscopy to obtain the dynamic and static structure factors of ultracold Fermi gases at high momentum in the unitarity and molecular Bose-Einstein condensate regimes. We have also performed quantum Monte Carlo calculations of the static properties, extending from the weakly coupled BCS regime to the strongly coupled Bose-Einstein condensate case, that show agreement with experiment at the level of a few percent.
We present a high-precision determination of the universal contact parameter in a strongly interacting Fermi gas. In a trapped gas at unitarity, we find the contact to be 3.06±0.08 at a temperature of 0.08 of the Fermi temperature in a harmonic trap. The contact governs the high-momentum (short-range) properties of these systems, and this low-temperature measurement provides a new benchmark for the zero-temperature homogeneous contact. The experimental measurement utilizes Bragg spectroscopy to obtain the dynamic and static structure factors of ultracold Fermi gases at high momentum in the unitarity and molecular Bose-Einstein condensate regimes. We have also performed quantum Monte Carlo calculations of the static properties, extending from the weakly coupled BCS regime to the strongly coupled Bose-Einstein condensate case, that show agreement with experiment at the level of a few percent.
This paper presents studies of the universal properties of strongly interacting Fermi gases using Bragg spectroscopy. We focus on pair-correlations, their relationship to the contact C introduced by Tan, and their dependence on both the momentum and temperature. We show that short-range pair correlations obey a universal law, first derived by Tan through measurements of the static structure factor, which displays a universal scaling with the ratio of the contact to the momentum C/q . Bragg spectroscopy of ultracold 6 Li atoms is employed to measure the structure factor for a wide range of momenta and interaction strengths, providing broad confirmation of this universal law. We show that calibrating our Bragg spectra using the f -sum rule leads to a dramatic improvement in the accuracy of the structure factor measurement. We also measure the temperature dependence of the contact in a unitary gas and compare our results to calculations based on a virial expansion.
We present a comprehensive experimental study of Tan's universal contact parameter in a two-component ultracold Fermi gas, using Bragg spectroscopy. The contact uniquely parameterizes a number of universal properties of Fermi gases in the strongly interacting regime. It is linked to the spin-antiparallel component of the static structure factor S ↑↓ ( k ) at high momenta, which can readily be obtained via Bragg scattering. Contact depends upon the relative interaction strength 1/( k F a ) and temperature T / T F , where k F is the Fermi wave vector, a is the s-wave scattering length and T F is the Fermi temperature. We present measurements of both of these dependencies in a cloud of 6 Li atoms and compare our findings to theoretical predictions. We also compare Bragg spectroscopic methods based on measuring the energy and momentum transferred to the cloud and examine the conditions under which the energy transfer method provides improved accuracy. Our measurements of the dynamic structure factor and contact are found to be in good agreement with theoretical predictions based on the quantum virial expansion.
The recently discovered universal thermodynamic behavior of dilute, strongly interacting Fermi gases also implies a universal structure in the many-body pair-correlation function at short distances, as quantified by the contact . Here, we theoretically calculate the temperature dependence of this universal contact for a Fermi gas in free space and in a harmonic trap. At high temperatures above the Fermi degeneracy temperature, T ≳ T F , we obtain a reliable non-perturbative quantum virial expansion up to third order. At low temperatures, we compare different approximate strong-coupling theories. These make different predictions, which need to be tested either by future experiments or by advanced quantum Monte Carlo simulations. We conjecture that in the universal unitarity limit, the contact or correlation decreases monotonically with increasing temperature, unless the temperature is significantly lower than the critical temperature, T ≪ T c ∼0.2 T F . We also discuss briefly how to measure the universal contact in either homogeneous or harmonically trapped Fermi gases.
We report measurements showing the universal behaviour of the static structure factor and both the temperature and interaction dependence of pair correlations in a strongly interacting Fermi gas. We utilize Bragg spectroscopy to obtain the static structure factor by recording excitation spectra of trapped clouds of ultracold 6Li atoms. Our results show clear evidence of strong short-range pair correlations above the critical temperature for superfluidity through the BEC-BCS crossover and agree well with theoretical calculations.