Abstract
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/(kFa) and temperature T/TF, where kF is the Fermi wave vector, a is the s-wave scattering length and TF is the Fermi temperature. We present measurements of both of these dependencies in a cloud of 6Li 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.
Highlights
We present a comprehensive experimental study of Tan’s universal contact parameter I in a two-component ultracold Fermi gas, using Bragg spectroscopy
Tan showed that the internal energy of a gas across the BEC–BCS crossover can be expressed as a functional of the momentum distribution at k and that the pair correlation function diverges as I/r 2 at short distance r < 1/kF [14, 19]
Theoretical calculations based on the quantum virial expansion (QVE) are shown to agree with measurements of the dynamic structure factor and contact at temperatures down to T 0.5TF
Summary
Tan’s exact universal relations, such as the adiabatic and virial theorems mentioned in the previous section, link many-body quantities such as the total energy and momentum distribution. The short-range structure in a quantum fluid depends upon the relative wave-function of the interacting particles, in this case fermions in different spin states. In a two-component (spinup/spin-down) Fermi gas, this is given by ψ↑↓(r ) ∝ 1/r − 1/a. Tan used this to show that, for length scales r0 < r < 1/kF, the spin-antiparallel pair-correlation function is given exactly by equation (2), which includes the contact as a pre-factor [14], g(2)(r ). In a two-component Fermi gas with an equal number of particles N /2 in each spin state, the structure factor contains two weighted contributions arising from correlations between particles in the same state and between particles in different states.
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