Contact and sum-rules in a homogeneous Fermi gas at unitarity

Scott Jensen, C. N. Gilbreth, Y. Alhassid

Biswaroop Mukherjee, Parth Patel, Zhenjie Yan +3 more

Tara E. Drake, Yoav Sagi, Rabin Paudel +1 more

Cécile Carcy, Sascha Hoinka, Marcus Lingham +4 more

We present an experimental study of the high-energy excitation spectra of unitary Fermi gases. Using focused beam Bragg spectroscopy, we locally probe atoms in the central region of a harmonically trapped cloud where the density is nearly uniform, enabling measurements of the dynamic structure factor for a range of temperatures both below and above the superfluid transition. Applying sum rules to the measured Bragg spectra, we resolve the characteristic behavior of the universal contact parameter, C, across the superfluid transition. We also employ a recent theoretical result for the kinetic (second-moment) sum rule to obtain the internal energy of gases at unitarity.

Joaquín E. Drut, Timo A. Lähde, Timour B. Ten

The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems known to date, as it saturates the unitarity bound on the quantum mechanical scattering cross section. The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length, and is currently realized in ultracold-atom experiments via Feshbach resonances. While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density. As a consequence, accurate quantitative predictions of the thermodynamic properties of the UFG require Monte Carlo calculations. However, significant progress has also been made with purely analytical methods. Notably, in 2005 Tan derived a set of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role. Recently, C has also been found to determine the prefactor of the high- frequency power-law decay of correlators as well as the right-hand-sides of shear- and bulk viscosity sum rules. The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibrium. In this talk we describe some of the known aspects of Fermi gases at and around unitarity, show our latest Monte Carlo results for the contact at finite temperature, and summarize the open questions in the field, some of which we are starting to answer using large-scale Monte Carlo calculations by adapting methods from Lattice QCD.

Joaquín E. Drut, Timo A. Lähde

The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems known to date, as it saturates the unitarity bound on the quantum mechanical scattering cross section.The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length, and is currently realized in ultracold-atom experiments via Feshbach resonances.While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density.As a consequence, accurate quantitative predictions of the thermodynamic properties of the UFG require Monte Carlo calculations.However, significant progress has also been made with purely analytical methods.Notably, in 2005 Tan derived a set of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role.Recently, C has also been found to determine the prefactor of the high-frequency power-law decay of correlators as well as the right-hand-sides of shear-and bulk viscosity sum rules.The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibrium.In this talk we describe some of the known aspects of Fermi gases at and around unitarity, show our latest Monte Carlo results for the contact at finite temperature, and summarize the open questions in the field, some of which we are starting to answer using large-scale Monte Carlo calculations by adapting methods from Lattice QCD.