Experimental studies of spin-imbalanced Fermi gases in 2D geometries

We study the thermodynamics of a quasi-two-dimensional Fermi gas, which is not quite two-dimensional (2D), but far from three dimensional (3D). This system offers opportunities to test predictions that cross interdisciplinary boundaries, such as enhanced superfluid transition temperatures in spin-imbalanced quasi-2D superconductors, and provides important benchmarks for calculations of the phase diagrams. In the experiments, an ultra-cold Fermi gas is confined in an infrared CO$_{2}$ laser standing-wave, which produces periodic pancake-shaped potential wells, separated by 5.3 $\mu $m. To study the thermodynamics, we load an ultra-cold mixture of N$_{1} \quad =$ 800 spin \textonehalf -up and N$_{2}$ \textless N$_{1}$ spin \textonehalf -down $^{6}$Li atoms into each well and image the individual cloud profiles as a function of interaction strength and spin imbalance N$_{2}$/N$_{1}$. The measured properties are in disagreement with 2D-BCS theory, but can be fit by a 2D-polaron gas model, where each atom is surrounded by a cloud of particle-hole pairs of the opposite spin. However, this model fails to predict a transition to a spin-balanced central region as N$_{2}$/N$_{1\, }$is increased.