Flattening a trapped atomic gas using a programmable optical potential in a feedback loop

We present a method for producing a flat, large-area Fermi gas of $^{6}\mathrm{Li}$ with a uniform area density. The method uses a programmable optical potential within a feedback loop to flatten the in-plane trapping potential for atoms. The optical potential is generated using a laser beam, whose intensity profile is adjusted by a spatial light modulator and optimized through measurements of the density distribution of the sample. The resulting planar sample exhibits a uniform area density within a region of about 480 $\textmu{}\mathrm{m}$ in diameter, and the standard deviation of the trap bottom potential is estimated to be $\ensuremath{\approx}{k}_{B}\ifmmode\times\else\texttimes\fi{}6.1$ nK, which is less than 20% of the transverse confinement energy. We discuss a dimensional crossover toward the two-dimensional regime by reducing the number of atoms in the planar trap, including the effect of the spatial variation of the transverse trapping frequency in the large-area sample.