Matter wave Fourier optics with a strongly interacting two-dimensional Fermi gas

We demonstrate and characterize an experimental technique to directly image the momentum distribution of a strongly interacting two-dimensional quantum gas with high momentum resolution. We apply the principles of Fourier optics to investigate three main operations on the expanding gas: focusing, collimation and magnification. We focus the gas in the radial plane using a harmonic confining potential and thus gain access to the momentum distribution. We pulse a different harmonic potential to stop the rapid axial expansion which allows us to image the momentum distribution with high resolution. Additionally, we propose a method to magnify the mapped momentum distribution to access interesting momentum scales. All these techniques can be applied to a wide range of experiments and in particular to study many-body phases of quantum gases.