An inhomogeneous density broadening, induced by harmonic trapping, causes local averaging of observables and washes out sharp features found near phase transitions. To solve this problem, several groups demonstrated in recent years the creation of homogeneous ultracold gases. Here we report on the first experimental realization of a homogeneous degenerate Fermi gas of 40K atoms in an optical box potential. For the density to be uniform, it is not enough to introduce exquisitely sharp repulsive walls, but it is crucial also to cancel the gravitational potential. This requirement turns out to be extremely challenging to achieve with 40K since the different spin states have different magnetic dipole moments, thus magnetic levitation cannot be used. We solve this problem by simultaneously applying a magnetic field gradient and an rf pulse that induces rapid Rabi oscillations between the two spin states and average out to zero the residual gravity. Using absorption imaging and in-situ Raman spectroscopy [1], we find that this procedure yields a homogeneous density distribution for both spins and does not lead to heating. We probe the normal state of the homogenous gas in the BEC-BCS crossover regime using our recently developed high-sensitivity rf spectroscopy technique [2] and extract the contact parameter of a homogeneous gas with high precision, which can be used to benchmark many-body theories.

[1] Constantine Shkedrov, Gal Ness, Yanay Florshaim, and Yoav Sagi, Phys. Rev. A 101, 013609 (2020).
[2] Constantine Shkedrov, Yanay Florshaim, Gal Ness, Andrey Gandman, and Yoav Sagi, Phys. Rev. Lett. 121, 093402 (2018).