Hall response and geometric squeezing of a degenerate Fermi gas

We report on the realization of a geometrically squeezed state of a rapidly rotating atomic Fermi gas and the measurement of its Hall response. Geometric squeezing relies on the non-commutativity of orbit center coordinates in a rotating frame - analogous to magnetron motion of ions in a magnetic field. A rotating, elliptical harmonic trap realizes the squeezing Hamiltonian for guiding center motion. The Fermi gas thus shrinks down in one direction to a size limited, via Pauli exclusion, to the width of the highest occupied cyclotron mode. In the orthogonal direction it expands exponentially, at a local speed given by the local Hall drift velocity, analogous to the E x B drift of charged particles in crossed electric and magnetic fields. Our work paves the way towards studying quantum Hall physics with atomic Fermi gases.