Two-dimensional quasi-ideal Fermi gas with Rashba spin-orbit coupling

We investigate the zero-temperature properties of a quasi-ideal Fermi gas with Rashba spin-orbit coupling. We find that the spin-orbit term strongly affects the speeds of zero sound and first sound in the Fermi gas, due to the presence of a third-order quantum phase transition. In addition, including a 2D harmonic confinement we show that also the shape of the density profile of the cloud crucially depends on the strength of the Rashba coupling.