Formation of a vortex lattice in a rotating BCS Fermi gas

We investigate theoretically the formation of a vortex lattice in a superfluid two-spin component Fermi gas in a rotating harmonic trap, in a BCS-type regime of condensed non-bosonic pairs. Our analytical solution of the superfluid hydrodynamic equations, both for the 2D BCS equation of state and for the 3D unitary quantum gas, predicts that the vortex free gas is subject to a dynamic instability for fast enough rotation. With a numerical solution of the full time dependent BCS equations in a 2D model, we confirm the existence of this dynamic instability and we show that it leads to the formation of a regular pattern of quantum vortices in the gas.