Spatial quench of Fermi-superfluid for extracting critical exponents

In ultracold atomic systems, the parameters in the Hamiltonian can be driven across a critical point to induce a quantum phase transition. The proximity effect of superconductivity has a similar setup where the interaction vanishes across an interface. We study interface properties of Fermi superfluid next to a normal Fermi gas. The inhomogeneous system is described by Bogoliubov-de-Gennes equations. The superfluid correlation penetrates the normal region. The frozen correlation length within the critical regime leads to scaling behavior. We follow the Kibble-Zurek mechanism to extract the critical exponents from the pairing correlation and compare to the Ginzburg-Landau theory. We also study step-function quench, which may establish a connection between atomic gases and superconductors.