Concept of the experiment. (A) Low-temperature phase diagram of the attractive Fermi gas at fixed temperature. In the normal, weakly interacting phase the two spin components move independently of each other in the QPC. In the superfluid phase large particle currents arise, whereas spin currents are strongly suppressed due to pairing. (B) Three-dimensional impression of the QPC, connected via an intermediate 2D region to large 3D reservoirs (shown only partly). (C) Effective potentials in the central region around the QPC along the transport axis y. It is the sum of the zero-point energy of the QPC (green dashed line: contribution from confinement along x), an attractive gate potential (purple dashed line), and the underlying harmonic trap (Materials and Methods). The black solid line corresponds to the parameters for which the conductance plateau in Fig. 3A is observed. Thin violet lines show how the effective potential evolves when is increased from to , whereas thin green lines depict the corresponding evolution when is increased from 13.2 kHz to 25.2 kHz. Note the two local minima of the effective potential at the entrance and exit of the QPC. (D) Absorption images of the and cloud components prepared before spin conductance measurements. (E) Chemical potentials and currents in the presence of a spin bias. (F) Absorption image of the atoms prepared for the particle transport, with identical bias for and (G) Chemical potentials and currents in the presence of a chemical potential bias.