The coupling of the spin of electrons to their motional state lies at the
heart of recently discovered topological phases of matter. Here we create and
detect spin-orbit coupling in an atomic Fermi gas, a highly controllable form
of quantum degenerate matter. We reveal the spin-orbit gap via spin-injection
spectroscopy, which characterizes the energy-momentum dispersion and spin
composition of the quantum states. For energies within the spin-orbit gap, the
system acts as a spin diode. To fully inhibit transport, we open an additional
spin gap, thereby creating a spin-orbit coupled lattice whose spinful band
structure we probe. In the presence of s-wave interactions, such systems should
display induced p-wave pairing, topological superfluidity, and Majorana edge
states
