“…where q = p y / defines the quasimomentum,Î is the identity matrix, andŜ x,y,z are the Pauli matrices for spin-1 particles. Unlike the nominal SO-coupling term qŜ z already discussed in Raman-dressed spin-1 atoms [42,43], the SO coupling we realize here is of the form qŜ 2 z , acting as an effective momentum-dependent quadratic Zeeman shift, a coupling between the spin tensor and linear momentum. This same term was recently proposed by Luo et al in a spin-1 atom by introducing an extra Raman laser [44].…”