Goos-Hänchen shifts in spin-orbit-coupled cold atoms

We consider a matter wave packet of cold atom gas impinging upon a step potential created by an optical light field. In the presence of spin-orbit coupling, the atomic eigenstates contain two types of evanescent states, one of which is an ordinary evanescent state with a pure imaginary wave vector while the other possesses a complex wave vector and is recognized as an oscillating evanescent state. We show that the presence and interplay of these two types of evanescent states can give rise to two different mechanisms for total internal reflection, and thus lead to an unusual Goos-H\"anchen (GH) effect. As a result, not only large positive but also large negative GH shifts can be observed in the reflected atomic beam. The dependence of the GH shift on the incident angle, energy, and height of the step potential is studied numerically.