Cavity-Assisted Dynamical Spin-Orbit Coupling in Cold Atoms

We consider ultracold atoms subjected to a cavity-assisted two-photon Raman transition. The Raman coupling gives rise to effective spin-orbit interaction which couples atom's center-of-mass motion to its pseudospin degrees of freedom. Meanwhile, the cavity photon is dynamically affected by the atom. This feedback between atom and photon leads to a dramatic modification of the atomic dispersion relation, and further leads to dynamical instability of the system. We propose to detect the change of cavity photon number as a direct way to demonstrate dynamical instability.