Cavity-Assisted Spin Orbit Coupling

We consider a single ultracold atom trapped inside a single-mode optical cavity, where a two-photon Raman process induces an effective coupling between atom's pseudo-spin and external center-of-mass (COM) motion. Without the COM motion, this system is described by the Jaynes-Cummings (JC) model. We show how the atomic COM motion dramatically modifies the predictions based on the JC model. We also investigated the situation when cavity pumping and decay are taken into account. We take a quantum Master equation approach to study this open system and again show how the cavity-induced spin-orbit coupling affects the properties of the system.