  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.
