Rashba cavity QED: a route towards the superradiant quantum phase transition.

We develop a theory of cavity quantum electrodynamics for a 2D electron gas in the presence of Rashba spin-orbit coupling and perpendicular static magnetic field, coupled to spatially nonuniform multimode quantum cavity photon fields. We demonstrate that the lowest polaritonic frequency of the full Hamiltonian can vanish for realistic parameters, achieving the Dicke superradiant quantum phase transition. This singular behaviour originates from soft spin-flip transitions possessing a non-vanishing dipole moment at non-zero wave vectors and can be viewed as a magnetostatic instability.