Nonlinear quantum optics for spinor slow light

We investigate quantum nonlinear effects at a level of individual quanta in a double-tripod atom-light coupling scheme involving two atomic Rydberg states. In such a scheme the slow light coherently coupled to strongly interacting Rydberg states represents a two-component or spinor light. The scheme provides additional possibilities for the control and manipulation of light quanta. A distinctive feature of the proposed setup is that it combines the spin-orbit coupling for the spinor slow light with an interaction between the photons, enabling generation of the second probe beam even when two-photon detuning is zero. Furthermore, the interaction between the photons can become repulsive if the one-photon detunings have opposite signs. This is different from a single-ladder atom-light coupling scheme in which the interaction between the photons is attractive for both positive and negative detunings as long as the Rabi frequency of the control beam is not too high.