  We investigate theoretically the deterministic generation of quantum states
with negative Wigner functions, by using giant non-linearities due to
collisional interactions between Rydberg polaritons. The state resulting from
the polariton interactions may be transferred with high fidelity into a
photonic state, which can be analyzed using homodyne detection followed by
quantum tomography. Besides generating highly non-classical states of the
light, this method can also provide a very sensitive probe for the physics of
the collisions involving Rydberg states.
