Photon-Photon Interactions via Rydberg Blockade

We develop the theory of light propagation under the conditions of
electromagnetically induced transparency (EIT) in systems involving strongly
interacting Rydberg states. Taking into account the quantum nature and the
spatial propagation of light, we analyze interactions involving few-photon
pulses. We demonstrate that this system can be used for the generation of
nonclassical states of light including trains of single photons with an avoided
volume between them, for implementing photon-photon quantum gates, as well as
for studying many-body phenomena with strongly correlated photons.