%0 Journal Article %J Physical Review Letters %D 2011 %T Photon-Photon Interactions via Rydberg Blockade %A Alexey V. Gorshkov %A Johannes Otterbach %A Michael Fleischhauer %A Thomas Pohl %A Mikhail D. Lukin %X 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. %B Physical Review Letters %V 107 %8 2011/9/22 %G eng %U http://arxiv.org/abs/1103.3700v1 %N 13 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.107.133602 %0 Journal Article %J Physical Review Letters %D 2010 %T Photonic Phase Gate via an Exchange of Fermionic Spin Waves in a Spin Chain %A Alexey V. Gorshkov %A Johannes Otterbach %A Eugene Demler %A Michael Fleischhauer %A Mikhail D. Lukin %X We propose a new protocol for implementing the two-qubit photonic phase gate. In our approach, the pi phase is acquired by mapping two single photons into atomic excitations with fermionic character and exchanging their positions. The fermionic excitations are realized as spin waves in a spin chain, while photon storage techniques provide the interface between the photons and the spin waves. Possible imperfections and experimental systems suitable for implementing the gate are discussed. %B Physical Review Letters %V 105 %8 2010/8/5 %G eng %U http://arxiv.org/abs/1001.0968v3 %N 6 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.105.060502