Controlled photon-photon interactions using Rydberg polaritons*

By coupling a strong optical transition to a highly-excited Rydberg state [1] it is possible to realise giant optical non-linearities [2] and hence strong photon-photon interactions [3-5]. A remaining challenge is to implement an interaction that does not distort the photon mode and hence to realise high-fidelity photonic quantum gates. In this talk we will discuss how to control the photon-photon interact using microwave fields [6] and how this could be used to implement deterministic non-linear optical computation [7].\\[4pt] [1] A. Mohapatra et al. Phys. Rev. Lett. {\bf 98}, 113003 (2007).\\[0pt] [2] J. Pritchard et al. Phys. Rev. Lett. {\bf 105}, 193603 (2010).\\[0pt] [3] Y. Dudin and A. Kuzmich, Science {\bf 336}, 887 (2012).\\[0pt] [4] T. Peyronel et al. Nature {\bf 488}, 57 (2012).\\[0pt] [5] D. Maxwell et al. Phys. Rev. Lett. {\bf 110}, 103001 (2013).\\[0pt] [6] D. Maxwell et al. arXiv:1308.1425\\[0pt] [7] D. Paredes-Barato and C. S. Adams, arXiv:1309.7933