5 v 1 1 F eb 1 99 9 Quantum limit of photon - photon interactions using electromagnetically induced transparency

Quantum limit of dissipation-free photon-photon interactions at the few photon level is studied in the context of giant Kerr nonlinearities in cavity electromagnetically induced transparency (EIT). It is shown that photon-photon interaction is largest when the cavity contains a single atom. In contrast to conventional nonlinearities, increasing the number of atoms cannot increase the interaction strength but will in general degrade the performance by enhancing dispersion. In the non-perturbative regime, the single-atom photonphoton interaction can be limited by lossy states excited from long-lived EIT states. Asymptotically, in the strong coupling limit, photon-photon interaction is determined by the single photon-atom coupling strength. Photon blockade occurs for single atoms but only partial blockade can occur for low dispersion and not at all in the high-dispersion limit of the multi-atom case. 42.50.Dv, 03.65.Bz, 42.50.Lc Typeset using REVTEX