### Large Kerr Nonlinearity and Photon Blockade

A fundamental challenge for nonlinear optics is the realization of systems able to mediate strong interactions between light fields at the single- or few-photon level in an environment with minimal dissipation. Stimulating this challenge in large part is the explosion of interest in quantum communication and quantum computing for which such conditional quantum dynamics is vital. For example, a strong Kerr-effect device with minimal losses is the missing required element for an optical realization of a universal quantum computer over continuous variables. A strong nonlinear interaction between single photons is required for high-efficiency Bell state analysis of photon pairs, which is in turn essential for the high-fidelity teleportation.

An interesting system that could yield sufficiently large nonlinearities has been proposed by A. Imamoglu and colaborators by making use of electromagnetically induced transparency (EIT) in a four-level atom to reduce decoherence rates. Predicted photon blockade effect work as follows: when first photon enters the cavity, large Kerr nonlinearity switches the cavity off the resonance with the incoming field, thus blocking the second (and subsequent) photons from entering before the first one leaks out. Original proposal was concerned with weak-coupling regime in a many-atom system. It was shown, however, that such a system yields predicted results only in a very narrow bandwidth around the central frequency of the field, due to strong nonlinear dispersion of the atomic medium. This implies that the photon blockade does not work well as a switch, because the response time of the system is very long.

As an alternative to the atomic medium, we have considered a single four-level atom in a high-finesse cavity. We have performed a thorough analysis of the system dynamics using a dressed states approach, and a numerical simulations of the full master equation for the system. It is shown that a photon blockade effect equivalent to that for an ideal Kerr nonlinearity can be obtained in this system.

But it is known that photon blockade can be achieved in a two-level atom system, described by Jaynes-Cummings model. We compare this model with the proposed EIT-Kerr scheme. The magnitude of the nonlinearity is limited by the single atom-cavity coupling strength in both systems. The principal advantage of the scheme based on EIT is the absence of quantum noise due to cavity and atomic dissipation, which in turn enables one to realise effective two-level behaviour for the atom-cavity system with long coherence times. The nonlinearity of the Jaynes-Cummings scheme decreases gradualy with increasing number of atoms. For the EIT-Kerr scheme it decreases abruptly for any number of atoms greater than one, but can be restored by introduction of an additional detuning in an atomic energy-level scheme.