Quantum logic gates using photon exchange interactions

Summary form only given. Nonlinear interactions between two photons are normally very weak because of the weak electric field associated with a single photon. We recently suggested that this difficulty could be avoided by relying on exchange interactions, which can have large effects even when there is no physical interaction at all between two particles. We consider two photons in well collimated beams that are incident upon an atomic vapor cell. The probability of there being two excited atoms in the medium is shown to be a factor of two larger in that case than if the two photons were incident upon two separate but otherwise identical media.