We theoretically investigate the quantum statistical properties of light transmitted through an atomic medium with strong optical nonlinearity induced by Rydberg–Rydberg van der Waals interactions. In our setup, atoms are located in a cavity and nonresonantly driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of the weak signal field and a strong control beam. To characterize the transmitted light, we compute the second-order correlation function . The simulations we obtained on the specific case of rubidium atoms suggest that the bunched or antibunched nature of the outgoing beam can be chosen at will by tuning the physical parameters appropriately.
The Optical Parametric Oscillator (OPO) has been one of the most versatile source of non-classical states of light. Usual configurations of such devices are a macroscopic second order nonlinear crystals inside an optical cavity. Recently the use of silicon photonics techniques allowed the implementation of high quality factor microcavities and OPOs which include several technological advantages over usual configuration as a small size, bigger bandwidth, CMOS compatibility, facility to engineer the dispersion properties and compatibility with commercial optical fiber communications. Nevertheless the nonlinearity present within these systems is a third order nonlinearity for which theoretical calculations lack in the literature. Here we describe theoretically the quantum properties of the light generated in an OPO with a third order nonlinearity. We showed that the effects of phase modulation (which are not present in the second order nonlinearity) and dispersion are determinant in the way that oscillation and entanglement is produced in the system. Despite of these effects, bipartite and tripartite entanglement is predicted with the use of the Schmidt modes formalism. We also describe the system when there are more modes exited within the cavity and a frequency comb is formed. In such a situation, using again the Schmidt modes formalism, multipartite entanglement was predicted as well.
A second-order nonlinearity has been proposed as a way to perform a conditional phase gate between two photons. The process involves combining the two photons into a single one (parametric up-conversion) and subsequently splitting that one into two photons identical to the original ones (parametric down-conversion), except for an overall phase shift. We show here that, when the multimode nature of the initial photon wave packets is considered, this approach suffers from the same difficulties as the third-order (Kerr-based) methods: specifically, the final state of the photons is inevitably spectrally distorted and entangled. The maximum fidelity appears to be limited to
F<0.4 for a free-space configuration, but we find that this could theoretically be pushed to $F\ensuremath{\simeq}0.6$ if the nonlinear medium is placed in an optical cavity. We show analytically that this latter result is identical to what one would obtain from a third-order nonlinear medium in the same arrangement.