Collective effects in biphoton generation of a four-wave-mixing process

Abstract

The generation of biphotons remains an important field of research, as several applications require such sources. For instance, some of their properties are fundamental in quantum communication, quantum computing, and quantum imaging. Pairs of spatially correlated photons can be generated using four-wave-mixing (FWM) processes, taking advantage of the third-order nonlinear susceptibility χ3 effect. A FWM configuration consists of two counter-propagating excitation fields acting on a cold atomic cloud which spontaneously generates pairs of photons in opposite directions through the nonlinear effect. Current theoretical models used to explain FWM in two-level systems have disregarded atomic interactions and considered an independent atom approach. Nevertheless, recent experiments have shown evidence of collective (superradiant) behavior in these types of systems. In this context, we seek to understand the contributions of dipole-dipole interactions in the generation of biphotons. To this end, we propose to use an ab initio model to describe FWM in cold atomic clouds, where dipole-dipole interactions are accounted for. Our exact simulations with N = 7 atoms are compatible with the results from recent experiments. Furthermore, to simulate systems with a larger number of particles we derived and implemented a new scheme considering exclusively the single- and double-excitation subspace that is able to simulate systems of more than N = 100 scatterers.