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Center for Nonlinear Studies |
We study the scaling of photon-photon correlations mediated by resonant interactions of photons with two-level emitters in a one-dimensional photonic waveguide. Recently a new theoretical approach based on the Bethe-ansatz technique has been developed to study transport in an open quantum impurity. Here we generalize the approach to study multiple emitters–for example, atoms or quantum dots. We derive the exact solution of single and two-photon scattering states, and corresponding photon transmission through the emitter ensemble. Correlations of photons at the both ends of the waveguide are examined carefully for one, two and three emitters. We show how various two-photon nonlinear effects, such as, spatial attraction and repulsion between photons as well as background fluorescence can be tuned by changing the number of emitters and the coupling between emitters (controlled by the separation). Finally we propose a simple scheme for non-reciprocal optical transmission in the waveguide by placing emitters with different transition energies. Our fully quantum-mechanical approach provides a better understanding of cascaded optical nonlinearity at the microscopic level.
Host: Kipton Barros, T-4 and CNLS