Multiple Emitters in a Waveguide: Non-Reciprocity and Correlated Photons at Perfect Elastic Transmission

TL;DR

This paper explores how multiple detuned emitters in a waveguide can produce non-reciprocal photon transmission and generate correlated photons through interference and inelastic scattering effects, with potential applications in quantum information processing.

Contribution

It demonstrates that a pair of detuned two-level systems can mimic a three-level system, revealing conditions for transparency, non-reciprocity, and photon correlations in waveguide QED setups.

Findings

A pair of detuned 2LS mimics a 3LS in photon interactions.

Transparency occurs at specific separations, quenching fluorescence.

Non-reciprocity arises from inelastic scattering near dark states.

Abstract

We investigate interference and correlation effects when several detuned emitters are placed along a one-dimensional photonic waveguide. Such a setup allows multiple interactions between the photons and the strongly coupled emitters, and underlies proposed devices for quantum information processing. We show, first, that a pair of detuned two-level systems (2LS) separated by a half wavelength mimic a driven {\Lambda}-type three-level system (3LS) in both the single- and two- photon sectors. There is an interference-induced transparency peak at which the fluorescence is quenched, leaving the transmitted photons completely uncorrelated. Slightly away from this separation, we find that the inelastic scattering (fluorescence) is large, leading to nonlinear effects such as non-reciprocity (rectification). We connect this non-reciprocity to inelastic scattering caused by driving a dark pole and so derive a condition for maximum rectification. Finally, by placing a true 3LS midway between the two 2LS, we show that elastic scattering produces only transmission, but inelastic scattering nevertheless occurs (the fluorescence is not quenched) causing substantial photon correlations.