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We analytically treat the scattering of two counter-propagating photons on a two-level emitter embedded in an optical waveguide. We find that the non-linearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could be quantified via a reduction in coincident clicks in a Hong-Ou-Mandel measurement setup, analogous to a linear beam splitter. Changes to the spectra and phase of the scattered photons, however, would lead to reduced interference with other photons when implemented in a larger optical circuit. We introduce suitable fidelity measures which account for these changes, and find that high values can still be achieved even when accounting for all properties of the scattered photonic state.
We develop a wavefunction approach to describe the scattering of two photons on a quantum emitter embedded in a one-dimensional waveguide. Our method allows us to calculate the exact dynamics of the complete system at all times, as well as the transm
Optical $chi^{(2)}$ non-linearity can be used for parametric amplification and producing down-converted entangled photon pairs that have broad applications. It is known that weak non-linear media exhibit dispersion and produce a frequency response. I
There has been rapid development of systems that yield strong interactions between freely propagating photons in one dimension via controlled coupling to quantum emitters. This raises interesting possibilities such as quantum information processing w
We describe a multi-mode quantum memory for propagating microwave photons that combines a solid-state spin ensemble resonantly coupled to a frequency tunable single-mode microwave cavity. We first show that high efficiency mapping of the quantum stat
Counter-propagating parametric conversion processes in non-linear bulk crystals have been shown to feature unique properties for efficient narrowband frequency conversion. In quantum optics, the generation of photon pairs with a counter-propagating p