Sorting quantum fields into different modes according to their Fock-space quantum numbers is a highly desirable quantum operation. In this Letter, we show that a pair of two-level emitters, chirally coupled to a waveguide, may scatter single- and two-photon components of an input pulse into orthogonal temporal modes with a fidelity ≳0.9997. We develop a general theory to characterize and optimize this process and observe an interesting dynamics in the two-photon scattering regime: while the first emitter gives rise to a complex multimode field, the second emitter recombines the field amplitudes and the net two-photon scattering induces a self-time reversal of the pulse mode. The presented scheme can be employed to construct logic elements for propagating photons, such as a deterministic nonlinear-sign gate with a fidelity ≳0.9995
@article{arxiv.2202.06992,
title = {Deterministic Photon Sorting in Waveguide QED Systems},
author = {Fan Yang and Mads M. Lund and Thomas Pohl and Peter Lodahl and Klaus Mølmer},
journal= {arXiv preprint arXiv:2202.06992},
year = {2022}
}