Photonic scattering in 2D waveguide QED: Quantum Goos-H\"anchen shift

TL;DR

This paper develops a scattering theory for 2D waveguide QED, revealing a quantum Goos-H"anchen shift that can be tuned by photon frequency and injection configuration, advancing understanding of higher-dimensional light-matter interactions.

Contribution

It introduces a comprehensive Green function-based scattering framework for 2D WQED and uncovers tunable quantum Goos-H"anchen shifts in multi-port photonic scattering scenarios.

Findings

Quantum Goos-H"anchen shift can be enhanced in backward scattering with off-centered injection.

Symmetry considerations lead to no shift when injecting into the center port.

Shift magnitude is proportional to the phase derivative with respect to transverse momentum.

Abstract

Quantum emitters coupled to traveling photons in waveguides, known as waveguide quantum electrodynamics (WQED), offer a powerful platform for understanding light-matter interactions and underpinning emergent quantum technologies. While WQED has been extensively studied in one dimension, two-dimensional (2D) WQED remains largely unexplored, where novel photonic scattering phenomena unique to higher dimensions are expected. Here, we present a comprehensive scattering theory for 2D WQED based on the Green function method. We show that the mean displacement between emitted and injected photons serves as a quantum analogue of the Goos-H\"anchen shift. When a photon is injected into a single off-centered port, the quantum Goos-H\"anchen (QGH) shift can be enhanced in backward scattering under resonant conditions with subradiant states. When a photon is injected into the center port, there is no QGH shift due to the mirror symmetry of structure. However, for multiple-port injection with transverse momentum, the QGH shift is recovered and proportional to the derivative of phase with respect to transverse momentum. Unlike the classical Goos-H\"anchen shift, these effects can be flexibly tuned by the injected photon's frequency. Our work provides a general framework for exploring and manipulating photonic scattering in complex WQED networks.