Long-range waveguide-quantum electrodynamics with left-handed transmission lines

TL;DR

This paper introduces a waveguide-QED system with a left-handed transmission line that provides native long-range interactions, enabling new possibilities for quantum information processing.

Contribution

It demonstrates how a left-handed transmission line can emulate a synthetic photonic lattice with tunable long-range couplings, unlike traditional short-range models.

Findings

The system exhibits algebraic localization of bound states.

Photon propagation is accelerated due to long-range interactions.

A unified framework links waveguide dispersion to state profiles.

Abstract

While engineering long-range light-matter interactions is the principal aim in waveguide-QED, ironically most of the building blocks rest on local short-range couplings, such as nearest-neighbor-coupled cavity arrays employed in canonical models. Here, we propose a waveguide-QED system with native long-range interactions, comprising a single emitter coupled to a left-handed transmission line (LHTL). Interestingly, the LHTL emulates a synthetic photonic lattice with a slow logarithmic decay of hopping amplitudes over a distance set entirely by the ratio of UV and IR cutoffs of line dispersion. Its intrinsic long-range nature manifests both in the properties of atom-photon bound and scattering states, which exhibit algebraic localization and accelerated photon propagation respectively. Using a method of 'running exponents', we develop a unified picture connecting waveguide dispersion to bound state and light front profiles obtained in the strong long-range hopping regime. These results motivate how transmission lines can enable multi-qubit information processing with tunable-range interactions.