Engineering photonic dispersion relation and atomic dynamics in waveguide QED setup via long-range hoppings

TL;DR

This paper demonstrates how to engineer linear and non-linear dispersion relations in waveguide QED systems using long-range hoppings, enabling precise control of atomic dynamics and directional radiation.

Contribution

It introduces a method to design arbitrary dispersion relations in coupled-resonator waveguides through tailored long-range hoppings, advancing control over atom-photon interactions.

Findings

Linear dispersion relations with chiral characteristics achieved.

Waveguides can serve as platforms for directional atomic radiation.

Arbitrary dispersion relations, including quadratic and cubic, can be realized.

Abstract

Non-trivial dispersion relations engineered in photonic waveguide for the precise control of atomic dynamics has recently attracted considerable attention. Here, we study a system in which atoms are coupled to one-dimensional coupled-resonator waveguides with long-range hoppings. By carefully engineering the jth-order nearest neighbor (JNN) hoppings between resonators, we construct linear dispersion relations with the chiral characteristic. To quantify the degree of linearity, we analyze the propagation fidelities of Gaussian wave packets in these waveguides. Furthermore, we demonstrate that such coupled-resonator waveguides can serve as versatile platforms for enabling directional atomic radiation and absorption. Beyond linear dispersion relations, more general forms, including quadratic and cubic relations, can also be achieved through tailored JNN-hoppings. Our study thus provides a unified framework for simulating atom-environment couplings with arbitrary dispersion relations.