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arXiv:1708.00902 · Physical Review A

Chirality, band structure, and localization in waveguide quantum electrodynamics

Imran M. Mirza, Jeremy G. Hoskins, John C. Schotland

Published Nov 2, 2017• 54 citations
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Abstract

Architectures based on waveguide quantum electrodynamics have emerged as promising candidates for quantum networks. In this paper, we analyze the propagation of single photons in disordered many-atom waveguides. We pay special attention to the influence of chirality (directionality of photon transport) on the formation of localized photonic states, considering separately the cases of disorder in the atomic positions and in the atomic transition frequencies.

DOI
10.1103/physreva.96.053804

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Architectures based on waveguide quantum electrodynamics have emerged as promising candidates for quantum networks. In this paper, we analyze the propagation of single photons in disordered many-atom waveguides. We pay special attention to the influence of chirality (directionality of photon transport) on the formation of localized photonic states, considering separately the cases of disorder in the atomic positions and in the atomic transition frequencies.
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Waveguide quantum electrodynamics (wQED) has become a central platform for studying collective light-matter interactions in low-dimensional photonic environments. While conventional wQED systems rely on uniform chirality or reciprocal emitter-waveguide coupling, we propose a structured wQED framework, where the coupling directionality of each emitter can be engineered locally to control excitation transport in an atom-nanophotonic interface. For different combinations of patterned coupling directionalities of the emitters, we identify four representative configurations that exhibit distinct dynamical behaviors: centering, wave-like, leap-frog, and dispersion excitations. Spectral analysis of the effective non-Hermitian Hamiltonian reveals that these dynamics originate from interferences among subradiant eigenmodes. Variance analysis further quantifies the spreading of excitation as functions of interatomic spacing and global chirality, showing tunable localization-delocalization transitions. Including nonguided losses, we find that the transport characteristics remain robust for realistic coupling efficiencies (beta >= 0.99). These results establish structured wQED as a practical route to manipulate excitation localization, coherence, and transport through programmable directionality patterns, paving the way for controllable subradiant transport and chiral quantum information routing.
We consider the quantum electrodynamics of single photons in arrays of one-way waveguides, each containing many atoms. We investigate both chiral and antichiral arrays, in which the group velocities of the waveguides are the same or alternate in sign, respectively. We find that in the continuum limit, the one-photon amplitude obeys a Dirac equation. In the chiral case, the Dirac equation is hyperbolic, while in the antichiral case it is elliptic. This distinction has implications for the nature of photon transport in waveguide arrays. Our results are illustrated by numerical simulations.