Subradiant edge states in an atom chain with waveguide-mediated hopping

Ciaran McDonnell1 and Beatriz Olmos1,2

1School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, Nottingham, NG7 2RD, United Kingdom
2Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany

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We analyze the topological and dynamical properties of a system formed by two chains of identical emitters coupled to a waveguide, whose guided modes induce all-to-all excitation hopping. We find that, in the single excitation limit, the bulk topological properties of the Hamiltonian that describes the coherent dynamics of the system are identical to the ones of a one-dimensional Su-Schrieffer-Heeger (SSH) model. However, due to the long-range character of the exchange interactions, we find weakening of the bulk-boundary correspondence. This is illustrated by the variation of the localization length and mass gap of the edge states encountered as we vary the lattice constant and offset between the chains. Most interestingly, we analytically identify parameter regimes where edge states arise which are fully localized to the boundaries of the chain, independently of the system size. These edge states are shown to be not only robust against positional disorder of the atoms in the chain, but also subradiant, i.e., dynamically stable even in the presence of inevitable dissipation processes, establishing the capacity of waveguide QED systems for the realization of symmetry protected topological phases.

The emergence of so-called edge states as a hallmark of a topological phase, e.g. electrons skipping along the boundaries of a 2D electon gas in the Quantum Hall effect, is well known in non-interacting systems and also in systems where short-ranged hopping is possible. In this paper, we demonstrate the presence of these edge states in a fully-connected system, i.e., where excitation hopping may happen across all nodes in the network. We base our theoretical study on a quantum optics platform that is nowadays not only experimentally feasible but also one of the candidates for the realization of quatum information processing: a gas of atoms coupled to a nanophotonic waveguide. We find that states that are localized on the boundaries of a chain of emitters can be created, which, moreover, possess an extremely long lifetime due to the presence of collective dissipation in the system.

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