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arXiv:2501.09417 · Physical Review Letters

Chiral Dissociation of Bound Photon Pairs for a Non-Hermitian Skin Effect

Jiaming Shi, Alexander N. Poddubny

Published May 27, 2025• 6 citations
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Abstract

We theoretically study the bound states of interacting photons propagating in a waveguide chirally coupled to an array of atoms. We demonstrate that the bound photon pairs can concentrate at the edge of the array and link this to the non-Hermitian skin effect. Unlike tight-binding non-Hermitian setups, the bound states in the waveguide-coupled array exhibit infinite radiative lifetimes when the array has an infinite size. However, in a finite array, non-Hermiticity and localization of bound pairs emerge due to their chiral dissociation into scattering states. Counterintuitively, when the photons are preferentially emitted to the right, the bound pairs are localized at the left edge of the array and vice versa.

DOI
10.1103/q6wr-2rt9

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We present a theoretical study of the two-particle spectrum ω(K)ω(K)ω(K) for the chiral waveguide QED setup of an array of two-level atoms directionally interacting with photons propagating along the waveguide. We demonstrate that for each pair center-of-mass momentum KKK there exist distinct solutions with ℑω≤0\Imω\le 0ℑω≤0 in the two-particle spectrum, corresponding to bound, antibound and resonance states, in addition to the continuum of scattering states. Contrary to previous studies, which showed the bound and resonance-state spectra only over a limited range of KKK, the calculated spectrum is consistent across all KKK values. An interesting finding is that the real part of the spectrum ℜω(K)\Re ω(K)ℜω(K) in the chiral model is gapless. The calculated dispersion law ω(K)ω(K)ω(K) provides an effective model for the bound photon pairs also in a finite-size array, manifesting the topological non-Hermitian skin effect.
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We study the emergence of two types of two-photon bounds states in waveguides of any chirality. Specifically, we present a systematic way of analytically determining the eigenstates of a system consisting of a waveguide coupled to a partially chiral, infinite array of equidistant two-level emitters. Using an effective Hamiltonian approach, we determine the properties of the two-photon bound states by determining their dispersion relation and internal structure. The bound states come in two varieties, depending on the two-photon momentum and emitter spacing. One of these states is a long-lived true bound state, whereas the other, a scattering resonance, decays in time via coupling to free two-photon states, leading to resonances and corresponding phase shifts in the photon-photon scattering.
We theoretically predict the formation of two-photon bound states in a two-dimensional waveguide network hosting a lattice of two-level atoms. The properties of these bound pairs and the exclusive domains of the parameter space where they emerge due to the interplay between the on-site photon blockade and peculiar shape of polariton dispersion resulting from the long-range radiative couplings between the qubits are investigated in detail. In addition, we analyze the effect of the finite-size system on localization characteristics of these excitations.
We study theoretically quantum eigenstates in an array of two-level atoms coupled to the waveguide. We show that this system features double-excited states where the two excitations are localized at the opposite edges of the array. Such bound states of distant excitations result from the long-ranged photon-mediated coupling in the waveguide setup, which mediates repulsion at larger distances. These results could be useful for the rapidly developing field of waveguide quantum electrodynamics, studying waveguide-coupled arrays of cold atoms or superconducting qubits.