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arXiv:2110.06093

Photonic Bound States and Scattering Resonances in Waveguide QED

Bastian Bakkensen, Yu-Xiang Zhang, J. Bjerlin, Anders Søndberg Sørensen

Published Oct 12, 2021• 4 citations
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Abstract

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.

DOI
10.48550/arxiv.2110.06093

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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.
One-dimensional confinement in waveguide quantum electrodynamics (QED) plays a crucial role to enhance light-matter interactions and to induce a strong quantum nonlinear optical response. In two or higher-dimensional settings, this response is reduced since photons can be emitted within a larger phase space, opening the question whether strong photon-photon interaction can be still achieved. In this study, we positively answer this question for the case of a 2D square array of atoms coupled to the light confined into a two-dimensional waveguide. More specifically, we demonstrate the occurrence of long-lived two-photon repulsive and bound states with genuine 2D features. Furthermore, we observe signatures of these effects also in free-space atomic arrays in the form of weakly subradiant in-band scattering resonances. Our findings provide a paradigmatic signature of the presence of strong photon-photon interactions in 2D waveguide QED.
We theoretically study the few-and many-body dynamics of photons in chiral waveguides.In particular, we examine pulse propagation through an ensemble of N two-level systems chirally coupled to a waveguide.We show that the system supports correlated multiphoton bound states, which have a welldefined photon number n and propagate through the system with a group delay scaling as 1=n 2 .This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system.For sufficiently many photons and sufficiently short systems, we show that linear combinations of n-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency.Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition.Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons.Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters.Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED.
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We study the problem of two-photon routing in waveguide QED ladders where a few two-level quantum emitters (QEs) are simultaneously coupled with two chiral waveguides. We analyze the routing probability in two regimes, namely, under a purely plane wave approximation (scattering case) and in the presence of photon-photon bound state formation. Within the scattering case, we examine the two-photon routing in the presence of up to five QEs, considering two possibilities separately: ideal-symmetric coupling and the critical coupling scenario. We examine the photon routing up to the two QEs for the bound state situation and compare the photon redirection efficiency with the corresponding scattering case. Our findings show the potential of utilizing chiral light-matter interactions in multi-photon and multi-emitter-based quantum networking protocols where interlinking among spatially distant nodes is required.
Bound states arise in waveguide QED systems with a strong frequency-dependence of the coupling between emitters and photonic modes. While exciting such bound-states with single-photon wave-packets is not possible, photon-photon interactions mediated by the emitters can be used to excite them with two-photon states. In this Letter, we use scattering theory to provide upper limits on this excitation probability for a general non-Markovian waveguide QED system and show that this limit can be reached by a two-photon wave packet with vanishing uncertainty in the total photon energy. Furthermore, we also analyze multi-emitter waveguide QED systems with multiple bound states and provide a systematic construction of two-photon wave packets that can excite a given superposition of these bound states. As specific examples, we study bound-state trapping in waveguide QED systems with single and multiple emitters and a time-delayed feedback.