Bound state in the continuum and multiple atom state transfer applications in a waveguide QED setup

TL;DR

This work demonstrates bound states in the continuum (BICs) in a bidirectional waveguide-QED setup where two spatially separated atomic arrays couple to a coupled-resonator waveguide with time-dependent couplings. The BICs create time-independent eigenfrequencies $\Omega_p$ and a standing-wave photonic channel between the arrays, enabling high-fidelity transfer of arbitrary single-excitation states via adiabatic and nonadiabatic protocols, with fidelities exceeding $>99\%$ and robustness to disorder and dissipation. The approach does not require nonreciprocal devices or chiral couplings, and scales to larger atomic arrays, offering a robust resource for quantum information processing in realistic waveguide platforms. By combining analytical proofs of $N_a$ BICs with numerical spectra and dynamic tunneling analyses, the paper provides a practical framework for BIC-enabled quantum state engineering in waveguide-QED systems.

Abstract

Bound states in the continuum (BICs) have been extensively exploited to enhance light--matter interactions in metamaterials, yet their emergence and utility in multi-atom waveguide platforms remain far less explored. Here we study atom--waveguide-dressed BICs in a one-dimensional coupled-resonator waveguide, where two spatially separated atomic arrays couple to distinct resonators with time-dependent strengths. We show that these BICs support a standing-wave photonic mode and enable the transfer of an arbitrary unknown quantum state between the two arrays with fidelities exceeding $99\%$. The protocol remains robust against both disorder and intrinsic dissipation. Our results establish BICs as long-lived resources for high-fidelity quantum information processing in waveguide-QED architectures.

Figures (6)

• Figure 1: Schematic of BIC-enabled state transfer between two atomic arrays in a coupled-resonator waveguide. The waveguide consists of coupled resonators with hopping strength $J$. Each array contains $N_a$ atoms and couples to the $N_1$th and $N_2$th resonators with time-dependent strengths $g(t)$ and $g'(t)$, respectively.
• Figure 2: (a) Imaginary parts of the eigenfrequencies of $\hat{H}'(t)$ as a function of the coupling ratio $g/g'$. (b) and (c) Dynamics of the AST and NAST fidelities, respectively. We set $J=2\pi\times 200\,{\rm MHz}$, $a=0.4J$, $N_{c}=41$, $N_{a}=3$, $\Delta N=20$, $\Omega_{1}=-2J\cos(11\pi/20)$, $\Omega_{2}=0$, and $\Omega_{3}=-2J\cos(9\pi/20)$ in all panels. The remaining parameters are $T=1.6061\,{\rm \mu s}$ in (b) and $T=0.1678\,{\rm \mu s}$ in (c).
• Figure 3: (a) Photonic dynamics during the NAST protocol. (b) NAST fidelity versus disorder strength $\delta$ for on-site frequency, inter-resonator hopping and atom-waveguide coupling disorder. (c) NAST fidelity as a function of the resonator decay rate $\kappa$ for different atomic energy-relaxation times $T_{1}$. (d) NAST fidelities for $100$ randomly sampled input states. Parameters are $J=2\pi\times200\,\mathrm{MHz}$, $a=2\pi\times80\,\mathrm{MHz}$, $T=0.1678\,\mathrm{\mu s}$, $N_{c}=41$, $\Delta N=20$, and $N_{a}=3$ in all panels. In (d), we set $T_{1}=10\,\mathrm{\mu s}$ and $\kappa=0.5\,\mathrm{MHz}$.
• Figure S1: (a) and (b) Partial energy spectra for $N_{a}=3$ and $N_{a}=4$, respectively. Solid lines represent BICs, dash-dotted lines denote the nearest scattering states, and dashed lines indicate other scattering states.
• Figure S2: (a) Dynamics of the NAST fidelity. (b) NAST fidelity as a function of the resonator decay rate $\kappa$ for different atomic energy-relaxation times $T_{1}$. (c) NAST fidelities for $100$ arbitrary input states. The parameters are $J=2\pi\times200\,{\rm MHz}$, $a=0.5J$, $T=0.4187\,{\rm \mu s}$, $N_{c}=101$, $\Delta N=50$, and $N_{a}=4$ in all panels. The state is chosen as $C_{1} = \sqrt{5}/5$, $C_{2} = (\sqrt{10}/5)e^{i\pi/5}$, $C_{3} = (\sqrt{5}/5)e^{i\pi/3}$, and $C_{4} = (\sqrt{5}/5)e^{i\pi/10}$ in (a) and (b). In (c), we set $T_{1}=10\,{\rm \mu s}$ and $\kappa=0.5\,{\rm MHz}$.