Quantum state preparation and transfer based on the bound state in the doublon continuum

TL;DR

This work identifies a bound state embedded in the doublon continuum (BIDC) in a four-atom, strongly interacting waveguide QED setup and shows how it can be harnessed for remote multi-atom entanglement and coherent state transfer. By deriving an effective doublon-based model and establishing a one-to-one mapping between the closed-system BIDC and the open-system dark state, the authors achieve high-fidelity dissipative preparation of the remote entangled state and demonstrate QST between distant type-II atom pairs with preserved amplitude and phase. The approach combines numerical diagonalization, an effective Hamiltonian after eliminating single-photon channels, and master-equation dynamics to validate both entanglement generation (fidelities around 0.97–0.99) and robust state transfer, including nonadiabatic regimes. Overall, the results provide a scalable resource for multi-particle entanglement generation and routing in strongly correlated photonic media, opening routes to interaction-protected quantum communication via many-particle BICs.

Abstract

Bound states in the continuum (BICs) have attracted intense interest, yet their many-particle counterparts remain largely unexplored in waveguide quantum electrodynamics. We identify and characterize a bound state embedded in the doublon continuum (BIDC) that emerges when four atoms couple to a coupled-resonator waveguide with strong on-site interaction. Exploiting this interaction-enabled BIDC, we show that (i) a distant, four-atom entangled state can be prepared with high fidelity, and (ii) quantum entangled states can be coherently transferred between spatially separated nodes. Our results establish a scalable mechanism for multi-particle state generation and routing in waveguide platforms, opening a route to interaction-protected quantum communication with many-particle BICs.

Figures (5)

• Figure 1: (a) Sketch of the waveguide QED setup. (b) The energy spectrum of the CRW.
• Figure 2: (a) The eigenenergy of the whole structure. (b) The atomic excitation probability amplitude. (c) The photon distribution of the BIDC. The two panels correspond to the one-photon component $P_{\rm{one}}$ and the two-photon component $P_{\rm{two}}$, respectively. For $P_{\rm{two}}(j)$, the numerical results are represented by the green bars, while the results from Eq. (\ref{['cmn']}) are shown by the purple circles. (d,e) The two-photon probability distribution of the eigenstates $q=78$ and $q=75$. (a-e) The parameters $N_c=148$, $N_1=0,N_2=8$, $U=6J$, $\Omega_i=\mathcal{E}_{\pi/2}/2$ and $g_i=0.1J$ ($i=1,2,3,4$).
• Figure 3: (a) The fidelity of $|D\rangle=(\mathcal{A}_1^\dagger -\mathcal{A}_2^\dagger)|G\rangle/{\sqrt{2}}$, with $g_1=g_3=g$ and $\Delta N=8$. The purple solid and red dot-dashed curves correspond to $t_0\rightarrow\infty$. The green dashed curve, with a driving time $t_0\simeq 7.3\times 10^{4}/J$, is otherwise identical to the purple solid curve. (b) The fidelity of $|D\rangle=(2\mathcal{A}_1^\dagger -\mathcal{A}_2^\dagger)|G\rangle/{\sqrt{5}}$ (the blue solid curve) and $|D\rangle=(4\mathcal{A}_1^\dagger +\mathcal{A}_2^\dagger)|G\rangle/{\sqrt{17}}$ (the purple dashed curve). The other parameters are set as $2\Omega=\mathcal{E}_{\pi/2}$ and $\eta=3\times10^{-5}J$.
• Figure 4: The excitation probability of atomic pairs in the long time (a) and short time (b) state transfer protocol. (c) The projection $P(t)$. (d) The angle of amplitude $\theta$. The parameters are given in the main text.
• Figure 5: The interaction strength $|f_K(r)|$.