Hybrid Single-Ion Atomic-Ensemble Node for High-Rate Remote Entanglement Generation

Abstract

Different quantum systems possess different favorable qualities. On the one hand, ensemble-based quantum memories are suited for fast multiplexed long-range entanglement generation. On the other hand, single-atomic systems provide access to gates for processing of information. Both of those can provide advantages for high-rate entanglement generation within quantum networks. We develop a hybrid architecture that takes advantage of these properties by combining trapped-ion nodes and nodes comprised of spontaneous parametric down conversion photon pair sources and absorptive memories based on rare-earth ion ensembles. To this end, we solve the central challenge of matching the different bandwidths of photons emitted by those systems in an initial entanglement-generation step. This enables the parallel execution of multiple probabilistic tasks in the initial stage. We show that our approach can lead to a significant speed-up for the fundamental task of creating ion-ion entanglement over hundreds of kilometers in a quantum network.

Figures (4)

• Figure 1: Sketch of the protocol and device setups. (a) The edge-nodes (EN) consist of a trapped ion (in a cavity) and a spontaneous parametric down conversion source with attached multi-mode memory (SPDC+M) connected by fiber optics. After wavelength converting the SPDC photon to match the ion wavelength, the photons are interfered on a beamsplitter (BS) and measured with heralding detectors labeled $\pm$. (b) The backbone is composed entirely of SPDC+M nodes interconnected by optical fibers and heralding detectors. (c) Memory-memory swaps are also implemented using fiber optics, BS, and heralding detectors. (d) Ion-ion entanglement generation is generated using a single-click protocol over the long distance $L$ spanned by the backbone network. To this end, (i) backbone and edge-node entanglement is generated in parallel using the setups depicted in (a),(b); (ii) a swap (c) is performed between the edge-nodes and the closest backbone link. (iii) Finally, a swap in the center links the ions. (e) Performing the single-click scheme twice enables the use of purification. We consider a purification where local CNOTs followed by measurement of both controlled systems in $\mathinner{|{1}\rangle}$ post-selects a Bell state of higher fidelity.
• Figure 2: Matching the SPDC and ion photon flux within the edge-nodes. The correlation function of the photon pair $\mu(t)F(t,t')$ of all time-bins (c) emitted by the SPDC is split into a slowly varying envelope $\mu(t)$ (a) that we can use to match to the atomic photon $\nu(t)$ (b). Conditioned on the heralding click, (d) a short photon is stored within one of the time-bins of the multi-mode (ensemble) memory unless it is lost. For illustration we use $T_a / T_c = 100$.
• Figure 3: Duration to prepare a Bell state with $99\%$ fidelity as a function of length comparing different protocols. The dotted yellow (dash dotted green) line corresponds to direct ion-ion entanglement generation using a single-click protocol (with an ion node in the center as a repeater). The dashed blue (solid purple) lines correspond to the protocol proposed in this work without (with) a central multi-mode repeater. We take the efficiencies $\eta_m = 0.8$, $\eta = \eta_0' = \eta_{\text{FC}} = 0.9$, and $\eta' = \eta_0' \eta_{\text{FC}}$. The BB has $N_{\text{BB}} = 1000$ multiplexing modes and an efficiency $\eta_{\text{BB}} = \eta_0' \eta_F(L/n)$ where $\eta_F(l)$ is the fiber transmission efficiency for distance $l$ and an attenuation of $0.2\,$dB$/$km and $n = 4 (2)$ with(out) a repeater. For direct ion-ion generation the photon efficiency is $\eta_{\text{FC}} \eta \eta_F(L)$. Furthermore we use a dark-count rate of $10^{-3}\,$Hz, a pulse duration of the ions of $10\,$µs, a acceptance window in the backbone of $1\,$µs (i.e., $N=10$), correlation duration of $100\,$ns, a detector resolution of $1\,$ns, and the speed of light in fiber as $2/3$ the vacuum speed of light.
• Figure 4: Optimal emission probabilities corresponding to the results displayed in Fig. 3 of the main text. The line styles encode the protocols and follow Fig. 3 of the main text. The thin lines in (b) correspond to the semi-analytic approach [see Eq. \ref{['eq:opt_theta']}]. In panel (a) we show the emission probability of the ions $\mathinner{|{\alpha_1}|}^2$, in (b) of the SPDC connecting memory and ions in the end-nodes $\mathinner{|{\beta_1}|}^2$ and in (c) of the SPDC within the BB $\mathinner{|{\gamma_1}|}^2$.