Heterogeneous entanglement between a trapped ion and a solid-state quantum memory

The gist The resulting entangled state achieves a fidelity of (89.21 ± 2.23)% and violates the CHSH-Bell inequality by 6 standard deviations (S = 2.328 ± 0.055), confirming nonlocality between two heterogeneous nodes

Hybrid Architecture

The paper demonstrates a prototype hybrid quantum network that entangles a trapped-ion node and a solid-state quantum memory node operating at distinct wavelengths This architecture establishes entanglement between a quantum processing module with a multiplexed quantum memory node, representing a key step toward a scalable, multifunctional quantum internet The conceptual architecture of the hybrid quantum network comprises heterogeneous nodes with distinct physical platforms and functionalities The two nodes are connected via a 90-m single-mode fiber (SMF) serving as the quantum channel

Entanglement Generation Process

The entanglement is generated between a trapped-ion (TI) processor node and a solid-state quantum memory (QM) node via a polarization-maintaining quantum frequency conversion (QFC) module A spin-entangled photon emitted from the TI node is frequency-converted via a polarizationmaintaining quantum frequency conversion (QFC) module and subsequently stored in, and retrieved on demand from a waveguide-integrated QM The process involves several steps, including excitation of the trapped 171Yb+ ion with a picosecond laser pulse at 369 nm to generate an entangled photon whose polarization is entangled with the ion spin This 369-nm photon is collected by a high-numerical-aperture (NA) objective lens and coupled into an SMF The QFC module implements a difference-frequency generation (DFG) process, converting the 369 nm photon to 580 nm while preserving its polarization-encoded quantum state

Node Specific Details

The TI node employs a high-optical-access ion trap, enabling efficient photon collection via an objective lens with a NA of 0.64, achieving a collection efficiency of approximately 10% and subsequent coupling into a 3-m SMF The QM node is based on a laser-written depressed-cladding optical waveguide fabricated on a 0.2% doped 153Eu3+: Y2SiO5 crystal, which supports waveguiding for arbitrary polarization states To enable polarization-independent storage, site-2 Eu3+ ions are utilized whose 7F0 ↔ 5D0 transition exhibits balanced absorption for light polarized along the crystal’s D1 and b axes On-demand readout is achieved via onchip electrodes that apply control electric pulses, following the Stark-modulated atomic frequency comb (SMAFC) protocol

Performance Metrics and Nonlocality

The resulting hybrid entanglement between the single spin in the TI node and the collective excitation in the QM node achieves a fidelity of (89.21 ± 2.23)% and violates the CHSH-Bell inequality by 6 standard deviations (S = 2.328 ± 0.055), confirming nonlocality between two heterogeneous quantum systems separated by 75 m The overall end-to-end efficiency—from the 369-nm input of QFC module to final retrieval at 580 nm is approximately 0.011% at a storage time of 1 µs The measured fidelity after frequency conversion is (89.12 ± 1.83)%, and the CHSH parameter obtained is S = 2.328 ± 0.055 based on 3,634 trials

Error Analysis

The total error budget for entanglement infidelity is estimated at 10.6%, which is consistent with the experimentally measured fidelity of (89.21 ± 2.23)% The main sources of error are summarized in Extended Table 1 and are discussed in detail below These include Ion decoherence error at 2.6 × 10−6, Phase error due to photon’s arrival-time jitter at 1.2 × 10−4, SPAM error of 0.7%, MW rotation error of 0.1%, QFC infidelity of 3.1%, Pulse excitation error of 3.3%, Collection of π photons at 0.5%, Dark noise (SNSPD+environment) at 2.7%, Photon-state-detection at 2.9 × 10−4, and QM storage error of 0.2%

Future Enhancements

For the TI node, the photon collection efficiency could be increased from the current 10% to exceeding 70% by combining cavity with trapped ion The number of qubits can be extended to hundreds through using QCCD architecture For the QM node, storage efficiency exceeding 80% is achievable by employing an impedance-matched optical cavity Incorporating these improvements would transform this hybrid architecture into a practical platform for enabling novel quantum computing architectures and distributed quantum networks The spectral overlap between the 580-nm photons and the Eu3+ memory is measured to be approximately 74% under ideal alignment

Conclusion on Entanglement

This successful integration of a heterogeneous single-atom processing node with an atomic-ensemble memory node establishes a key hardware foundation for scalable quantum networks The work establishes entanglement between a quantum processing module with a multiplexed quantum memory node, representing a key step toward a scalable, multifunctional quantum internet This work establishes entanglement between two distinct quantum nodes operating at distinct wavelengths, enabling a 6σ violation of the CHSH-Bell inequality The generated TI–QM entanglement was verified by QST of the joint ion-spin and retrieved-photon states, yielding a fidelity of (89.21 ± 2.23)%

Methods Summary

The experimental cycle comprises an 8-s QM preparation phase followed by a 250-s entanglement storage phase The storage phase is divided into multiple frames, each containing 100 µs of ion laser cooling followed by 100 sequential storage attempts The on-demand readout is achieved via the SMAFC protocol where the integer n is determined by the timing of the second electric pulse The overall efficiency of QFC module and QM node is about 0.011% at a storage time of 1 µs The total noise count rate is reduced to 0.007 Hz, resulting in a signal-to-noise ratio (SNR = Nsignal/Nnoise) for the TI–QM system reaching 28:1 The final fidelity of the ion–photon entangled state after frequency conversion is (89.12 ± 1.83)% The overall process matrix fidelity of the QFC module and 90-m SMF is (97.32 ± 0.14)% to the ideal identity matrix The stability of the 90-m SMF remains above 99.0% during the first 5 hours The spectral overlap between the flying qubits and the QM absorption profile is measured to be approximately 74% under ideal alignment

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1. textbfIncrease Entanglement Fidelity via QFC Optimization: The fidelity of (89.21 ± 2.23)% is consistent with that of the ion–photon state measured prior to storage. This suggests that optimizing the polarization-maintaining quantum frequency conversion (QFC) module and its internal conversion efficiency could push this fidelity closer to unity, directly improving the reliability of entanglement distribution between nodes in a quantum internet architecture.

2. textbfEnhance Storage Efficiency for Quantum Memory: The internal storage efficiency of SMAFC protocol is 31.0 ± 0.1% (28.9 ± 0.1%) for H⟩ (V⟩) as shown in Supplementary Fig 6c. By implementing the suggested improvements, such as employing an impedance-matched optical cavity [42] and potentially operating at specific magnetic fields to extend the storage time into the minute-scale regime [43], the AI system can store quantum information with significantly higher efficiency and longer coherence times.

3. textbfImprove Nonlocality Verification Robustness: For our TI–QM entangled state, we obtain S = 2.328 ± 0.055 (Fig. 4b), violating the classical limit by more than 6 standard deviations. By reducing the dominant noise sources—specifically addressing Ion decoherence error and Dark noise error—the AI system can achieve a higher signal-to-noise ratio, leading to a more statistically significant violation of the CHSH-Bell inequality, thereby providing stronger certification of nonlocal entanglement.

4. textbfStrengthen Quantum State Tomography (QST) Error Mitigation: The total error is 10.6%, which is consistent with the experimentally measured fidelity of (89.21 ± 2.23)%. By mitigating Phase error due to photon’s arrival-time jitter and reducing SPAM errors, the AI system can achieve a higher fidelity in reconstructing the density matrix, allowing for more accurate characterization of quantum state channels between heterogeneous nodes.