Uniting Quantum Processing Nodes of Cavity-coupled Ions with Rare-earth Quantum Repeaters Using Single-photon Pulse Shaping Based on Atomic Frequency Comb

TL;DR

The paper tackles the challenge of connecting cavity-coupled trapped-ion quantum processors with rare-earth-based quantum repeaters by introducing a cavity-enhanced atomic frequency comb memory that can reshape single-photon waveforms. It develops a physically grounded AFC model with an impedance-matching condition $\mathcal{C}=\mathcal{C}_{opt}$ and a protocol of partial readouts to achieve arbitrary, pure waveform shaping, then demonstrates through realistic Pr$^{3+}$:Y$_{2}$SiO$_{5}$ parameters that high efficiency and tailored output pulses are achievable. The authors show that the shaped AFC photons can be made spectrally and temporally indistinguishable from photons emitted by a cavity-coupled $^{40}$Ca$^{+}$ ion, enhancing Hong–Ou–Mandel interference and enabling high-fidelity, long-distance entanglement between distant ions. This work provides a practical route to scalable quantum networks by preserving photon purity and multimode capacity while bridging disparate quantum platforms. Key results include a mixed-ion fidelity bound $\,\mathcal{F}_{ion-ion}^{mixed}=\tfrac{1}{2}\left(1+V_{HOM}^{\infty 2}\right)$ and demonstrated improvements in heralding probabilities and entanglement fidelity via waveform shaping and filtration, under realistic detector and memory efficiencies.

Abstract

We present an architecture for remotely connecting cavity-coupled trapped ions via a quantum repeater based on rare-earth-doped crystals. The main challenge for its realization lies in interfacing these two physical platforms, which produce photons with a typical temporal mismatch of one or two orders of magnitude. To address this, we propose an efficient protocol that enables custom temporal reshaping of single-photon pulses whilst preserving purity. Our approach is to modify a commonly used memory protocol, called atomic frequency comb, for systems exhibiting inhomogeneous broadening like rare-earth-doped crystals. Our results offer a viable solution for uniting quantum processing nodes with a quantum repeater backbone.

Figures (14)

• Figure 1: Proposed architecture to connect cavity-coupled ions with two repeater chains, each producing dual-rail entanglement between extreme rare-earth quantum memories (see text for further definitions and explanations).
• Figure 2: Relevant energy structure for an AFC protocol considered here with a cavity-enhanced efficiency, see Text for the notations. Temporal shaping of the output waveform is obtained by substituting the readout $\pi$-pulse of the standard AFC protocol with a series of weaker partial control pulses with a sufficiently large temporal separation to allow the partial re-emission of the output field.
• Figure 3: Simulation of cavity-assisted AFC protocols implemented in Pr$^{3+}$:Y$_{2}$SiO$_{5}$. Left panels show the input field intensity $|\mathcal{E}_{in}(t)|^2$ (dash-dotted line), the storage $\pi$-pulse (light blue line) applied before the AFC rephasing time $2\pi/\Delta$ (grayed out), readout pulses (light blue lines), and output field intensity $\left|\mathcal{E}_{out}\right|^{2}$ (dark blue), synchronized and superimposed on a target mode wavefunction (light gray). In the case that the input field occupies an unknown time bin revealed after the storage pulse, two synchonization pulses (light blue lines) are added with a temporal separation (indicated by green double arrows) corresponding to the time delay between the storage pulse and the AFC rephasing time. Input and output intensities are renormalized w.r.t. the input maximal value, while control pulses are renormalized w.r.t. their maximal Rabi frequency. Right panels display filtered output signals, with a sharp cutoff below/above $\pm2\pi\times0.15$ MHz. Insets show the AFC efficiency of the output main component (blue rectangular indicators) and the conditional overlap between the output and the target waveform (circular indicators), without and with filtration. The numerical values are also provided. (a) Standard cavity-assisted AFC protocol with a single readout pulse. (b) Waveform shaping with a sequence of readout pulses separated by the echo duration. (c) Cropped-echo readout sequence, where the delay between the synchronization pulses is slightly increased to crop the subsequent echo (see the small output tail before the second synchronization pulse) and the delay between readout pulses is decreased so as to improve overlap with the target.
• Figure 4: (a) Photon waveform (renormalized field intensities w.r.t. their maximum) emitted by a single $^{40}$Ca$^{+}$ ion embedded in a cavity krutyanskiy_entanglement_2023 (orange) and in the ideal case where unwanted ion spontaneous emission is removed (green). The waveform associated with the photon used as input of the AFC memory (dash-dotted light blue) and the shaped waveform output filtered to discard the arches generated by the shaping (dark blue) are also shown. Synchronization (time offsets) between the waveforms is set to achieve the best possible visibilities. (b) HOM visibility as a function of the acceptance coincidence window between full photons emitted by a single ion and an AFC memory without (blue dash-dotted line with triangles) and with (orange solid line with triangles) waveform shaping. For comparison, the visibilities that would be obtained between a pure ion photon and an AFC photon with (green solid line with bullets) and without shaping (blue dash-dotted line with triangles) are also given.
• Figure S1: Proposed network architecture, with notations for the different modes involved.