Storage of photonic time-bin qubits for up to 20 ms in a rare-earth doped crystal

Long-distance quantum communication requires quantum repeaters and networks capable of distributing entanglement over long ranges. Atomic ensembles, particularly rare-earth-ion (RE) doped crystals, offer a promising approach for building such repeaters. These crystals provide multiplexing capabilities in various degrees of freedom, efficient storage, long optical and hyperfine coherence times, allowing for long-duration storage of optical quantum states. The longest reported spin storage time of optical states with a mean photon number of around 1 in RE doped solids was approximately 1 ms in ¹⁵¹Eu³⁺:Y₂SiO₅. However, near-term quantum repeaters need storage times of at least 10 ms, and ideally, hundreds of ms. A major challenge in achieving long-duration quantum storage is the noise introduced by dynamical decoupling (DD) sequences used to overcome inhomogeneous spin dephasing and spectral diffusion. This research addresses this challenge by applying dynamical decoupling and a small magnetic field to significantly extend the storage time of photonic qubits.

The authors review existing literature on quantum repeaters, focusing on schemes that utilize atomic ensembles and linear optics, stemming from the DLCZ proposal. They discuss the advantages of atomic ensembles for multiplexing, which is crucial for efficient entanglement distribution. The use of rare-earth-ion-doped crystals is highlighted due to their properties such as multiplexing capabilities, efficient storage, long coherence times, and the potential for long-duration, on-demand storage. The existing challenges of long-duration quantum storage in RE systems, particularly the noise introduced by DD sequences, are also discussed. Previous work on extending spin coherence times using error-compensating DD sequences and magnetic fields is reviewed, setting the stage for the current work.

The experiment utilizes an atomic frequency comb (AFC) spin-wave memory in a ¹⁵¹Eu³⁺:Y₂SiO₅ crystal. The AFC memory involves three key processes: the AFC echo, transfer pulses, and a radio-frequency (RF) sequence. The authors detail the optimization of these processes, including the choice of AFC periodicity (Δ), the design of efficient adiabatic, chirped HSH transfer pulses, and the selection of appropriate dynamical decoupling sequences (XY-4, XY-8, XY-16). The experimental setup includes a coherent laser at 580 nm, acousto-optic modulators for controlling optical channels, and a cryostat to cool the memory and filtering crystals to ~4 K. A small static magnetic field (1.35 mT) is applied along the crystal's D₁ axis to enhance the spin coherence time. Bright pulses are initially used to characterize the memory's efficiency decay curves as a function of storage time, using a Mims model to fit the data. Single-photon level performance is then evaluated, measuring signal-to-noise ratios and average input photon numbers per time mode. Finally, the storage of time-bin qubits is investigated, and a novel composite adiabatic read-out pulse (cHSH) is introduced to improve the efficiency of qubit analysis. Quantum state tomography is used to determine the fidelity of the stored qubits.

The research achieved a 40-fold increase in qubit storage time compared to the previous longest reported time in a solid-state device. The application of a 1.35 mT magnetic field significantly increased the spin coherence time. Six temporal modes were stored with a mean photon occupation number of approximately 1 for durations of 20 ms (SNR of 7.4 ± 0.5, efficiency of 7%), 50 ms (SNR of 5.6 ± 0.7, efficiency of 4.37%), and 100 ms (SNR of 2.5 ± 0.2, efficiency of 2.6%). Two time-bin qubits were stored for 20 ms, achieving a fidelity of 85 ± 2% with a mean photon number per qubit of 0.92 ± 0.04. The measured spin coherence time as a function of the number of DD pulses closely follows the expected n_D^-1/3 dependence. A novel composite adiabatic control pulse (cHSH) was developed for efficient qubit analysis. The main limitation to longer storage times is identified as technical challenges related to heating effects from the high-power DD pulses.

The significant increase in storage time achieved in this work demonstrates the effectiveness of combining a small magnetic field with dynamical decoupling techniques in rare-earth doped crystals. The high fidelity of stored time-bin qubits validates the quantum nature of the memory. The observed scaling of spin coherence time with the number of DD pulses suggests that even longer storage times are possible with further engineering improvements, primarily addressing heating issues. The results are highly relevant for the development of long-distance quantum communication systems, bringing the realization of quantum repeaters closer to practicality.

This paper reports a significant advance in the field of quantum memory, demonstrating long-duration storage of photonic qubits in a solid-state system. The achievement of 20 ms storage time with high fidelity for time-bin qubits is a crucial step towards building practical quantum repeaters. Future work should focus on improving heat dissipation to extend storage times further and explore different DD sequences to minimize noise.

The current limitation in storage time is mainly due to heating effects in the cryocooler caused by the high power of the DD pulses and the duty cycle of the sequence. This technical limitation could be addressed with improvements in the experimental setup to enhance heat dissipation. The lower efficiency observed at longer storage times at the single-photon level may be attributed to long-term fluctuations affecting optical alignment and fiber coupling. The read-out noise, while reduced by higher-order DD sequences, is not fully understood and requires further investigation.