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Physical review. B./Physical review. B

Monte Carlo simulation of the nuclear spin decoherence process in Eu3+ : Y2SiO5 crystals

You-Zhi Ma, You-Cai Lv, Tian-Shu Yang, Yu Ma, Zong‐Quan Zhou, Chuan‐Feng Li, Guang‐Can Guo

Published Jan 30, 2023• 9 citations
Publisher

Abstract

${\mathrm{Eu}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ crystals are promising candidates for quantum memories because their nuclear spin coherence lifetime can be extended to 47 seconds at a particular magnetic field. Although an extended coherence lifetime of 6 hours can be achieved with a large number of dynamic decoupling sequences, these pulses will also introduce unwanted noise. To realize quantum storage with a lifetime of hours, it is necessary to quantitatively characterize the spin decoherence process of ${\mathrm{Eu}}^{3+}$ ions to guide the experimental efforts. In practice, a number of limiting factors could impose a limit on the achievable spin coherence lifetime, which includes the spin inhomogeneous broadening of the ${\mathrm{Eu}}^{3+}$ ensemble and the homogeneity and stability of the external magnetic field. Here, we provide a Monte Carlo simulation model of the nuclear spin decoherence process of ${\mathrm{Eu}}^{3+}$ ions in ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ crystals, and these limiting factors are considered to provide an accurate prediction of the spin coherence lifetimes. This method is universal and can be applied to other rare-earth-ion-doped crystals.

DOI
10.1103/physrevb.107.014310

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This thesis investigates the coherence properties of the hyperfine transitions of the 151Eu3+ ions in Eu3+:Y2SiO5 and evaluates the potential of developing quantum memories using these transitions. Quantum memories for light with long storage times are required for quantum commu- nication applications. For these memories to be useful they need to have storage times long compared to the transmission times across the communication network. For a global optical communication network this requires storage time longer than 100 ms. Rare-earth doped crystals have been identified as a suitable storage material. The storage time of these systems is limited by the coherence time of the hyperfine transitions of the optically active rare-earth ions. In previous work it had been demonstrated that coherence times as long as 1.4 seconds could be achieved for hyperfine transitions in Pr3+:Y2SiO5 by ap- plying a particular magnetic field such that the first order Zeeman shift of the transition nulled. This technique is known as zero first-order Zeeman (ZEFOZ). Due to the relatively large second order Zeeman efficient of the transitions in Pr3+:Y2SiO5, an extension of the coherence time, significantly beyond the 1.4 second mark using ZEFOZ, is not expected. However, it has been predicted that coherence times more than two orders of magnitude longer could be achieved in Eu3+:Y2SiO5 due to the smaller second order Zeeman shifts associated with the relevant hyperfine transitions. The dominant decoherence mechanism for the hyperfine transitions in diluted Eu3+:Y2SiO5 is the magnetic field perturbations caused by the random spin reconfigu- ration of the Y3+ ions in the host. By applying the ZEFOZ technique, previously used in Pr3+:Y2SiO5, the sensitivity of the transition’s frequency to environmental magnetic field perturbations was significantly reduced. Further, this strong ZEFOZ magnetic field was also shown to induce a frozen core around the Eu3+ ion, which resulted in a signifi- cant suppression of the reconfiguration of the nearby Y3+ spins. The combined effect of the reduced sensitivity and frozen core effect allowed a decoherence rate of 8 × 10−5 s−1 over 100 milliseconds to be demonstrated. The observed decoherence rate is at least an order of magnitude lower than that of any other system suitable for an optical quantum memory. Furthermore, by employing dynamic decoherence control, a coherence time of 370 ± 60 minutes was achieved. This 6 hour coherence time observed here opens up the possibility of distributing quantum entanglement via the physical transport of memories as an alternative to optical communications. It was found that even at the critical point alignment the observed coherence times showed that the Y3+ spin flips remain the dominant decoherence mechanism. To aid in the development of future strategies to further extend the coherence time beyond 6 hours, a study of the Y3+ spin dynamics in the frozen core was conducted. Four of the Y3+ sites were resolved and a complete mapping of all frozen-core Y3+ sites was limited by the inhomogeneity of the applied magnetic field. The Rabi frequency, the coherence time and lifetime as well as the interaction strength with the Eu3+ ion of one of these Y3+ ions were measured. The observed lifetime of the Y3+ ion is 27 s, which is four orders of magnitude longer than the low field value. With the technique developed, a detailed understanding of the frozen-core dynamics is possible, which would allow an extension of the hyperfine coherence time of the Eu3+ ion towards the lifetime limit. In summary, this thesis provides a detailed characterisation of the decoherence mecha- nisms of the hyperfine transitions in Eu3+:Y2SiO5. The potential of using rare-earth doped crystals for the long-term storage of quantum information with applications to long-range quantum communications is identified. The demonstrated long coherence time of the quantum transitions for information storage allows a new way of entanglement distribu- tion: entanglement is transported by physically transporting the memory crystal rather than the light. This approach opens a new regime for both quantum communication and fundamental tests of quantum mechanics.
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Nuclear‑spin‑induced magnetic noise is one dominant decoherence source limiting hour‑scale coherent optical storage in Eu3+:Y2SiO5 (Eu:YSO). Appropriately oriented static external magnetic fields can suppress spin‑flip fluctuations and extend coherent retention time, yet unified quantitative predictions for usable field window, crystal axis preference and ZEFOZ (Zero‑First‑Order‑Zeeman) working points remain scarce. Built upon the phenomenological theory of coherence‑scale evolution established in our preceding work, spin‑magnetic perturbation is incorporated as an additional macroscopic decoherence channel. System characteristic parameters are calibrated against published low‑temperature spectroscopic benchmarks for Eu:YSO at 1.7 K. All internal microscopic evolution routines are not disclosed; only measurable forward‑looking outputs are presented. Quantitative experimentally‑testable predictions are reported: the favorable static‑magnetic‑field amplitude window is 0.11 T - 0.36 T with maximum lifetime enhancement factor up to 2.61 relative to zero‑field baseline; high‑field degradation threshold locates near 0.42 T; among three principal crystallographic axes, the D1 axis delivers optimal performance, D2 axis gives intermediate improvement, and D3 axis is unfavorable for long‑time storage. Under the preferred D1 orientation, the primary ZEFOZ working point occurs at 0.227 T, bringing an extra 32.4% suppression of residual magnetic noise and further lifting theoretical storage‑time upper bound. Practical tuning suggestions for cryogenic rare‑earth quantum‑memory setups are provided, together with explicit validity limits for the present phenomenological framework.
Abstract Quantum memory is a core enabling device for large-scale quantum networks, serving as the fundamental building block for quantum repeaters and transportable quantum memories. Among various physical platforms, rare-earth-ion-doped crystals stand out as one of the most promising solid-state candidates for long-lived photonic quantum memories, owing to their exceptionally long spin coherence time and their compatibility with integration. In this review, we first introduce the physical mechanisms underlying long-lived spin coherence in rare-earth systems, with particular emphasis on the zero-first-order-Zeeman transition and dynamical decoupling techniques. We then review the experimental progress in this field, highlighting three distinct lifetimes—the spin coherence time, the light storage time, and the quantum storage time—and covering experiments that have achieved hour-scale spin coherence, minute- to hour-scale light storage, and minute-scale single-photon-level quantum storage. Finally, we discuss the remaining challenges that hinder the realization of practical long-lived quantum memories, explore potential strategies to overcome these obstacles, and outline the prospects for their future applications in quantum networks.
Optical coherence and spin population dynamics in 171^{171}171Yb3+^{3+}3+:Y2_22​SiO5_55​ single crystals
171^{171}171Yb3+^{3+}3+-doped Y2_22​SiO5_55​ crystals are a promising platform for optical quantum memories in long-distance quantum communications. The relevance of this material lies in 171^{171}171Yb long optical and spin coherence times, along with a large hyperfine splitting, enabling long quantum storage over large bandwidths. Mechanisms affecting the optical decoherence are however not precisely known, especially since low-temperature measurements have so far focused on the 2 to 4 K range. In this work, we performed two- and three-pulse photon echoes and spectral hole burning to determine optical homogeneous linewidths in two 171 Yb:YSO crystals doped at 2 and 10 ppm. Experiments were performed in the 40 mK to 18 K temperature range, leading to linewidths between 320 Hz, among the narrowest reported for rare-earth ions, and several MHz. Our results show that above 6 K the homogeneous linewidth is mainly due to an elastic two-phonon process which results in a slow broadening with temperature, the homogeneous linewidth reaching only 25 kHz at 10 K. At lower temperatures, interactions with 89^{89}89Yb nuclear spin-flips, paramagnetic defects or impurities, and also Yb-Yb interactions for the higher concentrated crystal, are likely the main limiting factor to the homogeneous linewidth. In particular, we conclude that the direct effect of spin and optical excited state lifetime is a minor contribution to optical decoherence in the whole temperature range studied. Our results indicate possible paths and regimes for further decreasing the homogeneous linewidths or maintaining narrow lines at higher 171^{171}171Yb concentration.
Rare earth ion doped crystals are state-of-the-art platforms for processing quantum information, particularly thanks to their excellent optical and spin coherence properties at cryogenic temperatures. Experimental observations have shown that the application of a static magnetic bias field significantly improves the coherence times in the rare earth ions ensemble, but only a few studies have focused on its dependency as a function of both magnetic field direction and amplitude. This is especially true for magnetic field amplitudes under the mT, and for low magnetic dipole moment ions. In this paper, we investigate the relationship between the magnetic field parameters and the decoherence caused by magnetic dipole-dipole coupling with the nearest-neighbor nuclear spins in the crystal. The primary non-Kramers rare earth ions investigated here are europium and praseodymium, but we also extend our study to the ytterbium Kramers ion due to its low magnetic dipole in the mT range. We perform theoretical investigations and simulations of the energy structure and coherence time evolution and identify good correspondences between experimental and simulated spin echo data. This work allows us to pinpoint the most relevant decoherence mechanisms in the considered magnetic field regime, and to predict favorable magnetic configurations.