# Long-lived optical coherence and spin lifetimes in Eu3+:Y2O3 oxide ceramics for quantum memories

Shuping Liu, Miaomiao Ren, Wanting Xiao, Jun Wang, Yuting Liu, Diana Serrano, Philippe Goldner, Dingyuan Tang, Xiantong An, Fudong Wang, et al.

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Shuping Liu, Miaomiao Ren, Wanting Xiao, Jun Wang, Yuting Liu, et al. Long-lived optical coherence and spin lifetimes in Eu3+:Y2O3 oxide ceramics for quantum memories. Communications Physics, 2025, 8 (1), pp.338. 10.1038/s42005-025-02259-y. hal-05377402

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# Long-lived optical coherence and spin lifetimes in Eu³⁺:Y₂O₃ oxide ceramics for quantum memories

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Shuping Liu ©1,7 [x], Miaomiao Ren2,7, Wanting Xiao2,7, Jun Wang ©3, Yuting Liu4, Diana Serrano5,
Philippe Goldner5, Dingyuan Tang6, Xiantong An2, Fudong Wang ©1,2 [x] & Manjin Zhong ©1,2 [x]

Rare earth ions (REI) in solid materials are among the leading systems for quantum technology applications. However, developing practical REI quantum devices with long-lived coherent states remains challenging due to great difficulties in growing high-quality REI materials and incomplete understanding of their decoherence mechanisms. In this work, we report a long optical coherence time of 422 ± 11 µs for the ⁷F₀ → ⁵D₀ transition, as well as a lifetime exceeding 30 hours for the ⁷F₀ hyperfine spin states in Eu³⁺:Y₂O₃ optical ceramics. We identify the absence of two-level-system induced optical decoherence in short-range-ordered crystals and a decoherence mechanism caused by perturbing magnetic centers that were not detected previously below 1.5 K. Furthermore, we demonstrate coherent light storage over 5 µs by using the atomic frequency comb protocol. These results provide a promising proof-of-principle demonstration of quantum memory using Eu³⁺:Y₂O₃ optical ceramic system, highlighting its significant potential for practical quantum applications.

Quantum technologies typically use two-level superposition states as the fundamental resource (quantum bit, qubit) to realize advanced computing, sensing and communicating functionalities<fnref n="1" />⁻³. Rare earth ions (REI) are inherently suitable qubit carriers with outstanding coherence properties, which are enabled by their abundant and less-perturbed 4f-4f optical transitions and optically addressable spin states⁴⁻⁶. During recent years, REI doped bulk single crystals with low-magnetic-moment host matrices have received considerable attention for developing core quantum devices, such as quantum memories⁷,⁸, microwave-to-optical transducers⁹, quantum processors¹⁰ and single photon sources¹¹. Strong efforts have recently been launched towards versatile REI systems and material topologies, intended for flexible structure design and better integrability. Remarkable progress have been achieved, for instance, in REI optical ceramics, nanoparticles, thin films and molecules in all-optical control of REI nuclear spins¹²,¹³, fast modulation of REI emissions¹⁴, efficient optical spin initialization¹⁵,¹⁶, nanoscale frequency-multiplexed quantum storage¹⁷ and even REI-diamond hybrid quantum system designs¹⁸.

Nevertheless, a challenge to develop REI systems for practical quantum technology application is that the coherence properties of REI are

commonly deteriorated by perturbations from local environments, whose nature are not comprehensively understood. Notably, interactions of REI with dynamical disorder modes, so called two-level-system (TLS) have been observed in many REI doped single crystals¹⁹⁻²², and ascribed to be the dominant decoherence mechanisms in REI doped nanoparticles and ceramics²³,²⁴. As yet, the nature and origin of the TLS are not completely identified. On the other hand, it remains a difficult problem to control the fabrication of REI materials with less environment fluctuations and superior coherence properties, due to a lack of clear understanding of the correlation between the microstructure and the decoherence processes. The growth and reproducibility of high-quality REI single crystals are also impeded by the ultrahigh melting temperatures of many host matrices.

In this work, we demonstrate a record optical coherence time of 422 ± 11 µs for the Eu³⁺:Y₂O₃ material system, along with an efficient suppression of TLS decoherence dynamics in our Eu³⁺:Y₂O₃ optical ceramics, which are fabricated at a temperature far below Y₂O₃'s melting point (T_m=2400 °C). We also identify a decoherence mechanism in ultra-low temperature regime. By comparing the microstructure, low temperature EPR and the optical coherence property of the ceramics, we clarify the role of

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e-mail: liushuping@iqasz.cn; wangfd@sustech.edu.cn; zhongmj@sustech.edu.cn

<footnote n="1">¹International Quantum Academy, and Shenzhen Branch, Hefei National Laboratory, Shenzhen, 518048, China. ²Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China. ³School of Physics and Electronic Engineering, Jiangsu Key Laboratory of Advanced Laser Materials and Devices, Jiangsu Normal University, Xuzhou, 221116, China. ⁴School of Integrated Circuit, Harbin Institute of Technology, Shenzhen, 518055, China. ⁵Institut de Recherche de Chimie Paris (IRCP), Chimie ParisTech, PSL University, CNRS, Paris, F-75005, France. ⁶Future Technology School, Shenzhen Technology University, Shenzhen, 518118, China. ⁷These authors contributed equally: Shuping Liu, Miaomiao Ren, Wanting Xiao.</footnote>
different kinds of defects in the TLS and the decoherence process of Eu³⁺ ions. A ground hyperfine state lifetime of more than 30 h and an atomic frequency comb (AFC) memory with 5 µs storage time are also demonstrated. This study motivates further developments of REI optical ceramics for potential quantum memory applications, and provides guidance to improve the coherence properties of a variety of REI systems by means of chemical and physical manipulations.

# Results

## Microstructure and perturbing center characterizations

The Eu³⁺:Y₂O₃ optical ceramics we studied were fabricated by vacuum sintering followed by hot-isostatic pressing (HIP) processes and post-annealing treatment, in which the Y₂O₃ nano-powders were synthesized by co-precipitation method from 99.99% purity raw materials (See Methods and Supplementary Note 1), shown in Fig. 1a. As Fig. 1b and Supplementary Fig. 1 depict, even without using any sintering aids, the 0.012%, 0.02% and 0.1% Eu³⁺ doped ceramics show high transparency as well as very dense microstructures. No secondary phase is observed both inside of the grains and at grain boundaries, consistent with the pure Y₂O₃ cubic phase verified by powder X-ray diffraction (XRD) measurement (Supplementary Fig. 2). The high-resolution transmission electron microscopy (HRTEM) image in Fig. 1b shows good crystalline structure of the grain boundary area, where clear and clean boundary with a thickness within 10 nm is observed (see

more HRTEM images and analysis in Supplementary Fig. 3). The electron energy loss spectroscopy (EELS) of oxygen K edge of the ceramic (Fig. 1d) contains two sharp structures a and b at about 534 eV and 539 eV, with the latter being more intense than the former. This result is in agreement with the findings from stoichiometric Y₂O₃, rather than reduced Y₂O₃²⁺. This suggests that a 10-hour-long air-annealing treatment can significantly reduce the density of oxygen vacancies, which are considered one of the main perturbing sources in the matrix²³.

Electron paramagnetic resonance (EPR) measurements reveal also a rather small amount of oxygen interstitial defects in our optical ceramics. As shown in Supplementary Note 2 and Supplementary Fig. 4, both F⁺ centers (oxygen vacancies with one electron left, g=1.970) and O₂⁻ (oxygen interstitials, g=2.0358, g⊥=2.0028)²⁶ are hardly observed in our ceramics at room temperature (RT), which is distinct from previous reports²⁷. At 100 K, one can observe only the g⊥ signal of O₂⁻ centers clearly (Fig. 1e) when compared with the reference Eu³⁺:Y₂O₃ nanoparticles. It is worth noting that the 0.1% Eu³⁺ sample exhibits a much lower O₂⁻ intensity as well as two additional weaker peaks at about 3300 G. This is attributed to the different fabrication procedures used for this sample. Weaker EPR signals of other point defects are also observed at lower magnetic fields, as shown in Fig. 1f. These may originate from impurities introduced from raw materials or ceramic fabrication process. Further measurements, such as elemental analysis, are required to confirm the specific species responsible.

<figure><img src="image_5.png" /><figcaption>**Fig. 1 |** Microstructure and perturbing centers in Eu³⁺:Y₂O₃ ceramics.</figcaption></figure>

a Photographs of the ceramics from left to right with Eu³⁺ concentrations of 0.012%, 0.02% and 0.1%, respectively. b Scanning electron microscope (SEM) image of representative sample (0.012% Eu³⁺). c High-resolution transmission electron microscopy (HRTEM) image of the ceramic shows good crystalline structure of the grain boundaries. d The electron energy loss spectroscopy (EELS) of oxygen K edge after background subtraction near the grain boundary of the sample. e Low

temperature electron paramagnetic resonance (EPR) spectra of oxygen related point defects in the matrix. The spectrum of 0.3% Eu³⁺:Y₂O₃ nanoparticles is given as a reference, in which two typical signals are identified: center I interstitial superoxide anions O₂⁻ (g‖ = 2.0358, g⊥ = 2.0028) and center II charged oxygen vacancies F⁺(g = 1.976), respectively. f Broad band scanning of the EPR spectra indicates other weaker defects (feature i and ii) with unpaired electrons.
## High-resolution and coherent optical spectroscopy

The RT photoluminescence (PL) spectra of Eu³⁺:Y₂O₃ ceramics are shown in Supplementary Fig. 5. Among the ⁵D<sub>J</sub> = 0, 1, 2) → ⁷F<sub>J</sub> (= 0, 1, 2, 3) optical transitions, the weak ⁵D₀ → ⁷F₀ (J = 0 → J = 0) transition at about 581 nm is insensitive to magnetic fluctuations of the local environments, making it preferred for quantum technologies²⁸. Therefore, the following experiments performed from about 40 mK to 11 K are mainly focused on this transition. The relevant energy levels and ground-state hyperfine structure of ¹⁵¹Eu³⁺ in Y₂O₃ are shown in Fig. 2a. Experimental setups, including a highly stable laser system and a dilution fridge, are shown in Fig. 2b and detailed in Supplementary Fig. 6.

At 4.2 K, the ⁷F₀ → ⁵D₀ transition of the ensemble Eu³⁺ ions occurs at 580.8862 nm (ω = 516095 GHz) in vacuum and exhibits a much narrower inhomogeneous linewidth than that at room temperature (Fig. 2c). This is ascribed to the suppression of two-phonon Raman processes²⁹. A Lorentzian function can fit well the lineshape, giving a full width at half maximum (FWHM, Γᵢₘh) of 4.34 GHz, 6.03 GHz and 10.76 GHz for the 0.012%, 0.02%, and 0.1% Eu³⁺ sample, respectively. The former value is more than 1 GHz narrower than 0.004% Eu³⁺:Y₂O₃ single crystal (Γᵢₘh = 5.5 GHz)¹⁹, indicating a good suppression of static perturbations in our ceramics. The larger Γᵢₘh observed in the 0.1% and 0.02% Eu³⁺ ceramics are attributed to the higher doping level and larger amount of O₂⁻ centers that detected by EPR measurements (Fig. 1e), respectively.

Compared to inhomogeneous broadening, optical homogeneous linewidth Γ<sub>h</sub> (Γ<sub>h</sub> = 1/(πT<sub>2</sub>)), or optical coherence time T<sub>2</sub> is of key importance for quantum technologies and is extremely sensitive to dynamic perturbations, such as phonons, electric or magnetic field fluctuations and

TLS. As displayed in Fig. 2d, the optical T<sub>2</sub> of Eu³⁺, measured by two-pulse photon echo technique below 100 mK (2PPE, see Methods and Supplementary Fig. 7), is observed the longest in the 0.1% Eu³⁺ sample which possesses the largest optical Γ<sub>inh</sub> but the lowest O₂⁻ density. As a contrast, the shortest T<sub>2</sub> is obtained in the sample containing the highest O₂⁻ density (Fig. 1e). This reveals that the decoherence effect induced by O₂⁻ centers is more severe than the instantaneous spectral diffusion (ISD) effect induced by Eu³⁺ themselves³⁰ and other point defects observed in Fig. 1f. It is worth noting that the optical T<sub>2</sub> we measured in 0.012%, 0.02% and 0.1% Eu³⁺ ceramics are 190 ± 9 µs, 146 ± 5 µs and 422 ± 11 µs, respectively. Such values are 2-10 times longer than that reported in previous optical ceramics and nanoparticles²⁵,³¹,³². The optical T<sub>2</sub> of 0.1% Eu³⁺ ceramic even compares favorably with that of the best Eu³⁺:Y₂O₃ single crystals ever reported (T<sub>2</sub> = 130-420 µs)³³. Moreover, the optical coherence performance of our ceramics display a minimal spectral diffusion of subkilohertz over 1 ms time scale (Supplementary Fig. 8), indicating the high quality of the optical ceramics.

The population lifetime of ⁷F₀ ground hyperfine states T₁s are also measured on the 0.012% Eu³⁺ ceramic using hole burning technique (Supplementary Fig. 9)³⁴. The results are shown in Fig. 2e. It is expected that the hole area detected at 6.5 K and 10 K exhibits a multiexponential decay behavior. This can be attributed to the different spin-lattice relaxation rates among the ± 1/2, ± 3/2 and ± 5/2 hyperfine levels of both the ¹⁵¹Eu³⁺ and ¹⁵³Eu³⁺ isotopes in the materials³⁵. Based on the fitting, the hole lifetimes measured at 10 K and 6.5 K are T₁s = 0.21 ± 0.06 h (46% Contribution), 2.3 ± 0.8 h (54% Contribution) and T₁s = 1.1 ± 0.3 h (28% Contribution), 32 ± 8 h (72% Contribution), respectively. At higher temperatures, the weights of the two decay components tend to become more equal, a trend

<figure><img src="image_6.png" /><figcaption>**Fig. 2 | High resolution and coherent optical spectroscopic experiments.**</figcaption></figure>

a ⁷F₀ → ⁵D₀ optical transition and ⁷F₀ ground-state hyperfine structure of ¹⁵¹Eu³⁺ in Y₂O₃. b Experimental design and set-up, the λ/2 stands for half-wave plate, PBS for polarizing beam splitter, AOM for acousto-optic modulator, λ/4 for quarter-wave plate, PD for photodiode. c Inhomogeneous linewidth of the optical transition measured by detecting the photoluminescence (PL) at 4.2 K. Solid lines: Lorentzian fit corresponding to a full width at half maximum of 4.34 GHz, 6.03 GHz and 10.76 GHz for the 0.012%, 0.02% and 0.1% Eu³⁺ doping samples, respectively. The transition frequency at 0 detuning corresponds to 516095 ± 1 GHz

(580.8862 ± 0.003 nm) for the sample. d Two-pulse photon-echo (2PPE) decays measured below 100 mK for Eu³⁺:Y₂O₃ optical ceramics with different Eu³⁺ concentrations. The optical T₂ values are derived by fitting the echo decay curves according to A = A₀ exp[−(2τ/T₂)²] (solid line). In the inset shows the echo signal detected at 2τ = 380 µs, revealing good signal to noise ratio. e Spectral hole area decays measured at 6.5 K and 10 K, respectively for the 0.012% ceramic. Solid lines: double exponential fits. The schematics on top of (c–e) describe the pulse sequences used in the experiments. The error bars correspond to ± 1 standard error.
similar to that observed in Erbium-doped silica glass fibers³⁶. It is worth noting that the longer component of $T_{1,s}$ at 6.5 K is 32 ± 8 h, which is more than 2 orders of magnitude longer than that obtained in previous optical ceramics ($T_{1,s}$ = 15 ± 5 min at 6 K)³⁷ and also comparable to that of the best Eu³⁺:Y₂O₃ single crystal³⁸. This result indicates that the hyperfine spin state lifetime of Eu³⁺ is not limited by the nature of polycrystalline ceramics. Therefore, a theoretical spin coherence time ($T_{2,s}$ = 2$T_{1,s}$) exceeding two days is predicted in such ceramics, highlighting their potential for high-performance quantum storage. However, achieving this limit experimentally remains challenging due to additional dephasing mechanisms, including magnetic noise from the surrounding spin bath, residual paramagnetic impurities, and fluctuations in local electric and magnetic fields.

## Optical decoherence mechanisms

The temperature dependence of $\Gamma_h$ which measured at 40 mK-11 K without magnetic field is shown in Fig. 3a. It is seen that the $\Gamma_h$ values of all the ceramics start to increase rapidly at T > 8 K. This is consistent with the two-phonon Raman (TPR) scattering process ($T_2 \propto T^7$)²³. At temperatures below 8 K, it was reported that the $\Gamma_h$ was limited by TLS in most of amorphous and less-ordered crystals. Such mechanism typically results in a nearly linear change of $\Gamma_h$ along temperatures ($T_2 \propto T$)¹⁹,³¹. However, the TLS effect is not observed in the 0.012% and 0.02% Eu³⁺ samples, and is observed very weakly in the 0.1% Eu³⁺ one. Notably, when temperature decreases from about 1.5 K down to subkelvin region, a dramatic non-linear decrease of $\Gamma_h$ is observed in all samples. Such decoherence dynamics still exist after applying an external magnetic field of 3 T during measurements, as shown in the inset of Fig. 3a. To the best of our knowledge, this phenomenon has not been observed previously in Eu³⁺:Y₂O₃, either in single crystal or in polycrystalline systems.

Herein, we deduce that there exist some other sources of Eu³⁺ decoherence that are not identified before. By considering the TPR, TLS and a spectral diffusion model caused by possible perturbing centers³⁹:

$$ \Gamma_h(T) = \Gamma_0 + A \operatorname{sech}^2 \left( \frac{\xi}{2k_B T} \right) + \alpha_{\text{TLS}} T + \alpha_{\text{TPR}} T^7 \quad (1) $$

where $\Gamma_0$ is the residual homogeneous broadening and $\xi$ the parameter given by the energy splitting of the perturbing centers in the environment. $\xi$ can also be described by the energy difference between two states $\xi = g_{\text{env}}\mu_B B$, where $g_{\text{env}}$ is the effective g-factor of the randomly oriented perturbing centers, $\mu_B$ the Bohr magneton, B the magnetic field. T is the temperature, $k_B$ is the Boltzmann constant, $\alpha_{\text{TLS}}$ and $\alpha_{\text{TPR}}$ are the TLS and TPR coupling constant, respectively.

The fit, shown as the solid line in Fig. 3a, gives good agreement with experimental results. The best-fit parameters to Eq. (1) are given in Supplementary Table 1. It is observed that $\alpha_{\text{TLS}} = 0$ for both the 0.012% and 0.02% Eu³⁺ samples, and is 0.14 kHz/K for the 0.1% Eu³⁺ ceramic. The later value, nevertheless, is over 4 times smaller than that of previous Eu³⁺:Y₂O₃ optical ceramics²³, and 2 orders of magnitude smaller than that of relevant nanoparticles⁴⁰. This confirms the efficient suppression and even elimination of the TLS effect in our ceramics. The presence of unknown perturbing centers is evidenced, whose energy splitting are characterized by $\xi/2k_B = 0.47-0.9$ K in the absence of magnetic field. Under B = 3 T, the energy splitting for the 0.012% Eu³⁺ sample is observed enlarged from 0.47 K to 0.85 K. This indicates the paramagnetic nature of the perturbing centers. Calculation from $\xi = g_{\text{env}}\mu_B B$ gives an effective $g_{\text{env}}$ factor of 0.84.

At subkelvin temperatures, the $\Gamma_h$ exhibits a small further decrease with external magnetic fields for the 0.012% and 0.02% Eu³⁺ samples (Fig. 3b) and very little variation for the 0.1% Eu³⁺ one (Fig. 3c). Though the data of the former two present higher experimental uncertainty, a fit is made to the same spectral diffusion model described in Eq. (1) and shown as the solid line in Fig. 3b,

$$ \Gamma_h(B) = \Gamma_0 + A \operatorname{sech}^2 \left( \frac{g_{\text{env}}\mu_B B}{2k_B T} \right) \quad (2) $$

where $\Gamma_0$, $g_{\text{env}}$, $\mu_B$, B, T, and $k_B$ the same meaning in Eq (1). This fit gives $g_{\text{env}} = 0.35-0.51$ (Supplementary Table 2), which is consistent with that derived from Fig. 3a. Therefore, we conclude that perturbations from these perturbing centers can be significantly suppressed by lowering the temperature to the subkelvin level, and can be further suppressed by applying an external magnetic field.

## Coherent light storage demonstration

As shown in Fig. 4a, we finally demonstrate coherent optical storage in Eu³⁺:Y₂O₃ optical ceramics by using atomic frequency comb (AFC) memory protocol⁴¹ (See details in Supplementary Fig. 10). Fig. 4b presents the periodic frequency comb structure spanning about 12 MHz range within the inhomogeneous line of the ceramics. By optimizing the comb parameters, specifically the teeth separation $\Delta$ and tooth width $\gamma$, a comb finesse $F = \Delta/\gamma$ of 2-2.5 was used and storage times of 0.5-5 µs were achieved. The storage efficiency $\eta$ is 0.11 % at a storage time $t_s = 0.5\mu$s, consistent with the theoretical predications shown in Fig. 4c.

It is worth noting that the comb finesse was kept low in this work in order to maintain a relatively high effective optical depth (OD) and thereby optimize the memory efficiency, as the initial absorption is very low in our

<figure><img src="image_7.png" /><figcaption>Fig. 3 | Optical decoherence mechanism studies. a Temperature dependence of optical $\Gamma_h$ for Eu³⁺:Y₂O₃ optical ceramics with different Eu³⁺ concentrations. In the inset are the zoomed $\Gamma_h$ of the 0.012% Eu³⁺ sample in 40 mK-4.5 K region measured with and without a magnetic field of 3 T. Solid lines: fits to the data using Eq. (1). b Magnetic field dependence of $\Gamma_h$ for the 0.012%, 0.02% Eu³⁺ samples measured at 88 mK. Solid lines are fits to the data using the spectral diffusion model in Eq. (1).</figcaption></figure>

c Magnetic field dependence of $\Gamma_h$ for the 0.1% Eu³⁺ sample measured at 46 mK. The inset shows the two-pulse photon echo (2PPE) decay curves for the 0.1% Eu³⁺ sample, measured both without and with an applied 3 T magnetic field. Solid lines: fitting curves according to $A = A_0 \exp[-(2\tau/T_2)^\gamma]$. The error bars correspond to ± 1 standard error.
<figure><img src="image_8.png" /><figcaption>**Fig. 4** | Coherent light storage demonstrations in Eu³⁺:Y₂O₃ optical ceramics by using atomic frequency comb (AFC) protocol. a The storage process: the black line is the input pulse (intensity × 10⁻²) and the red line is storage echo of 1 µs. In the insert are AFC echoes with variable storage times obtained by changing AFC tooth separations. The longest storage time reaches 5 µs and the output pulse at 0.5 µs with</figcaption></figure>

<figure><img src="image_9.png" /></figure>

a storage efficiency of 0.1% in agreement with theory. b The AFC structure with varying comb finesses, generated via optical pumping within the inhomogeneous line of ⁷F₀ → ⁵D₀ transition of Eu³⁺ ions. c Theoretical storage efficiencies as a function of optical depth. The inset shows a zoomed region where the 0.1% value at optical depth of 0.1 aligns well with our experimental results.

sample. Although a higher finesse (e.g., *F* = 5) with both smaller *Δ* and *γ* could be realized by our stabilized laser system, it would substantially reduce the effective OD and thus severely degrade the storage efficiency, despite enabling longer storage times. This trade-off between storage time and efficiency is inherent to the AFC protocol and is governed by both the *F* and OD of the comb. Therefore, the relatively short storage time obtained in this experiment does not reflect a fundamental limitation of the material or laser stability, but rather results from a deliberate choice to balance efficiency and storage time under current constraints. Nevertheless, the storage time can be extended further through several strategies, such as transferring the optical storage to spin-wave storage, and implementing advanced dynamic decoupling control techniques. Storage efficiency can also be enhanced by employing multi-pass configurations, increasing the doping concentration, and coupling the sample to an optical cavity to improve absorption. Similar strategies have already shown success in single crystal systems<sup>42,43</sup>.

## Discussion

The longest optical $T_2$ we achieved for the Eu³⁺:Y₂O₃ optical ceramics is 422 ± 11 µs, which is about 2-10 times longer than the previous optical ceramics and nanoparticles<sup>23,32</sup>. The ⁷F₀ hyperfine spin states lifetime is obtained as 32 ± 8 h at 6.5 K, which is more than 2 orders of magnitude longer than that in previous reports. Both the optical $T_2$ and the ⁷F₀ hyperfine spin states lifetime compare favorably with the best Eu³⁺:Y₂O₃ single crystals ever reported<sup>33,38</sup>, revealing that they are not limited by the polycrystalline nature of optical ceramics.

We demonstrate successful coherent light storage in such optical ceramics with a storage time of 5 µs and efficiency consistent with theoretical expectations. To the best of our knowledge, this report presents optical storage in an optical ceramic, establishing a platform that extends beyond single crystals. In particular, this platform is highly promising for scalable, high-efficiency practical quantum memory and integrated quantum devices. Compared to melt-grown single crystals<sup>44</sup>, optical ceramics enables rapid and cost-effective fabrication of large samples with uniform dopant distribution and higher doping levels, without introducing significant stain or spectral inhomogeneities. These features are critical for large-scale quantum memories that require consistent coherence properties and high

memory efficiencies. Additionally, optical ceramics offer better mechanical strength and greater design flexibility, allowing precise control over composition and geometry. These properties make them ideal for fabricating complex structures that can be readily integrated into advanced quantum architectures. Their polycrystalline nature also provides opportunities for isolating and addressing single ions at engineered grains or interfaces, which is valuable for cavity QED and future quantum network applications.

Furthermore, from the temperature dependence of the $\Gamma_h$, we see the efficient suppression of TLS effect in the 0.012% and 0.02% Eu³⁺ ceramics, in which higher density of $O_2^-$ centers as well as shorter optical $T_2$ are found when compared to the 0.1% Eu³⁺ sample. This suggests that the TLS may be not dominated by the oxygen related point defects in the crystalline lattices, which contrasts previous reports<sup>23,45</sup>. Based on the microstructure, low-temperature EPR, and optical decoherence dynamic studies, we propose that the TLS is most possibly caused by high-dimensional defects, such as dislocations and/or grain boundaries in the microstructure. This is reasonable since a larger number of Eu³⁺ ions, which located near grain boundaries or dislocations, are being excited in the 0.1% Eu³⁺ ceramic, taking into account the higher Eu³⁺ concentration and longer optical pass length of this sample. This statement can also explain the decrease of $\alpha_{TLS}$ and $\Gamma_h$ that recently reported on oxygen plasma treated Eu³⁺:Y₂O₃ nanoparticles<sup>40</sup>, in which more F⁺ point defects were induced and high-dimensional defects were healed by the treatment<sup>32,46</sup>.

A decoherence mechanism is identified at temperatures below 1.5 K. This is found to be caused by perturbing magnetic centers, which were not detected in previous studies, with an estimated g-factor of 0.84. This value is much smaller than that of oxygen related defects ($O_2^-$ and F⁺ centers) and other magnetic impurities (g > 2), but the related signals are not detected by low temperature EPR measurements. As a result, we deduce that these perturbing magnetic centers may come from trace impurities in raw materials, or localized low energy phonon modes in the microstructures<sup>24</sup>. Further study is still needed to clarify the origin of them. Nevertheless, the findings about the decoherence mechanisms in this work will be highly instructive not only in optimizing the coherence performance of various existing REI materials, but also in exploring novel REI quantum systems with tailorable properties.
# Methods

## High performance optical ceramic fabrication

The Eu³⁺:Y₂O₃ optical ceramics were fabricated through co-precipitation, ball milling, vacuum sintering without sintering aids, hot isostatically pressing (HIP) and subsequently post air-annealing processes (detailed in Supplementary Note 1). After being polished and cut, the fabricated 0.012% and 0.02% Eu³⁺ ceramics with an optical length of 4 mm and the 0.1% Eu³⁺ one with 14 mm were used for high resolution spectroscopic experiments. The optical coherence times of the samples are considered to remain unaffected by length differences. However, a longer sample can yield a stronger echo signal due to the increased number of Eu³⁺ ions interacting with the laser pulses. It should be noted that longer samples may also exhibit broader inhomogeneous linewidths, as the laser pulses can address more Eu³⁺ ions which are located at grain boundaries or defect centers.

## Microstructure and perturbing center characterizations

The microstructure of the ceramics was observed with a scanning electron microscope (SEM, zeiss). Local structures nearby grain boundaries and the electron energy loss spectrum (EELS) were measured by high resolution transmission electron microscope (HRTEM, TECNAI G2F30, Thermo Fisher) which equipped with a GATAN-PEELS spectrometer. Electric paramagnetic resonance (EPR) experiments were carried out at 100 K by using a Bruker EMXPlus-10/12 spectrometer and at 4.5 K, 20 K, 50 K, RT by using a CIQTEK EPR100 spectrometer. The specific radiation frequency used in the two setup differs slightly (v = 9.31 GHz for the former and v = 9.54 GHz for the later one), resulting in a small shift in the observed EPR peak for the same species. The same amount of ground powders was used for each sample in measurements conducted with the same setup.

## Cryogenic temperature, high-resolution and coherent optical spectroscopy

The ceramics were placed on a homebuilt mount in a dilution fridge (LD400, Bluefors), whose lowest temperature reaches to ~10 mK without load. A high precision three-dimensional vector superconducting magnet (American Magnetics Inc.) was equipped to provide external magnetic field up to B = 5 T in Z axis. A highly stabilized diode laser (Toptica, 10 kHz linewidth) was used to initialize and excite the $7F_0 \rightarrow 5D_0$ optical transition of $^{151}$Eu$^{3+}$ ions in C$_2$ symmetry site of Y$_2$O$_3$ at 580.8862 nm (516095 GHz). The pulse sequences was gated with a double pass acousto-optic modulator (AOM) which is driven by an arbitrary waveform generator(AWG). The transmitted signals were detected by PD or PMT detectors, followed with suitable filters.

The inhomogeneous linewidth, AFC optical memory performance, optical T$_2$, ground hyperfine state lifetime T$_{1,s}$ were measured by using optical pumping, 2PPE and hole-burning techniques, respectively. The related laser pulse sequences and detailed parameters used in this work were detailed in Supplementary Note 3.

# Data availability

The data that support the findings of this study are available from the corresponding author on request.

Received: 12 March 2025; Accepted: 1 August 2025;

Published online: 18 August 2025

# References

1. Kimble, H. J. The quantum internet. *Nature* **453**, 1023 (2008).

2. Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. *Rev. Mod. Phys.* **89**, 035002 (2017).

3. Gisin, N. & Thew, R. Quantum communication. *Nature Photonics* **1**, 165–171 (2007).

4. Wolfowicz, G. et al. Quantum guidelines for solid-state spin defects. *Nature Reviews Materials* **6**, 906–925 (2021).

5. Zhong, M. et al. Optically addressable nuclear spins in a solid with a six-hour coherence time. *Nature* **517**, 177 (2015).

6. Rikuto, F., Yizhong, H., Jun, Y., Haitao, Z. & Tian, Z. Subkilohertz optical homogeneous linewidth and dephasing mechanisms in Er³⁺:Y₂O₃ ceramics. *Physical Review B* **101**, 214202 (2020).

7. Liu, X. et al. Heralded entanglement distribution between two absorptive quantum memories. *Nature* **594**, 41–45 (2021).

8. Zhong, T. et al. Nanophotonic rare-earth quantum memory with optically controlled retrieval. *Science* **357**, 1392–1395 (2017).

9. Xie, T., Fukumori, R., Li, J. & Faraon, A. Scalable microwave-to-optical transducers at single photon level with spins 2407.08879 https://arxiv.org/abs/2407.08879 (2024).

10. Ruskuc, A., Wu, C.-J., Rochman, J., Choi, J. & Faraon, A. Nuclear spin-wave quantum register for a solid-state qubit. *Nature* **602**, 408–413 (2022).

11. Ourari, S. et al. Indistinguishable telecom band photons from a single er ion in the solid state. *Nature* **620**, 977–981 (2023).

12. Serrano, D., Karlsson, J., Fossati, A., Ferrier, A. & Goldner, P. All-optical control of long-lived nuclear spins in rare-earth doped nanoparticles. *Nature Communications* **9**, 2127 (2018).

13. Karlsson, J., Kunkel, N., Ikesue, A., Ferrier, A. & Goldner, P. Nuclear spin coherence properties of $^{151}$Eu$^{3+}$ and $^{153}$Eu$^{3+}$ in a Y$_2$O$_3$ transparent ceramic. *Journal of Physics: Condensed Matter* **29**, 125501 (2017).

14. Casabone, B. et al. Dynamic control of purcell enhanced emission of erbium ions in nanoparticles. *Nature Communications* **12**, 3570 (2021).

15. Kumar, K. S. et al. Optical spin-state polarization in a binuclear europium complex towards molecule-based coherent light-spin interfaces. *Nature Communications* **12**, 2152 (2021).

16. Serrano, D. et al. Ultra-narrow optical linewidths in rare-earth molecular crystals. *Nature* **603**, 241–246 (2022).

17. Fossati, A. et al. A frequency-multiplexed coherent electro-optic memory in rare earth doped nanoparticles. *Nano Letters* **20**, 7087–7093 (2020).

18. Balaşa, I. G. et al. Rare earth-diamond hybrid structures for optical quantum technologies. *Advanced Optical Materials* **12**, 2401487 (2024).

19. Flinn, G. P. et al. Anomalous optical dephasing in crystalline Y$_2$O$_3$:Eu$^{3+}$. *Journal of Luminescence* **58**, 374–379 (1994).

20. Macfarlane, R. M., Sun, Y., Cone, R. L., Thiel, C. W. & Equall, R. W. Optical dephasing by disorder modes in yttrium orthosilicate (Y$_2$SiO$_5$) doped with Eu$^{3+}$. *Journal of Luminescence* **107**, 310–313 (2004).

21. Macfarlane, R. M., Könz, F., Sun, Y. & Cone, R. L. Spectral hole burning and optical dephasing in disordered crystals - Pr$^{3+}$:LiNbO$_3$ and Pr$^{3+}$:SBN. *Journal of Luminescence* **86**, 311–315 (2000).

22. Thiel, C. W., Sinclair, N., Tittel, W. & Cone, R. L. Optical decoherence studies of Tm$^{3+}$:Y$_3$Ga$_5$O$_{12}$. *Physical Review B* **90**, 214301 (2014).

23. Kunkel, N. et al. Dephasing mechanisms of optical transitions in rare-earth-doped transparent ceramics. *Physical Review B* **94** (2016).

24. Macfarlane, R. M., Sun, Y., Sellin, P. B. & Cone, R. L. Optical decoherence in Er$^{3+}$-doped silicate fiber: evidence for coupled spin-elastic tunneling systems. *Phys Rev Lett.* **96**, 033602 (2006).

25. Travlos, A., Boukos, N., Apostolopoulos, G. & Dimoulas, A. Oxygen vacancy ordering in epitaxial layers of yttrium oxide on si (001). *Applied Physics Letters* **82**, 4053–4055 (2003).

26. Singh, V. et al. Nir to visible up-conversion, infrared luminescence, thermoluminescence and defect centres in Y$_2$O$_3$:Er phosphor. *Journal of Physics D: Applied Physics* **42**, 065104 (2009).

27. Kunkel, N., Bartholomew, J., Binet, L., Ikesue, A. & Goldner, P. High-resolution optical line width measurements as a material characterization tool. *Journal of Physical Chemistry C* **120**, 13725–13731 (2016).

28. Könz, F. et al. Temperature and concentration dependence of optical dephasing, spectral-hole lifetime, and anisotropic absorption in Eu$^{3+}$:Y$_2$SiO$_5$. *Physical Review B* **68**, 085109 (2003).

29. Lafitte-Houssat, E. et al. Optical and spin inhomogeneous linewidths in $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$. *Optical Materials: X* **14**, 100153 (2022).
30. Huang, J., Zhang, J. M., Lezama, A. & Mossberg, T. W. Excess dephasing in photon-echo experiments arising from excitation-induced electronic level shifts. *Physical Review Letters* **63**, 78–81 (1989).

31. Bartholomew, J. G., Lima, K. D., Ferrier, A. & Goldner, P. Optical line width broadening mechanisms at the 10 khz level in $Eu^{3+}:Y_2O_3$ nanoparticles. *Nano Letters* **17**, 778–787 (2017).

32. Liu, S. et al. Defect engineering for quantum grade rare-earth nanocrystals. *ACS Nano* **14**, 9953–9962 (2020).

33. Macfarlane, R. M. & Shelby, R. M. Sub-kilohertz optical linewidths of the $^7F_0-^5D_0$ transition in $Y_2O_3:Eu^{3+}$. *Optics Communications* **39**, 169–171 (1981).

34. Goldner, P., Ferrier, A. & Guillot-Noël, O. Rare earth-doped crystals for quantum information processing. *Handbook on the Physics and Chemistry of Rare Earths* **46**, 1–78 (2015).

35. Kröll, S., Syed, H., Kinos, A., Shi, C. & Rippe, L. Microscopic model of spin flip-flop processes in crystals doped by rare-earth ions. *Physical Review B* **106**, 184109 (2022).

36. Bornadel, M. et al. Hole burning experiments and modeling in erbium-doped silica glass fibers down to millikelvin temperatures: evidence for ultra-long population storage 2412.16013 https://arxiv.org/abs/2412.16013 (2024).

37. Kunkel, N. et al. Rare-earth doped transparent ceramics for spectral filtering and quantum information processing. *APL Materials* **3**, 096103 (2015).

38. Babbitt, W. R., Lezama, A. & Mossberg, T. W. Optical dephasing, hyperfine structure, and hyperfine relaxation associated with the 580.8 nm $^7F_0-^5D_0$ transition of europium in $Eu^{3+}:Y_2O_3$. *Physical Review B* **39**, 1987–1992 (1989).

39. Böttger, T., Thiel, C. W., Sun, Y. & Cone, R. L. Optical decoherence and spectral diffusion at 1.5 µm in $Er^{3+}:Y_2SiO_5$: versus magnetic field, temperature, and $Er^{3+}$ concentration. *Physical Review B* **73**, 075101 (2006).

40. Fossati, A. et al. Optical line broadening mechanisms in rare-earth doped oxide nanocrystals. *Journal of Luminescence* **263**, 120050 (2023).

41. Afzelius, M. et al. Demonstration of atomic frequency comb memory for light with spin-wave storage. *Physical Review Letters* **104**, 040503 (2010).

42. Chanelière, T., Ruggiero, J., Bonarota, M., Afzelius, M. & Le Gouët, J.-L. Efficient light storage in a crystal using an atomic frequency comb. *New Journal of Physics* **12**, 023025 (2010).

43. Afzelius, M. & Simon, C. Impedance-matched cavity quantum memory. *Physical Review A* **82**, 022310 (2010).

44. Böttger, T., Reinemer, G. D., Thiel, C. W. & Cone, R. L. Optical spectroscopy, magnetic g tensors, and decoherence studies of magnetic dipole transitions of $Er^{3+}$ at $C_{3v}$-symmetry lattice sites in $Y_2O_3$ at 1.5 µm. *Physical Review B* **111**, 045119 (2025).

45. Perrot, A. et al. Narrow optical homogeneous linewidths in rare earth doped nanocrystals. *Phys Rev Lett.* **111**, 203601 (2013).

46. Wu, S. et al. Dislocation exhaustion and ultra-hardening of nanograined metals by phase transformation at grain boundaries. *Nature Communications* **13**, 5468 (2022).

## Acknowledgements

We thank Dr. Wang Jun's team in fabrication and optimization of the high transparency $Eu^{3+}:Y_2O_3$ transparent ceramics and Dr. Kangwei Xia in EPR measurements. This work was supported by the Innovation Program for Quantum Science and Technology (No. 2021ZD0301204), the National

Natural Science Foundation of China (Grant Nos. 12304454, 62105130, 11904159 and 12004168), National Key Research and Development Program of China (Grant No. 2022YFB3605800), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021A1515110191), Guangdong Innovative and Entrepreneurial Research Team Program (Grant No. 2019ZT08X324), the Key-Area Research and Development Program of Guangdong Province (Grant No. 2018B030326001) and The Science, Technology and Innovation Commission of Shenzhen Municipality (KQTD202108110900-49034).

## Author contributions

S.L., F.W. and M.Z. conceived and supervised the project. J.W. and D.T. synthesized the optical ceramics and involved in the conceptual development of the project. S.L. performed the XRD, SEM, TEM, low temperature EPR, steady-state PL studies. S.L., M.R. W.X. and X.A. carried out the low temperature, high resolution and coherent spectroscopy and AFC light storage measurements. D.S. and P.G. discussed the experimental procedures and results. S.L. and Y.L. wrote the manuscript. All the authors have read and commented on the manuscript.

## Competing interests

The authors declare no competing interests.

## Additional information

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s42005-025-02259-y.

**Correspondence** and requests for materials should be addressed to Shuping Liu, Fudong Wang or Manjin Zhong.

**Peer review information** *Communications Physics* thanks Erhan Saglamyurek, Haitao Zhang for their contribution to the peer review of this work. A peer review file is available.

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