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Physical review. B./Physical review. B

Dephasing mechanisms of optical transitions in rare-earth-doped transparent ceramics

Nathalie Kunkel, John G. Bartholomew, Sacha Welinski, Alban Ferrier, Akio Ikesue, Philippe Goldner

Published Nov 1, 2016• 30 citations
Publisher

Abstract

We identify and analyze dephasing mechanisms that broaden the optical transitions of rare-earth ions in randomly oriented transparent ceramics. The study examines the narrow $^{7}F_{0}\phantom{\rule{4pt}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{4pt}{0ex}}^{5}D_{0}$ transition of ${\mathrm{Eu}}^{3+}$ dopants in a series of ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ ceramic samples prepared under varying conditions. We characterize the temperature and magnetic field dependence of the homogeneous linewidth, as well as long-term spectral diffusion on time scales up to 1 s. The results highlight significant differences between samples with differing thermal treatments and ${\mathrm{Zr}}^{4+}$ additive concentrations. In particular, several distinct magnetic interactions from defect centers are observed, which are clearly distinguished from the broadening due to interactions with two-level systems and phonons. By minimizing the broadening due to the different defect centers, linewidths of the order of 4 kHz are achieved for all samples. The linewidths are limited by temperature-dependent interactions and by an interaction that is yet to be identified. Although the homogeneous linewidth can be narrowed further in these ceramic samples, the broadening is now comparable to the linewidths achieved in rare-earth-ion--doped single crystals. Thus, this work emphasizes the usefulness of studying ceramics to gain insights into dephasing mechanisms relevant to single crystals and suggests that ceramics may be an interesting alternative for applications in classical and quantum information processing.

DOI
10.1103/physrevb.94.184301

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We identify and analyze dephasing mechanisms that broaden the optical transitions of rare-earth ions in randomly oriented transparent ceramics. The study examines the narrow 7F0\ensuremath↔5D0^{7}F_{0}\phantom{\rule{4pt}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{4pt}{0ex}}^{5}D_{0}7F0​\ensuremath↔5D0​ transition of Eu3+{\mathrm{Eu}}^{3+}Eu3+ dopants in a series of Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ ceramic samples prepared under varying conditions. We characterize the temperature and magnetic field dependence of the homogeneous linewidth, as well as long-term spectral diffusion on time scales up to 1 s. The results highlight significant differences between samples with differing thermal treatments and Zr4+{\mathrm{Zr}}^{4+}Zr4+ additive concentrations. In particular, several distinct magnetic interactions from defect centers are observed, which are clearly distinguished from the broadening due to interactions with two-level systems and phonons. By minimizing the broadening due to the different defect centers, linewidths of the order of 4 kHz are achieved for all samples. The linewidths are limited by temperature-dependent interactions and by an interaction that is yet to be identified. Although the homogeneous linewidth can be narrowed further in these ceramic samples, the broadening is now comparable to the linewidths achieved in rare-earth-ion--doped single crystals. Thus, this work emphasizes the usefulness of studying ceramics to gain insights into dephasing mechanisms relevant to single crystals and suggests that ceramics may be an interesting alternative for applications in classical and quantum information processing.
Inhomogeneous and homogeneous linewidth are reported in a Eu3+{}^{3+}3+ doped transparent Y2{}_{2}2​O3{}_{3}3​ ceramic for the 7{}^{7}7F0{}_{0}0​-5{}^{5}5D0{}_{0}0​ transition, using high-resolution coherent spectroscopy. The 8.7-GHz inhomogeneous linewidth is close to that of single crystals, as is the 59-kHz homogeneous linewidth at 3 K (T2{T}_{2}T2​ === 5.4 $\ensuremath{\mu}$s). The homogeneous linewidth exhibits a temperature dependence that is typical of a crystalline environment, and additional dephasing observed in the ceramic is attributed to magnetic impurities or defects introduced during the synthesis process. The absence of Eu3+{}^{3+}3+segregation at the grain boundaries, evidenced through confocal microfluorescence, further indicates that the majority of Eu3+{}^{3+}3+ions in the ceramic experience an environment comparable to a single crystal. The obtained results suggest that ceramic materials can be competitive with single crystals for applications in quantum information and spectral hole burning devices, beyond their current applications in lasers and scintillators.
Homogeneous linewidths below 10 kHz are reported for the first time in high-quality Eu3+ doped Y 2O3 transparent ceramics. This result is obtained on the 7F0→5D0 transition in Eu3+ doped Y 2O3 ceramics and corresponds to an improvement of nearly one order of magnitude compared to previously reported values in transparent ceramics. Furthermore, we observed spectral hole lifetimes of ∼15 min that are long enough to enable efficient optical pumping of the nuclear hyperfine levels. Additionally, different Eu3+ concentrations (up to 1.0%) were studied, resulting in an increase of up to a factor of three in the peak absorption coefficient. These results suggest that transparent ceramics can be useful in applications where narrow and deep spectral holes can be burned into highly absorbing lines, such as quantum information processing and spectral filtering.
Rare-earth dopants in solids are conducive of sharp optical transitions and long spin coherence at cryogenic temperatures. While superb coherences are routine in high-quality bulk crystals, the more versatile materials such as rare-earth doped nanoparticles and ceramics have suffered from excessive decoherence due to disorder. This work reports a surprisingly narrow linewidth of Er in Y2{}_{2}2​O3{}_{3}3​ ceramics made with industry-standard synthesis technique, putting it on par with the best single crystalline counterpart. The ultranarrow linewidth also helps clarify decoherence pathways within the matrix.
We identify the physical mechanisms responsible for the optical homogeneous broadening in Eu 3+:Y 2 O 3 nanoparticles to determine whether rare-earth crystals can be miniaturized to volumes less than λ 3 while preserving their appeal for quantum technology hardware. By studying how the homogeneous line width depends on temperature, applied magnetic field, and measurement time scale, the dominant broadening interactions for various temperature ranges above 3 K were characterized. Below 3 K the homogeneous line width is dominated by an interaction not observed in bulk crystal studies. These measurements demonstrate that broadening due to size-dependent phonon interactions is not a significant contributor to the homogeneous line width, which contrasts previous studies in rare-earth ion nanocrystals. Importantly, the results provide strong evidence that for the 400 nm diameter nanoparticles under study the minimum line width achieved (45 ± 1 kHz at 1.3 K) is not fundamentally limited. In addition, we highlight that the expected broadening caused by electric field fluctuations arising from surface charges is comparable to the observed broadening. Under the assumption that such Stark broadening is a significant contribution to the homogeneous line width, several strategies for reducing this line width to below 10 kHz are discussed. Furthermore, it is demonstrated that the Eu 3+ hyperfine state lifetime is sufficiently long to preserve spectral features for time scales up to 1 s. These results allow integrated rare-earth ion quantum optics to be pursued at a submicron scale and, hence, open up directions for greater scaling of rare-earth quantum technology.
Rare Earth (RE) ion doped nanomaterials are promising candidates for a range of quantum technology applications. Among RE ions, the so-called Kramers' ions possess spin transitions in the GHz range at low magnetic fields, which allows for high-bandwidth multimode quantum storage, fast qubit operations as well as interfacing with superconducting circuits. They also present relevant optical transitions in the infrared. In particular, Er3+{\mathrm{Er}}^{3+}Er3+ has an optical transition in the telecom band, while Nd3+{\mathrm{Nd}}^{3+}Nd3+ presents a high-emission-rate transition close to 890 nm. In this paper, we measure spectroscopic properties that are of relevance to using these materials in quantum technology applications. We find the inhomogeneous linewidth to be 10.7 GHz for Er3+{\mathrm{Er}}^{3+}Er3+ and 8.2 GHz for Nd3+{\mathrm{Nd}}^{3+}Nd3+, and the excited state lifetime T1{T}_{1}T1​ to be 13.68 ms for Er3+{\mathrm{Er}}^{3+}Er3+ and $540\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}$ for Nd3+{\mathrm{Nd}}^{3+}Nd3+. We study the dependence of homogeneous linewidth on temperature for both samples, with the narrowest linewidth being 379 kHz (T2=839{T}_{2}=839T2​=839 ns) for Er3+{\mathrm{Er}}^{3+}Er3+ measured at 3 K, and 62 kHz (${T}_{2}=5.14\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{s}$) for Nd3+{\mathrm{Nd}}^{3+}Nd3+ measured at 1.6 K. Further, we investigate time-dependent homogeneous linewidth broadening due to spectral diffusion and the dependence of the homogeneous linewidth on magnetic field to get additional clarity of mechanisms that can influence the coherence time. In light of our results, we discuss two applications: single qubit-state readout and a Fourier-limited single photon source.
A homogeneous linewidth of $85.6\ifmmode\pm\else\textpm\fi{}4.4\text{ }\text{ }\mathrm{kHz}$ is reported in 60 nm Eu3+{\mathrm{Eu}}^{3+}Eu3+ doped Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ nanocrystals at 1.3 K. This linewidth was measured by two-pulse photon echoes on highly scattering powders using heterodyne detection. Spectral diffusion was also investigated by three-pulse photon echoes and resulted in a limited broadening of the homogenous linewidth of about 250 kHz over $120\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$. Compared to achievable Rabi frequencies, in the range of several MHz, these values show that rare earth doped nanocrystals can be useful for applications in optical quantum information processing.