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Physical Review Letters

Narrow Optical Homogeneous Linewidths in Rare Earth Doped Nanocrystals

Armand Perrot, Philippe Goldner, Domitille Giaume, Marko Lovrić, Christian Andriamiadamanana, Rogéria Rocha Gonçalves, Alban Ferrier

Published Nov 12, 2013• 54 citations
Publisher

Abstract

A homogeneous linewidth of $85.6\ifmmode\pm\else\textpm\fi{}4.4\text{ }\text{ }\mathrm{kHz}$ is reported in 60 nm ${\mathrm{Eu}}^{3+}$ doped ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ 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.

DOI
10.1103/physrevlett.111.203601

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A homogeneous linewidth of 85.6\ifmmode±\else\textpm\fi4.4  kHz85.6\ifmmode\pm\else\textpm\fi{}4.4\text{ }\text{ }\mathrm{kHz}85.6\ifmmode±\else\textpm\fi4.4  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  \ensuremathμs120\text{ }\text{ }\ensuremath{\mu}\mathrm{s}120  \ensuremathμs. 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.
We show that rare-earth (RE-) doped glasses can have homogeneous linewidths as narrow as 287 kHz at (4)He temperatures. This is far narrower than others reported in glasses in the same temperature range and is suitable for precise spectral hole burning and spatial-spectral holographic applications. It is known that cw spectral hole burning linewidth measurements of RE ions in glasses are hindered by the presence of spectral diffusion but, even in glasses, application of a magnetic field can freeze out RE spin-spin interactions responsible for spectral diffusion and isolate the remaining contribution of two-level systems (TLSs). The Er(3+):2G2S glasses have unusually low TLS contributions, making it possible to study the real homogeneous linewidth using photon echo measurements. The contribution from TLSs is only 170 T(1.3) kHz when subjected to a field of 5 T.
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.
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 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.
Rare earth (RE) doped crystals are promising materials for quantum information processing (QIP). In particular, Eu3+:Y2O3 bulk crystals present long optical coherent lifetimes (T2), a fundamental parameter for QIP. In this thesis, we investigated this system at the nanoscale, which could be used to build hybrid devices where RE are coupled to other quantum systems. This work focuses on the development of Eu3+: Y2O3 particles with sub-wavelength size and on the static and dynamical contributions to Eu3+ optical linewidth. Systems with different particle and crystallite sizes were prepared using homogeneous precipitation. Optical inhomogeneous linewidths were found to decrease with high temperature annealing and reached values close to those of bulk crystals, showing that low defect concentrations can be obtained. A quasi-linear correlation with Raman linewidths was also observed. T1 population decays were measured by fluorescence and found longer than in the bulk, in good agreement with a model based on an effective refractive index model. Optical T2 were investigated by photon echo (PE) and holeburning techniques. We observed a coherence lifetime of 7.1 µs at 1.7 K in a 0.5 % Eu3+ doped sample, the highest value reported for any nanocrystal. Temperature dependence and spectral diffusion studies indicate that structure fluctuations and spin flips dominate dephasing.
Quantum state lifetimes T_{2}, or equivalently homogeneous linewidths Γ_{h}=1/πT_{2}, are a key parameter for understanding decoherence processes in quantum systems and assessing their potential for applications in quantum technologies. The most common tool for measuring narrow optical homogeneous linewidths, i.e., long T_{2}, is the measurement of coherent photon echo emissions, which however gives very weak signal when the number of emitters is small. This strongly hampers the development of nanomaterials, such as those based on rare earth ions, for quantum communication and processing. In this work, we propose, and demonstrate in an erbium doped crystal, a measurement of photon echoes based on incoherent fluorescence detection and its variance analysis. It gives access to T_{2} through a much larger signal than direct photon echo detection, and, importantly, with a laser which is incoherent over the measurement timescale, on the order of a few T_{2}. Our results thus open the way to efficiently assess the properties of a broad range of emitters and materials for applications in quantum nanophotonics.
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.