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arXiv:1811.05248 · Physical review. B./Physical review. B

Probing interacting two-level systems with rare-earth ions

Dapeng Ding, David van Driel, L. M. C. Pereira, Jared F. Bauters, Martijn J. R. Heck, G. Welker, M. J. A. de Dood, A. Vantomme, John Edward Bowers, W. Löffler, Dirk Bouwmeester

Published Jan 29, 2020• 8 citations
arXivHTMLPDF

Abstract

Two-level systems (TLS) in amorphous materials limit coherence times of a number of solid-state quantum devices. Interactions between TLS become prominent below 100 mK, but the coupling mechanism and statistical properties are still unclear. Here we determine the homogeneous linewidth of ytterbium ions $({\mathrm{Yb}}^{3+})$ in silica glass at 10--80 mK by using photon echo techniques as a probe of TLS. First, the homogeneous linewidth can be reduced by applying a magnetic field of 0.3 T. This effect is due to reduced magnetic interactions between adjacent ${\mathrm{Yb}}^{3+}$. Secondly, we observe saturation of the linewidth below 50 mK to a level of approximately 30 kHz, which is much larger than the lifetime-limited value of 0.2 kHz. This saturation behavior is in conflict with the coupling to independent TLS. We show that this effect can be explained by coherently coupled TLS.

DOI
10.1103/physrevb.101.014209

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Two-level systems (TLS) in amorphous materials limit coherence times of a number of solid-state quantum devices. Interactions between TLS become prominent below 100 mK, but the coupling mechanism and statistical properties are still unclear. Here we determine the homogeneous linewidth of ytterbium ions (Yb3+)({\mathrm{Yb}}^{3+})(Yb3+) in silica glass at 10--80 mK by using photon echo techniques as a probe of TLS. First, the homogeneous linewidth can be reduced by applying a magnetic field of 0.3 T. This effect is due to reduced magnetic interactions between adjacent Yb3+{\mathrm{Yb}}^{3+}Yb3+. Secondly, we observe saturation of the linewidth below 50 mK to a level of approximately 30 kHz, which is much larger than the lifetime-limited value of 0.2 kHz. This saturation behavior is in conflict with the coupling to independent TLS. We show that this effect can be explained by coherently coupled TLS.
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.
Erbium-doped solids are promising candidates for fiber-based quantum networks due to their emission wavelength, which aligns with the telecom band over which optical fibers exhibit minimal loss. Among these, erbium-doped silica fiber (EDF) stands out for its availability, ease of use, and seamless integration with existing fiber-optic infrastructure. In this work, using the two-pulse photon-echo (2PPE) technique, we measured the homogeneous linewidth of the 4 I 13/2 ↔ 4 I 15/2 optical transition under varying magnetic fields and temperatures. We observed an effective homogeneous linewidth of approximately 8 kHz at ∼7mK at an optimal magnetic field of 0.09 T, representing over two orders of magnitude improvement compared to earlier reports measured at T ≈700mK. We also present a comprehensive model for the combined magnetic field and temperature dependency of the effective homogeneous linewidth. Additionally, we employed three-pulse photon-echo (3PPE) measurements to investigate spectral diffusion and decoherence processes and conclude that Two-Level System (TLS) effects are significantly suppressed at sufficiently low temperatures, below ∼100mK.
The $^{2}F_{7/2}\ensuremath{\leftrightarrow}^{2}F_{5/2}$ optical transitions of Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+ doped into Y3Al5O12{\mathrm{Y}}_{3}\mathrm{A}{\mathrm{l}}_{5}{\mathrm{O}}_{12}Y3​Al5​O12​ (YAG) were studied for potential quantum information and photonic signal processing applications. Absorption and fluorescence spectroscopy located the energy levels of the ground 2F7/2^{2}F_{7/2}2F7/2​ and excited 2F5/2^{2}F_{5/2}2F5/2​ manifolds, allowing inconsistencies between previous assignments of crystal field splittings in the literature to be resolved. These measurements reveal an unusually large splitting between the first and second levels in both the ground and excited multiplets, potentially providing for reduced sensitivity to thermally induced decoherence and spin-lattice relaxation. Spectral hole burning through two-level saturation was observed, determining the excited state lifetime to be 860 \ensuremath{\mu}s and resolving ambiguities in previous fluorescence measurements that were caused by the large radiation trapping effects in this material. Optical decoherence measurements using two-pulse photon echoes gave a homogeneous linewidth of 18 kHz for an applied magnetic field of 1 T, narrowing to 5 kHz at 2.5 T. The observed decoherence was described by spectral diffusion attributed to $\mathrm{Y}{\mathrm{b}}^{3+}\mathrm{\ensuremath{-}}\mathrm{Y}{\mathrm{b}}^{3+}$ magnetic dipole interactions. Laser absorption determined an inhomogeneous linewidth of 3.6 GHz for this transition in this 0.05%-doped crystal, which is narrower than for any other rare-earth-ion transition previously studied in the YAG host. The temperature dependence of the transition energy and linewidth of the lowest 2F7/2^{2}F_{7/2}2F7/2​ to lowest 2F5/2^{2}F_{5/2}2F5/2​ transition centered at 968.571 nm measured from 4 K to 300 K was well described by phonon scattering at higher temperatures, with an additional anomalous linear temperature-dependent broadening at temperatures below 80 K. Two magnetically inequivalent subgroups of Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+ ions were identified when a magnetic field was applied along the $\ensuremath{\langle}111\ensuremath{\rangle}$ axis, as expected for the D2{D}_{2}D2​ sites in the cubic symmetry crystal, with ground and excited state effective ggg-values of gg=3.40{g}_{\mathrm{g}}=3.40gg​=3.40 (3.34) and ge=1.04{g}_{\mathrm{e}}=1.04ge​=1.04 (2.01), respectively. Together with the convenient diode laser wavelength of this transition, our study suggests that Yb3+\mathrm{Y}{\mathrm{b}}^{3+}Yb3+:YAG is a promising material system for spectral hole burning and quantum information applications.
Understanding decoherence in cryogenically cooled rare-earth-ion doped glass fibers is of fundamental interest and a prerequisite for applications of these material in quantum information applications. Here we study the coherence properties in a weakly doped erbium silica glass fiber motivated by our recent observation of efficient and long-lived Zeeman sublevel storage in this material and by its potential for applications at telecommunication wavelengths. We analyze photon echo decays as well as the potential mechanisms of spectral diffusion that can be caused by coupling with dynamic disorder modes that are characteristic for glassy hosts, and by the magnetic dipole-dipole interactions between Er3+{\mathrm{Er}}^{3+}Er3+ ions. We also investigate the effective linewidth as a function of magnetic field, temperature, and time, and then present a model that describes these experimental observations. We highlight that the operating conditions (0.6 K and 0.05 T) at which we previously observed efficient spectral hole burning coincide with those for narrow linewidths (1 MHz)---an important property for applications that has not been reported before for a rare-earth-ion doped glass.
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 (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.