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Optics Letters

Exceptionally narrow homogeneous linewidth in erbium-doped glasses

Y. Sun, R. L. Cone, Laurent Bigot, B. Jacquier

Published Nov 9, 2006• 22 citations
Publisher

Abstract

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.

DOI
10.1364/ol.31.003453

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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.
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.
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.
Solids containing rare earth (RE) ions have attracted spectroscopists' attention since the beginning of this century.In the last 30 years, their extremely narrow spectral features in combination with the use of non linear spectroscopy have served to sensitively measure ion-solid interactions and to progressively observe narrower homogeneous linewidths.The potential for using RE ion doped crystals as optical storage materials and processors has lately been a driving force in their investigations, Here, the ratio of inhomogeneous to homogeneous linewidth is regarded as an adequate measure of storage density and can become as big as 10 7 at cryogenic temperatures.Therefore, the analysis of line broadening is of fundamental as well as applied interest.This work is concerned with the investigation of interactions of RE ions with their environment.By means of a laser with a kilohertz resolution and non-linear spectroscopy, spectral dynamics as a function of intrinsic, external electric field, or light-pulse induced perturbations are analyzed on different time scales.In the first part, the theoretical background for the spectroscopy of RE ion doped crystals is outlined.The energy levels are presented and it is shown that due to their electronic properties RE ions have spectrally narrow electronic transitions, sometimes in the sub-kHz regime.The investigations of these narrow spectral features on the seconds to minutes time scale require very stable tunable laser sources.At present, such devices are not commercially available.In the second part, the performance of ahorne built laser system is characterized using persistent spectral holes, The results show that frequency selective materials can be used as powerful tools for the high resolution Vlll Abstract spectral analysis of laser sources.Complementary to that, they give a measure for the long term evolution of the spectral holes for the particular hole burning substance.In the third part, the effect of an external electric field on RE ion doped crystals is investigated.It is shown that for these systems the electric field induced frequency shifts are fully reversible.A general theory of Stark splittings of RE doped crystals is introduced and two methods are presented which allow for the determination of the magnitude and orientation of the electric dipole moment differences with sub-degree accuracy.Finally in the last part, spectral line broadening mechanisms of RE ion doped crystals are discussed and investigated by means of two-pulse photon echoes.Through variation of the experimental parameters, a discrimination between the different contributions is partly achieved and characteristic properties for different dephasing mechanisms are presented.In combination with the measurements from the third part, quantitative predictions of the electric dipole-dipole induced broadening are carried out, which are compared to the experimental results,
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.