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arXiv:2411.06532 · Physical Review Letters

Incoherent Measurement of a Sub-10 kHz Optical Linewidth

Félix Montjovet-Basset, Jayash Panigrahi, Diana Serrano, Alban Ferrier, Emmanuel Flurin, Patrice Bertet, Alexey Tiranov, Philippe Goldner

Published Jul 25, 2025• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1103/xkp5-v9m8

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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.
Atomic-like emitters in the solid state serve as important resources in the advancement of future quantum networks. In particular, intra-4f optical transitions of rare earth ions exhibit excellent coherence properties thanks to the shielding effect of outer electrons. Still, the presence of various dephasing channels in solid state hosts introduces additional decoherence beyond the radiative decay, causing the coherence time of most rare earth doped materials to be over an order of magnitude lower than the radiative limit. Such obstacle prevents the emission of indistinguishable photons from rare earth ions, which is an essential requirement for various quantum applications. In this work, we perform optical coherence study on erbium ions doped in thin-film lithium niobate by patterning photonic crystal resonators with quality factor around 100 k and sub-λ3 mode volume. Leveraging the combination of long coherence and strong Purcell enhancement in the cavity, we show that the coherence time measured with photon echo approaches the radiative limit (80%), representing a 50-fold improvement compared to the waveguide case. Our results present promising prospects toward utilizing rare earth doped materials as quantum repeaters and sources of indistinguishable photons.
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.
Rare-earth emitters in solids are well suited for implementing efficient, long-lived quantum memory coupled to integrated photonics for scalable quantum technologies. They are typically introduced as dopants in a solid-state host, but this introduces disorder and limits the available density of emitters. Stoichiometric materials can offer high densities with narrow optical linewidths. The regular spacing of emitters also opens possibilities for quantum information processing and collective effects. Here, we show narrow optical linewidths in a layered stoichiometric crystalline material, NaEu(IO_{3})_{4}. We observed an inhomogeneous linewidth of 2.2(1) GHz and a homogeneous linewidth of 120(4) kHz. Using spectral hole-burning techniques, we observe a hyperfine spin lifetime of 1.9(4) s. Furthermore, we demonstrate an atomic frequency comb delay of up to 800 ns.
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 method is introduced for quantitatively analyzing photon echo decay measurements to characterize excitation-induced decoherence resulting from the phenomenon of instantaneous spectral diffusion. Detailed analysis is presented that allows fundamental material properties to be extracted that predict and describe excitation-induced decoherence for a broad range of measurements, applications and experimental conditions. Motivated by the need for a method that enables systematic studies of ultra-low decoherence systems and direct comparison of properties between optical materials, this approach employs simple techniques and analytical expressions that avoid the need for difficult to measure and often unknown material parameters or numerical simulations. This measurement and analysis approach is demonstrated for the 3 H 6 to 3 H 4 optical transition of three thulium-doped crystals, Tm 3+ :YAG, Tm 3+ :LiNbO 3 and Tm 3+ :YGG, that are currently employed in quantum information and classical signal processing demonstrations where minimizing decoherence is essential to achieve high efficiencies and large signal bandwidths. These new results reveal more than two orders of magnitude variation in sensitivity to excitation-induced decoherence among the materials studied and establish that the Tm 3+ :YGG system offers the longest optical coherence lifetimes and the lowest levels of excitation-induced decoherence yet observed for any known thulium-doped material.