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arXiv:2412.10403

Homogeneous Linewidth Behaviour of Narrow Optical Emitters at Sub-kelvin Temperatures

Xiuji Lin, M. T. Hartman, Philippe Goldner, Bess Fang, Yann Le Coq, Signe Louise Seidelin

Published Dec 6, 2024• 0 citations
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Abstract

We explore the properties of ultra-narrow spectral holes in ensembles of solid-state emitters in crystals over a range of sub-kelvin temperatures, with a focus on their potential application in frequency stabilization schemes as an alternative to ultrastable cavities. We investigate how the parameters used to burn the spectral hole impact its shape, and how these factors determine the minimum achievable linewidth. In addition to the stability of the hole's center frequency, the linewidth and contrast play a crucial role in frequency locking. At sub-kelvin temperatures, the temperaturedependent T^7 broadening from two-phonon Raman scattering is expected to be negligible, and the spectral hole's linewidth should therefore remain constant in this interval. We observe however a linear broadening with increasing temperature, highlighting the need for further investigation into the mechanisms governing the linewidth at ultra-low temperatures.

DOI
10.48550/arxiv.2412.10403

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We explore the properties of ultra-narrow spectral holes in ensembles of solid-state emitters in crystals over a range of sub-kelvin temperatures, with a focus on their potential application in frequency stabilization schemes as an alternative to ultrastable cavities. We investigate how the parameters used to burn the spectral hole impact its shape, and how these factors determine the minimum achievable linewidth. In addition to the stability of the hole's center frequency, the linewidth and contrast play a crucial role in frequency locking. At sub-kelvin temperatures, the temperaturedependent T^7 broadening from two-phonon Raman scattering is expected to be negligible, and the spectral hole's linewidth should therefore remain constant in this interval. We observe however a linear broadening with increasing temperature, highlighting the need for further investigation into the mechanisms governing the linewidth at ultra-low temperatures.
We explore the properties of ultranarrow spectral holes in ensembles of solid-state emitters in crystals over a range of sub-kelvin temperatures, as a new step toward leveraging their exceptional coherence properties more effectively. As an example, we consider the potential gain observed in their application in frequency stabilization schemes. We investigate how the parameters used to burn the spectral hole impact its shape, and how these factors determine the minimum achievable linewidth. In addition to the stability of the hole's center frequency, the linewidth and contrast play a crucial role in frequency locking. At sub-kelvin temperatures, the temperature-dependent T7 broadening from two-phonon Raman scattering is expected to be negligible, and the spectral hole's linewidth should therefore remain constant in this interval. We observe however a linear broadening with increasing temperature, highlighting the need for further investigation into the mechanisms governing the linewidth at ultra-low temperatures.
The coherence properties of optical emitters in crystals are critical for quantum technologies and optical frequency metrology. Cooling to sub-kelvin temperatures can significantly enhance their coherence, making it essential to identify the key parameters governing emitter and host crystal behavior in this ultra cold regime. We investigate a Czochralski-grown europium doped yttrium orthosilicate crystal, and we report measurements of the heat capacity, a parameter fundamental to evaluating thermal noise limits in metrology schemes based on spectral hole stabilization in such samples. In parallel, we characterize optical coherence via photon echo measurements as a function of temperature. Below 1 K, where phonon contributions diminish, two-level systems (TLS) associated with crystal imperfections may emerge as a limiting factor. A linear-in-temperature term in the heat capacity serves as a signature of TLS, and from our data, we establish an upper bound on this contribution. This, combined with the optical homogeneous linewidth from photon-echo measurements being constant in the interval from 300 mK to 2 K demonstrates a minimal TLSrelated effects in our sample. These findings highlight the promise of ultralow-temperature operation for enhancing the performance of optical quantum devices based on doped crystals.
We investigate the frequency response of narrow spectral holes in a doped crystal structure as a function of temperature below 1 K. We identify a particular regime in which this response significantly deviates from the expected two-phonon Raman scattering theory. Namely, near 290 mK, we observed a behavior exhibiting a temperature-dependent frequency shift of zero to first order. This is of particular interest for applications that require high frequency stability, such as laser frequency stabilization, as by operating the scheme at this specific point would result in the spectral hole frequency being highly immune to temperature fluctuations, providing the potential for a laser fractional frequency instability as low as ∼2×10^{-22} at 1 s.
The coherence properties of optical emitters in crystals are crucial for quantum technologies and optical frequency metrology. Cooling to sub-kelvin temperatures can markedly enhance coherence, making it important to identify the parameters governing emitter and host crystal behavior in this regime. We investigate a Czochralski-grown europium-doped yttrium orthosilicate crystal, reporting measurements of its heat capacity and optical coherence. Heat capacity not only informs thermal noise limits in metrology schemes but can also reveal two-level systems (TLS) arising from crystal imperfections via a linear-in-temperature term. Below 1 K, where phonon contributions are suppressed, TLS can drive decoherence, leading to a linear broadening of the homogeneous linewidth. From our data, we place an upper bound on the TLS contribution. This, together with constant optical linewidths between 300 mK and 2 K measured via photon-echo lifetimes, is consistent with a minimal TLS effects in our sample. A low level of TLS is particularly important for the performance of optical quantum devices based on doped crystals, since their presence could otherwise limit further improvements in coherence at sub-kelvin temperatures.
The homogeneous linewidth of the transition I15/24−I13/24 in highly doped erbium fibers and its dependence with temperature in the range from 10 to 50 K are experimentally characterized using spectral hole burning. The homogeneous linewidth dependence with temperature is quadratic above 20 K where homogeneous broadening is dominated by two-phonon Raman processes, and linear at lower temperatures where direct phonon processes occur. This characteristic power-law dependence was also derived from transmittance measurements. The solution of nonlinear field equations using the results obtained from our experiments predicts that Gaussian probe pulses propagate at subluminal speed through the narrow spectral holes burned in erbium-doped fibers. For gigahertz pulses in the telecommunication window, a fractional delay as high as 0.6 is predicted.
Using an ultrastable continuous-wave laser at 580 nm we performed spectral hole burning of Eu(3+):Y(2)SiO(5) at a very high spectral resolution. The essential parameters determining the usefulness as a macroscopic frequency reference, linewidth, temperature sensitivity, and long-term stability, were characterized using a H-maser stabilized frequency comb. Spectral holes with a linewidth as low as 6 kHz were observed and the upper limit of the drift of the hole frequency was determined to be 5±3 mHz/s. We discuss the necessary requirements for achieving ultrahigh stability in laser frequency stabilization to these spectral holes.