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arXiv:2408.11703

Using slow light to enable laser frequency stabilization to a short, high-Q cavity

David Gustavsson, Marcus Lindén, Kevin J. Shortiss, Stefan Kröll, Andreas Walther, Adam Kinos, Lars Rippe

Published Aug 21, 2024• 0 citations
arXivHTMLPDF

Abstract

State-of-the-art laser frequency stabilization is limited by miniscule length changes caused by thermal noise. In this work, a cavity-length-insensitive frequency stabilization scheme is implemented using strong dispersion in a $21\,\mathrm{mm}$ long cavity with a europium-ion-doped spacer of yttrium orthosilicate. A number of limiting factors for slow light laser stabilization are evaluated, including the inhomogeneous and homogeneous linewidth of the ions, the deterioration of spectral windows, and the linewidth of the cavity modes. Using strong dispersion, the cavity modes were narrowed by a factor $1.6\cdot 10^5$, leading to a cavity linewidth of $3.0\,\mathrm{kHz}$ and a $Q$ factor of $1.7\cdot 10^{11}$. Frequency stabilization was demonstrated using a cavity mode in a spectral transparency region near the center of the inhomogeneous profile, showing an overlapping Allan deviation below $6\cdot 10^{-14}$ and a linear drift rate of $3.66\,\mathrm{Hz}/\mathrm{s}$. Considering improvements that could be implemented, this makes the europium-based slow light laser frequency reference a promising candidate for ultra-precise tabletop frequency stabilization.

DOI
10.48550/arxiv.2408.11703

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State-of-the-art laser frequency stabilization is limited by miniscule length changes caused by thermal noise. In this work, a cavity-length-insensitive frequency stabilization scheme is implemented using strong dispersion in a 21 mm21\,\mathrm{mm}21mm long cavity with a europium-ion-doped spacer of yttrium orthosilicate. A number of limiting factors for slow light laser stabilization are evaluated, including the inhomogeneous and homogeneous linewidth of the ions, the deterioration of spectral windows, and the linewidth of the cavity modes. Using strong dispersion, the cavity modes were narrowed by a factor 1.6⋅1051.6\cdot 10^51.6⋅105, leading to a cavity linewidth of 3.0 kHz3.0\,\mathrm{kHz}3.0kHz and a QQQ factor of 1.7⋅10111.7\cdot 10^{11}1.7⋅1011. Frequency stabilization was demonstrated using a cavity mode in a spectral transparency region near the center of the inhomogeneous profile, showing an overlapping Allan deviation below 6⋅10−146\cdot 10^{-14}6⋅10−14 and a linear drift rate of 3.66 Hz/s3.66\,\mathrm{Hz}/\mathrm{s}3.66Hz/s. Considering improvements that could be implemented, this makes the europium-based slow light laser frequency reference a promising candidate for ultra-precise tabletop frequency stabilization.
State-of-the-art laser frequency stabilization is limited by miniscule length changes caused by thermal noise. In this work, a cavity-length-insensitive frequency stabilization scheme is implemented using strong dispersion in a 21 mm long cavity with a europium-ion-doped spacer of yttrium orthosilicate. A number of limiting factors for slow light laser stabilization are evaluated, including the inhomogeneous and homogeneous linewidth of the ions, the deterioration of spectral windows, and the linewidth of the cavity modes. Using strong dispersion, the cavity modes were narrowed by a factor 1.6 × 10 5 , leading to a cavity linewidth of 3.0 kHz and a Q factor of 1.7 × 10 11 . Frequency stabilization was demonstrated using a cavity mode in a spectral transparency region near the center of the inhomogeneous profile, showing an overlapping Allan deviation below 6 × 10 −14 and a linear drift rate of 3.66 Hz s −1 . Considering improvements that could be implemented, this makes the europium-based slow light laser frequency reference a promising candidate for ultra-precise tabletop frequency stabilization.
In this thesis the application of slow light effects to the area of laser stabilisation is investigated. The frequency stability of lasers locked to external cavities is limited by the stability of the modes in the reference cavity. By using dispersive slow light effects the effective length of a cavity can be increased by several orders of magnitude, without a proportional increase in the sensitivity to fluctuations in cavity length, thereby yielding a net increase in stability. The effects are achieved through spectral hole burning in cryogenically cooled rare-earth ion doped crystals. Two sets of experiments are carried out, the first focusing on hole burning and the second focusing laser locking. Linewidths and frequency drift of the cavity spectrum are studied. Feedback control using an error signal generated from the slow light cavity is demonstrated, but successfully locking the laser is still yet to be achieved.
Spectral hole burning in rare earth doped crystal can provide frequency references based on the optical transition of the dopant ions [1] . The narrow spectral patterns can be used to improve laser frequency stabilization [2] , [3] and provide a new generation of ultra-stable lasers with lower thermal noise benefiting from the cryogenic environment and better quality factor of the crystal than the amorphous glass typically used in the Fabry-Perot cavity. We utilize Europium doped yttrium silicon oxide (Eu:YSO) in our experiments, which allow realization of long lived (hours or more depending on temperature) narrow spectral holes ( kHz or less) well suited for high precision experiment applications. We will describe our novel double-heterodyne detection method [4] , used to decrease the detection noise, as well as experiments assessing quantitatively the sensitivity of the spectral pattern to crystal deformation [5] , [6] , application of electric field [7] and temperature fluctuations. We currently demonstrate a state-of-the-art laser frequency stability at 1.7 × 10 − 15 at 1s [4] , limited by the latter effect, for which improvement strategies have been demonstrated elsewhere [2] and which we are currently implementing. The other effects which we have quantitatively studied are compatible with a few 10 − 18 frequency stability at 1s time scale. This work is particularly promising in the context of optical frequency lattice clocks, for which the ultra-stable laser used for probing the clock transition is a strong limiting factor of the frequency stability.
This project sets out to frequency stabilize external cavity diode lasers of wavelengths λ = 935 nm and 739 nm, with an eye to Ytterbium-171 ion trapping.The desired laser linewidths were below 1 MHz at 1 second observation time and the desired long term frequency drifts were below a megahertz over the course of a few hours.To stabilize the lasers, two Pound-Drever-Hall laser frequency stabilisation systems were designed, constructed and characterized.The optical frequency references used were sub-megahertz linewidth optical cavities with Invar spacers.These cavities were designed and constructed inhouse.The achieved long term stability of the stabilized lasers was 1 MHz/h over a 5 hour measurement period.The laser frequency long term stabilities are limited by the thermal stabilities of the cavity spacers.The post stabilisation laser frequency noise was lowered when compared to the free running lasers.This was observed by determining the laser frequency noise power spectral densities.From the frequency noise power spectral densities lower bounds on the locked laser linewidths were established.This lower bound is 11.92 kHz for the 739 nm wavelength laser at 1 second observation time and 5.4 kHz for the 935 nm wavelength laser.An additional system was designed and constructed ii
Laser frequency stabilization giving a 500-Hz Allan deviation for a 2-ms integration time with drift reduced to 7 kHz/min over several minutes was achieved at 1536 nm in the optical communication band. A continuously regenerated spectral hole in the inhomogeneously broadened 4I15/2(1)4I13/2(1){}^{4}{I}_{15/2}{(1)}^{4}{I}_{13/2}(1)4I15/2​(1)4I13/2​(1) optical absorption of an Er3+:Y2SiO5{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Er3+:Y2​SiO5​ crystal was used as the short-term frequency reference, while a variation on the locking technique allowed simultaneous use of the inhomogeneously broadened absorption line as a long-term reference. The reported frequency stability was achieved without vibration isolation. Spectral hole burning frequency stabilization provides ideal laser sources for high-resolution spectroscopy, real-time optical signal processing, and a range of applications requiring ultra-narrow-band light sources or coherent detection; the time scale for stability and the compatibility with spectral hole burning devices make this technique complementary to other frequency references for laser stabilization.