Temperature-dependent mechanical losses of Eu$^{3+}$:Y$_{2}$SiO$_{5}$ for spectral hole burning laser stabilization

TL;DR

This study measures the mechanical loss and quality factors of Eu$^{3+}$:Y$_2$SiO$_5$ crystals at various temperatures to assess their suitability for ultra-stable laser stabilization using spectral hole burning, demonstrating exceptionally low thermal noise.

Contribution

It provides the first detailed temperature-dependent mechanical loss measurements of Eu$^{3+}$:Y$_2$SiO$_5$ crystals relevant for ultra-low-noise laser stabilization.

Findings

Maximum Q factor of 3676 at low temperature

Estimated fractional frequency instability below 2.5×10⁻¹⁸ at 300 mK

Thermal noise limit lower than current ultra-stable laser references

Abstract

We investigate the mechanical loss characteristics of Eu$^{3+}$:Y$_2$SiO$_5$$\unicode{x2013}$a promising candidate for ultra-low-noise frequency stabilization through the spectral hole burning technique. Three different mechanical oscillators with varying surface-to-volume ratios and crystal orientations are evaluated. In this context, we perform mechanical ringdown and spectral measurements spanning temperatures from room temperature down to $15\,\mathrm{K}$. By doing so, we measure a maximum mechanical quality factor of $Q=3676$, corresponding to a loss angle of $\phi=2.72\times 10^{-4}$. For a spectral hole burning laser stabilization experiment at $300\,\mathrm{mK}$, we can estimate the Allan deviation of the fractional frequency instability due to Brownian thermal noise to be below $\sigma_{\delta \nu/\nu_0} = 2.5\times 10^{-18}$, a value lower than the estimated thermal-noise limit of any current cavity-referenced ultra-stable laser experiment.