Sub-kelvin measurement of silicon thermal expansion with a Fabry-P\'erot cavity stabilized laser

TL;DR

This study measures silicon's thermal expansion coefficient at sub-kelvin temperatures using a silicon Fabry-Perot cavity, providing the lowest-temperature data and demonstrating ultra-stable laser stabilization at these temperatures.

Contribution

It presents the first sub-kelvin measurement of silicon's CTE and develops a theoretical model to match experimental data, advancing ultra-stable laser technology.

Findings

CTE of silicon reaches 3.5 ± 0.4 × 10^{-13} K^{-1} at 655 mK

First measurement of silicon's CTE below 1 K

Demonstrates ultra-stable laser stabilization at sub-kelvin temperatures

Abstract

In this letter, we report the measurement of the coefficient of thermal expansion (CTE) of single-crystal silicon from 655 mK to 16 K using an ultra-stable laser based on a single-crystal silicon Fabry-Perot cavity. Below 1 K temperatures, the CTE is in the $10^{-13}$ K$^{-1}$ range with a lowest point at $\boldsymbol{\alpha(}655$ mK$ \boldsymbol{)=} 3.5 \pm 0.4 \times 10^{-13}$ K$^{-1}$. We produce a theoretical model based on Debye and Einstein models to effectively approximate the CTE measured in this temperature range. This is the lowest-temperature CTE measurement of silicon to date, as well as the lowest operating temperature for an ultra-stable Fabry-Perot cavity for laser frequency stabilization.