Development of a laser stabilized on an ultra-stable silicon cryogenic Fabry-Perot cavity for dark matter detection

TL;DR

This paper reports the development of an ultra-stable silicon cryogenic Fabry-Perot cavity laser system designed for detecting ultra-light dark matter through length fluctuations, achieving high frequency stability near 10$^{-17}$.

Contribution

The work introduces a highly stable silicon-based cryogenic cavity with a projected fractional frequency stability of 3×10$^{-17}$ for dark matter detection, including advancements in vibration and thermal noise reduction.

Findings

Achieved a projected fractional frequency stability of 3×10$^{-17}$

Developed a cryogenic silicon cavity with active vibration noise reduction

Demonstrated mechanical response suitable for ultra-light dark matter detection

Abstract

Astrophysical observations suggest the existence of an unknown kind of matter in the Universe, in the frame of the $\Lambda$CDM model. The research field of dark matter covers an energy scale going from massive objects to ultra-light scalar fields, which are the focus of the present work. It is supposed that ultra-light scalar fields affect the length of objects, whereas the speed of light stays unchanged. It follows that Fabry-Perot cavities are ideal tools for ultra-light dark matter detection since the fluctuations in the length of a cavity can be detected on the frequency of the laser stabilized to it. At FEMTO-ST, we have set up an ultra-stable silicon cavity suitable for a test of detection of ultra-light dark matter in an energy range close to 10$^{-10}$ eV. Our 14 cm cavity is composed of two mirrors optically bonded to an ultra-rigid spacer, with each element made in single-crystal of silicon, and cooled at 17 K in order to cancel the first order thermal expansion coefficient of the silicon spacer. The projected fractional frequency stability of the laser is $3 \times 10^{-17}$, mainly limited by the thermal noise of the amorphous dielectric reflective coatings. To reach this remarkable stability, several effects have to be reduced below the thermal noise limit. While the contribution of the residual amplitude modulation is now acceptable, we are currently implementing a laser power lock with residual fluctuations lower than 3~nW and a piezoelectric-based servo loop to actively reduce the vibration noise that has to be inferior to $-110 \textrm{~dB(m s}^{-2})^2/\textrm{Hz}$ at 1 Hz. Here, we present both the status of the development of our ultra-stable laser and the mechanical response of the cavity in the presence of ultra-light dark matter.