# 1.5 $\mu$m lasers with sub 10 mHz linewidth

## TL;DR

This paper demonstrates the creation of ultrastable 1.5 μm lasers stabilized to silicon cavities at 124 K, achieving linewidths below 10 mHz and coherence times up to 60 seconds, advancing optical frequency standards.

## Contribution

The study introduces a method to stabilize lasers to silicon cavities at cryogenic temperatures, achieving unprecedented linewidths and coherence times limited by thermal Brownian noise.

## Key findings

- Laser linewidth as low as 5 mHz at 194 THz
- Phase coherence times up to 60 seconds
- Flicker noise floor of 4×10⁻¹⁷ for 0.8 s to tens of seconds

## Abstract

We report on two ultrastable lasers each stabilized to independent silicon Fabry-P\'erot cavities operated at 124 K. The fractional frequency instability of each laser is completely determined by the fundamental thermal Brownian noise of the mirror coatings with a flicker noise floor of $4 \times 10^{-17}$ for integration times between 0.8 s and a few tens of seconds. We rigorously treat the notorious divergencies encountered with the associated flicker frequency noise and derive methods to relate this noise to observable and practically relevant linewidths and coherence times. The individual laser linewidth obtained from the phase noise spectrum or the direct beat note between the two lasers can be as small as 5 mHz at 194 THz. From the measured phase evolution between the two laser fields we derive usable phase coherence times for different applications of 11 s and 60 s.