Absolute and relative stability of an optical frequency reference based on spectral hole burning in Eu$^{3+}$:Y$_2$SiO$_5$

TL;DR

This paper evaluates the stability and drift of an optical frequency reference based on spectral hole burning in Eu$^{3+}$:Y$_2$SiO$_5$, demonstrating its potential for high-precision timekeeping and frequency standards.

Contribution

The study provides comprehensive measurements of spectral hole burning in Eu$^{3+}$:Y$_2$SiO$_5$, establishing its stability and drift characteristics for optical frequency references.

Findings

Fractional frequency drift rate of 5e-18 s$^{-1}$ with a spectral hole reference.

Short-term stability of 1e-15 τ$^{-1/2}$ improving to 2.5e-16 at 540s.

Spectral hole patterns in different crystals show stability of 7e-16 τ$^{-1/2}$.

Abstract

We present and analyze four frequency measurements designed to characterize the performance of an optical frequency reference based on spectral hole burning in \EuYSO. The first frequency comparison, between a single unperturbed spectral hole and a hydrogen maser, demonstrates a fractional frequency drift rate of $5 \times 10^{-18}$ s$^{-1}$. Optical-frequency comparisons between a pattern of spectral holes, a Fabry-P\'erot cavity, and an Al$^+$ optical atomic clock show a short-term fractional frequency stability of $1 \times10^{-15} \tau^{-1/2}$ that averages down to $2.5^{+1.1}_{-0.5} \times 10^{-16}$ at $\tau = 540~s$ (with linear frequency drift removed). Finally, spectral hole patterns in two different \EuYSO crystals located in the same cryogenic vessel are compared, yielding a short-term stability of $7 \times10^{-16} \tau^{-1/2}$ that averages down to $5.5^{+1.8}_{-0.9} \times 10^{-17}$ at $\tau = 204$~s (with quadratic frequency drift removed).