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Unexplained phase shift in acceleration sensitivity measurements

Ascertain the physical origin of the small residual phase shift observed between the global linear fit and the measured cavity‑stabilized laser frequency during the acceleration sensitivity measurement of the cryogenic sapphire cavity at 10 K, specifically for drives corresponding to rotational acceleration about the Y-axis (αY) and linear vertical acceleration (Z).

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Background

The paper measures the cryogenic cavity’s acceleration sensitivity by driving each rigid-body degree of freedom (three linear and three rotational) and fitting the resulting cavity‑stabilized laser frequency changes to a linear model using simultaneously recorded accelerometer data. This procedure is performed at the operating temperature of 10 K.

In the figure presenting these measurements, the authors note a small residual phase shift between the model fits and the observed frequency response for the rotational Y-axis drive (αY) and the vertical linear drive (Z). The cause of this phase shift is not identified, indicating an unresolved issue in either the mechanical response, sensing, or analysis chain that affects those particular drive conditions.

References

We observe a small residual phase shift between fits and the frequency data \mathrm{\hat{\alpha}_Y} and \mathrm{\hat{Z}}, which is currently unexplained.

— Cryogenic sapphire optical reference cavity with crystalline coatings at $\mathrm{ 1 \times 10^{-16}}$ fractional instability (2404.14310 - Valencia et al., 22 Apr 2024) in Figure caption for “Acceleration sensitivity measurement at 10 K” (Fig. accFits), Section 3, Subsubsection “Acceleration Sensitivity”