Demonstration that Differential Length Changes of Optical Cavities are a Sensitive Probe for Ultralight Dark Matter

Abstract

Measurements of differential length oscillations of Fabry-Perot cavities provide a sensitive and promising approach to searching for scalar ultralight dark matter (ULDM). The initial demonstration sets direct lower bounds that are one to two orders of magnitude lower for two model ULDM distributions -- a standard galactic halo and a relaxion star bound to Earth -- ranging over a decade of ULDM mass and Compton frequency. The demonstration suggests how a much higher sensitivity to a much larger ULDM mass range can be obtained.

Figures (7)

• Figure 1: (a) Side view of the vibrationally-isolated cryostat. (b) Schematic of the optical probe of the differential length variations of two cavities.
• Figure 2: (a) Orange curve is a normalized analytic curve showing the expected ULDM lineshape in the SHM. Zoom in of the filtered strain ASD in (a) around 50 kHz with $\approx 3\,\mu {\rm Hz}$ RBW. (b) The averaged ASD of the differential optical strain, $\widetilde{h}(f)$, with and without filtering through the ULE cavity.
• Figure 3: (a) Qualitative magnitude and phases of two cavities' individual mechanical transfer functions (Eq. (\ref{['eq:TF_mech']})), $H_{{ {\rm M,\,L/S}}}$ for the long/short cavity, and the detector response function $A_{{\rm det}}$ (Eq. (\ref{['eq:A_det']})). (b) Dashed curves represent $A_{\rm det}$ for the lowest and highest data-driven estimates for the mechanical resonances of the two cavities with $Q_{{ {\rm M}}} \sim 10^{4}$. The black curve conservatively takes their minimum to set ULDM limits.
• Figure 4: Bounds on $d_{m_{\rm e}}$ as a function of ULDM Compton frequency, for the SHM (a) and for a relaxion star bound to Earth (b), with limits from cavity-fiber Savalle_2021_PRL and Cs-cavity Tretiak_2022_PRL direct ULDM detectors, alongside indirect bounds from equivalence principle (EP) tests Antypas_2022_arXiv and a theoretically motivated target Tsai_2023_nastro.
• Figure 5: Bounds for the SHM for a much larger range of $d_{m_{\rm e}}$ and Compton frequencies compared to other bounds set by direct and indirect measurements, our sensitivity projections and theoretical limits. A zoom in of the dashed red box is shown in Fig. \ref{['fig:d_me']} (a). See main text for details.