Searching for Dark Matter with an Optical Cavity and an Unequal-Delay Interferometer

We propose a new type of experiment that compares the frequency of a clock (an ultrastable optical cavity in this case) at time $t$ to its own frequency some time $t\text{−}T$ earlier, by “storing” the output signal (photons) in a fiber delay line. In ultralight oscillating dark matter (DM) models, such an experiment is sensitive to coupling of DM to the standard model fields, through oscillations of the cavity and fiber lengths and of the fiber refractive index. Additionally, the sensitivity is significantly enhanced around the mechanical resonances of the cavity. We present experimental results of such an experiment and report no evidence of DM for masses in the [$4.1\times {10}^{-11}$, $8.3\times {10}^{-10}$] eV region. In addition, we improve constraints on the involved coupling constants by one order of magnitude in a standard galactic DM model, at the mass corresponding to the resonant frequency of our cavity. Furthermore, in the model of relaxion DM, we improve on existing constraints over the whole DM mass range by about one order of magnitude, and up to 6 orders of magnitude at resonance.

Figure 1

Experimental setup. A 1542 nm laser source is locked to an ultrastable cavity. The beam is then split between three arms and recombined to have access to the DM signal (long vs AOM arms) and the experimental reference (short vs AOM arms).

Figure 2

PSD of phase fluctuations $S_{\mathrm{\Delta }\mathrm{\Phi }}(f)$ of the signal for the 52 km fiber (in blue). The modeled cavity noise floor is shown in black, with the grey line indicating the 95% detection threshold [44] which reveals several significant peaks (in red).

Figure 3

95% confidence upper limits on $d_e$ and $d_{m_e}$ in the usual galactic DM model (top) and in the Earth relaxion halo one (bottom). Sensitivity peaks are at the mechanical resonance frequencies of the cavity. The solid black line corresponds to the constraints set by the Eöt-Wash torsion balance experiments [10, 26, 49] while the red line corresponds to a more recent experiment [17]. Narrow frequency bands excluded from these constraints because of systematic effects are given in Table 1. Note that the frequency and amplitude of the resonance peaks may differ from those shown by $\sim 5\%$ because of the uncertainty in ${\omega }_n$ and $Q_n$, as indicated by the grey error bars.