First Measurements of High Frequency Cross-Spectra from a Pair of Large Michelson Interferometers

Measurements are reported of the cross-correlation of spectra of differential position signals from the Fermilab Holometer, a pair of colocated 39 m long, high power Michelson interferometers with flat broadband frequency response in the MHz range. The instrument obtains sensitivity to high frequency correlated signals far exceeding any previous measurement in a broad frequency band extending beyond the 3.8 MHz inverse light-crossing time of the apparatus. The dominant but uncorrelated shot noise is averaged down over $2\times 10^8$ independent spectral measurements with 381 Hz frequency resolution to obtain $2.1\times {10}^{-20}\mathrm{m}/\sqrt{\mathrm{Hz}}$ sensitivity to stationary signals. For signal bandwidths $\mathrm{\Delta }f>11\mathrm{kHz}$, the sensitivity to strain $h$ or shear power spectral density of classical or exotic origin surpasses a milestone ${\mathrm{PSD}}_{\delta h}<t_p$ where $t_p=5.39\times {10}^{-44}/\mathrm{Hz}$ is the Planck time.

Figure 1

Schematic of the two colocated interferometers and associated data acquisition channels. The two devices are optically and electrically isolated to eliminate cross talk.

Figure 2

Accumulated power spectra with 3.81 kHz resolution enlarged to frequencies near the free spectral range. In the upper panel, the two upper curves show the output PSD (averaged over the two photodetectors) for each interferometer. Below that are two curves showing the expected noise in the cross-correlation based on $\sqrt{N_{\text{spectra}}}$ averaging of the PSDs and the observed magnitude of the cross-correlation data. The lower panel plot is on a linear scale and is the real part of the cross-correlation spectrum. This is the signal integrated in Fig. 3. Both panels also show an example broadband model spectrum with Planckian normalization as given by Eq. (1).

Figure 3

The upper panel shows the predicted measurement significance (model signal or instrument noise) in each frequency bin as well as its integral. The lower panel shows the frequency integrated measurement with a shaded $1\sigma$ uncertainty limit along with the integrated model spectrum. Both are normalized to the predicted model amplitude. The shaded region around the model curve is the 10% calibration uncertainty. The gray bands are frequencies vetoed using ancillary and housekeeping data.