  Measurements are reported of the cross-correlation of spectra of differential
position signals from the Fermilab Holometer, a pair of co-located 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 $\Delta f > 11$ kHz, the sensitivity to strain
$h$ or shear power spectral density of classical or exotic origin surpasses a
milestone $PSD_{\delta h} < t_p$ where $t_p= 5.39\times 10^{-44}/\mathrm{Hz}$
is the Planck time.
