Experimental limits for low-frequency space-time fluctuations from ultrastable optical resonators

It has been suggested that space-time might undergo fluctuations because of its intrinsic quantum nature. These fluctuations would pose a fundamental limit to the ability of measuring distances with arbitrary precision, beyond any limitations due to standard quantum mechanics. Laser interferometers have recently been proposed as being suited for a search for the existence of space-time fluctuations. Here we present results of a search for space-time fluctuations of very low fluctuation frequencies, in the range from 1 μHz to 0.5 Hz. Rigid optical interferometers made out of sapphire and operated at cryogenic temperature were used. We find an upper limit of $1\times {10}^{-24}{\mathrm{Hz}}^{-1}$ for the normalized distance noise spectral density at 6 μHz, and of $1\times {10}^{-28}{\mathrm{Hz}}^{-1}$ above 5 mHz, and establish an experimental limit for the parameter of a recently proposed random-walk hypothesis.