Measurements of liquid surface fluctuations at sub-shot-noise levels with Michelson interferometry

Surface fluctuation spectra of liquids are measured to unprecedented precision, down to 3 orders of magnitude below the shot-noise level using averaged correlations of interferometry measurements. This allows us to investigate the limits in our current theoretical understanding of these phenomena. The spectrum derived from hydrodynamical considerations agrees well with the observed results for water. However, for oil, deviations are seen at high frequencies (1 MHz), perhaps indicating its more complex underlying physics. The measurements are made possible by dualizing the Michelson interferometry measurements and employing the averaged correlation of signals, in which the shot noise is statistically reduced. The method works in the presence of the quantum noise of a coherent state of light. The optical part of the experimental setup is essentially the same as that of Michelson interferometry so that the method can be applied when Michelson interferometry can be used. Furthermore, the measurement method requires a relatively low light power and a short time so that it has a wide range of applicability.