Optimal Detection Scheme for Shot-Noise-Limited Phase Estimation in Passive Classical-Light Interferometry

Driven in part by the extreme requirements of gravitational-wave detection, recent research about interferometric phase estimation has focused on the use of nonclassical states of light in order to beat the shot-noise limit, allowing further improvements in sensitivity once the detected optical power has been maximized. Still, for a large class of interferometric applications, the efficient use of these states remains prohibitively complicated. Seeking simple improvements to instruments illuminated by classical laser light, we revisit the passive or unmodulated Mach-Zehnder interferometer by structuring the estimation problem in the form of a linear model for which an unbiased estimator attaining the Cramer-Rao bound is easily computed. This paper compares the performance of such linear and efficient estimators for several detection schemes used with two-output and four-output (in-phase and quadrature) interferometers. We find that the independent monitoring of all available output ports leads to an overall sensitivity that is, in most cases, better than that of balanced detection and single-output detection. In addition, it allows the cancellation of the technical amplitude noise contribution at all operating phases without resorting to modulation techniques. This seldom used but simple detection scheme should therefore be considered when designing instruments for operation close to and perhaps below the shot-noise limit.