Science 337, 1514–1517 (2012)

Hidehiro Yonezawa and researchers from Japan and Australia have demonstrated unconstrained tracking of an optical phase that varies stochastically over time. Most notably, the tracking was performed over a substantial angular range, with no post-selected data or loss compensation. The researchers employed a phase-squeezed beam modulated by a classically generated Wiener process, which ensured the stochastic nature of the varying phase. They then estimated the phase by employing the Kalman filter, a real-time feedback-based algorithm. The researchers report that, contrary to popular belief, more squeezing does not always improve the measurement precision. They optimized the squeezing amount by considering the magnitude and bandwidth of the phase noise, as well as the amplitude of the phase-squeezed beam, and were able to achieve an efficient phase-tracking scheme with a mean square error of 15 ± 4% below the coherent-state limit.