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The real-time phase tracking has a large number of applications in the precise measurement of various physical parameters. The classical limit of fiber phase tracking has been realized with homodyne detection under a low photon flux (typically ~ 106 s−1). However, it is still difficult to approach the coherent state limit when measuring a weak phase fluctuation in real time by using a larger photon flux. In this work, we propose a fiber Mach–Zehnder system and experimentally demonstrate a nearly quantum-limited phase tracking with mean photon numbers of ∼ 3.7 × 10 10 s−1. In the experiment, the input state is a continuous-mode coherent state and an adaptive Kalman filter is used to construct a phase-locked loop. We effectively track a very weak random phase varying between − 0.07 and + 0.07 radians, and the minimum mean-squared error is optimized to 2.5 × 10 - 5 which approaches the coherent state limit. Our method has potentially applications for fiber-based real-time sensing and measurements. [ABSTRACT FROM AUTHOR]

Phase resolution at the shot noise limit can be achieved with coherent states and on–off measurement. However, the estimation of an unknown phase using this scheme is still missing. Here, we experimentally demonstrate an ab initio phase estimation at the shot noise limit using on–off measurement and efficient Bayesian inference algorithm. The performance of the schemes with and without real-time feedback control is compared. The scheme with feedback control eliminates the ambiguity in the phase estimation and accelerates the convergence to true value. The shot noise limit that defines the ultimate precision is saturated independent of the true phase after about 150 rounds of measurement and feedback control. Our protocol may find important applications in practical precision metrology when only a limited number of measurements are allowed. [ABSTRACT FROM AUTHOR]