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 \(\sim3.7 \times 10^{10}\) 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 \(2.5 \times 10^{ - 5}\) which approaches the coherent state limit. Our method has potentially applications for fiber-based real-time sensing and measurements.

实时相位跟踪在各种物理参数的精确测量中具有大量应用。光纤相位跟踪的经典极限已通过在低光子通量（通常〜10 ⁶  s ^-1）下的零差检测实现。但是，当通过使用较大的光子通量实时测量微弱的相位波动时，仍然很难达到相干状态极限。在这项工作中，我们提出了一个光纤Mach–Zehnder系统，并通过实验证明了光子数平均为\（\ sim3.7 \ times 10 ^ {10} \） s ^-1的近量子限制的相位跟踪。。在实验中，输入状态为连续模式相干状态，自适应卡尔曼滤波器用于构建锁相环。我们有效地跟踪了一个非常弱的随机相位，其变化范围介于-0.07和+ 0.07弧度之间，并且最小均方误差被优化为\（2.5 \ times 10 ^ {-5} \），接近了相干态极限。我们的方法在基于光纤的实时感测和测量中具有潜在的应用。