In optical metrological protocols to measure physical quantities, it is, in principle, always beneficial to increase photon number n to improve measurement precision. However, practical constraints prevent the arbitrary increase of n due to the imperfections of a practical detector, especially when the detector response is dominated by the saturation effect. In this work, we show that a modified weak measurement protocol, namely, biased weak measurement significantly improves the precision of optical metrology in the presence of saturation effect. This method detects an ultra-small fraction of photons while maintains a considerable amount of metrological information. The biased pre-coupling leads to an additional reduction of photons in the post-selection and generates an extinction point in the spectrum distribution, which is extremely sensitive to the estimated parameter and difficult to be saturated. Therefore, the Fisher information can be persistently enhanced by increasing the photon number. In our magnetic-sensing experiment, biased weak measurement achieves precision approximately one order of magnitude better than those of previously used methods. The proposed method can be applied in various optical measurement schemes to remarkably mitigate the detector saturation effect with low-cost apparatuses.

在测量物理量的光学计量协议中，原则上增加光子数n总是有益的提高测量精度。但是，实际的限制条件会阻止由于实际检测器的缺陷而导致n的任意增加，尤其是当检测器响应受饱和效应支配时。在这项工作中，我们表明，在存在饱和效应的情况下，改进的弱测量协议（即，偏置的弱测量）可以显着提高光学计量的精度。此方法可检测极小部分的光子，同时保留大量的计量信息。偏置的预耦合导致后选择中光子的额外减少，并在光谱分布中产生一个消光点，该消光点对估计的参数极其敏感并且难以饱和。所以，可以通过增加光子数来持续增强Fisher信息。在我们的磁传感实验中，有偏的弱测量获得的精度比以前使用的方法提高了大约一个数量级。所提出的方法可以应用于各种光学测量方案中，以显着减轻低成本设备的检测器饱和效应。