Ultrasensitive Parameter Estimation Based On Quantum Weak Value Measurement

Quantum measurement always plays a significant role as one of five postulates of quantum mechanics,which is one of two fundamental theories in modern physics.With the development of science and technology,the range of exploration is expanding and has gone deep into the world of quantum.We have a more profound understanding about quantum mechanics and quantum measurement in this process,which also promotes the improvement of technology and measurement accuracy.Quantum weak value measurement comes out on this background and has drew much attention owing to its effect of amplifying weak signal and widespread application.Some weak effects are usually difficult to be detected by traditional methods in present technology condition,this article present a series of studies about ultrasensitive parameter estimation in theory and experiment based on the amplification effect of weak value measurement.The main contents are as follows.1.Measurement of ultralow velocities based on weak value measurement.Owing to the fact that it is difficult to measure the doppler frequency shift introduced by ultralow velocities in frequency domain,we covert it to the time domain and use weak val-ue measurement to amplify the time shift introduced by velocities.Here we construct a near destructive interference velocity measurement device where its probe is a Gaussian pulse mod-ulated by acoustic-optics modulator,system is a near destructive Michelson interferometer,and the weak couple between probe and system is introduced by the movement of mirror in one arm of interferometer.We have experimentally demonstrated the validity of this method where the minimum velocity arrives the order of nm/s and its precision is bounded by Cramer-Rao bound(short noise limit),all of that match well with the predictions of theory.2.Measurement of angular velocities based on weak value measurement.Here we introduce a polarization-dependent angular velocity measurement system consisting of two Glan prisms and a true zero-order half wave plate,where a Gaussian pulse acts as the meter.The angular velocities measurements results agree well with theoretical predictions and its uncertainties are bounded by the Cramer-Rao bound.We also investigate uncertainties of angular velocities for different number of detected photons and the smallest reliable post-selection probability.3.High precision measurement of temperature changes based on weak value measurement.High precision measurement of temperature changes is of great significance in modern tech-nology.It is usually hard to measure ultrasensitive temperature changes directly.Based on the fact that temperature changes can cause the phase changes between the o and e light,here we construct a polarization-dependent weak-value-based system to amplify this phase changes and convert to measurement of the intensity of light,from which we can infer the temperature changes of multi order quartz wave plate.The precision is 9 times higher than the balanced homodyne detection,which demonstrates that weak value measurement has some advantages in presence of technical noise.4.Using the power recycling and signal recycling technique to improve the intensity of detected light and corresponding signal-to-noise ratio(SNR).The weak value amplification comes at the sacrifice of great reduction of detected signal.This gain and loss balance each other,leading to the same SNR of the measured parameter as would be found if the measurement was made directly,provided the system is ideal.Here we propose the power recycling and signal recycling scheme to reuse the abandoned light,where a cavity is formed by inserting a partially transmitting mirror in the input or output port of mea-surement system.We have showed three recycling weak value measurement schemes including power recycling velocity measurement,power recycling angular velocity measurement and signal recycling velocity measurement based on the velocity and angular velocity measurement exper-iments.In our analysis,these three schemes can all increase the intensity of detected light and the SNR.However,the amplification effect in power or signal recycling schemes is not as good as the standard weak measurement owing to the walk-off effect.Besides,the signal recycling scheme has some technical advantages over the power recycling scheme.Finally we compare power recycling weak measurement with the joint weak measurement and find they both have different features,which can be applied to different occasions.