Quantum Metrology Studies Based On Adaptive Feedback

The improvement of measurement accuracy can not only verify the existing physical theories,but also promote the development of new theories and technologies.For example,phase measurements can be used to measure any relative displacement with subwavelength accuracy,which has been used in cosmology,nanotechnology and medicine.Due to the limitations of the physical properties,such as shot noise and uncertainty principle,the accuracy that can be achieved by classical measurement is the shot noise limit.Exploring how to use quantum resources to improve the measurement accuracy has given rise to quantum metrology,which is an emerging research directions.After decades of research,it is found that the shot noise limit is generally saturated only at a specific phase point,in other words,the measurement accuracy at other phase points cannot reach the shot noise limit.It is very difficult to find the measurement method which can reach the shot noise limit at all phase points.To reach the shot noise limit,the majority of measurement methods need two conditions: 1)measurement times N??;2)the true value of the phase to be estimated can maximize fisher information.A similar phenomenon exists in most quantum measurement schemes that break shot noise limit.However,these two conditions are not always satisfied.This paper focuses on the application of adaptive control in quantum metrology.The specific research contents are as follows:(1)The Ab initio phase estimation based on on-off measurement and real-time feedback.Different from the previous Ab initio phase estimation based on the coherent state and MZ interferometer,we added an adaptive feedback control system to one arm of the MZ interferometer.In this work,300 measurements were made in phase estimation with or without feedback.In the process of adaptive phase estimation,an effective Bayesian algorithm is used to update the conditional probability distribution of the phase after each round of measurement.Compared with the non-feedback scheme,this scheme can achieve the deterministic phase estimation,and there are not two uncertain estimated phases like the non-feedback control.In addition,in the case of any true phase,the estimation accuracy can reach the shot noise limit after about 150 steps of measurement.This kind of adaptive phase estimation can be extended to multi-parameter estimation problems.(2)Random phase estimation based on SU(1,1)nonlinear interferometer.At present,the main research object of quantum measurement is the static phase.However,it is not enough to measure the fixed phase,because many of the signals we are interested in are changing randomly with time.For example,observing the Brownian motion of small particles in a liquid is the problem of random signal estimation that changes in real time.Therefore,the second work of this paper is to propose an Ornstein-Uhlenback stochastic optical phase estimation with a SU(1,1)nonlinear interferometer.In this scheme,the input state of the SU(1,1)nonlinear interferometer is coherent state,and the detection method at the output is balanced homodyne detection.At the same time,we give real-time adaptive feedback phase to one arm of the nonlinear interferometer and the local oscillating light at the homodyne detection.Compared with the traditional MZ interferometer,the mean square error of random phase prediction,tracking and smoothing are obviously reduced under the same photon number flux.In addition,there is an optimal parametric amplification factor which minimizes the mean square error.Finally,we can reach the random Heisenberg limit and break the minimum mean square error under standard measurements.(3)Random phase tracking research based on two-photon entangled state.Firstly,the beam-like single photon source is generated by BBO nonlinear crystal and the two-photon entangled state is prepared based on Hong-Ou-Mandel interference.Then,the Ornstein-Uhlenback random phase tracking scheme based on two-photon entanglement is proposed.In this scheme,we have used the effective Bayesian theory which is based on rejection filter,and the feedback phase is determined based on the steepness of the posterior probability distribution.Finally,we realized the Ornstein-Uhlenback random phase tracking experimentally and the mean square error is below the random shot noise limit.