| Optical phase estimation,one of the research directions of physics frontier,is critical to the development of quantum communication,gravitational wave detection,quantum key distribution,etc.,and has made significant breakthroughs in measuring position,rotation,dynamic motion,magnetic field and gravitational waves.The fundamental limit of optical phase estimation is limited by quantum mechanics.For a specific physical system,an important direction of optical phase estimation is to develop measurement methods and experimental techniques that can approach or even exceed the standard quantum limit.In recent years,in order to improve the measurement accuracy,various phase estimation algorithm and adaptive phase estimation systems emerge.While improving the accuracy,researchers are also committed to miniaturize,integrate these precision measurement systems.Due to fiber’s small size,immunity to electromagnetic interference,durability to harsh environments,and flexibility of directly embedding into the structured system,fiber sensors have been widely used in the fields of optical precision measurement such as high sensitive strain sensors and fiber optic gyroscopes.Fiber system can be used as a platform for precision phase measurement experiments and is suitable to serve as a bridge between practical precise measurement setups and adaptive phase estimation systems.In this paper,fiber-based adaptive balanced homodyne detection system is mainly studied to realize the quantum-limit measurement for the random phase signal.Besides,fiber-based adaptive interferometer phase tracking system is also built to realize the real-time tracking of the random signal.The details are listed as follows:1.We construct a fiber homodyne system to detect Ornstein-Uhlenbeck random signals.We use an electric-optic amplitude modulator to generate a pair of sidebands at 1.5MHz as input state.After interacting with the random signal,the input beam interferes with local oscillator in a 50/50 fiber beam splitter.Then,the homodyne detection is performed to obtain the optimal estimation of the random signal.In order to achieve the optimal estimation of Ornstein-Uhlenbeck random signal(1kHz),we designed two phase-locked loops to ensure the system works at the optimal measurement point.One phase-locked loop is designed below 100Hz to suppress environmental disturbances,while the other uses Kalman filter theory to achieve real-time optimal estimation.When the photon flux is～106 and the range of random phase signal is ±2.4,the measured MSE has gone beyond the theoretical value from the standard heterodyne theory and is in good agreement with the adaptive filter theory,which proves the achievement of a quantum-limited phase tracking in fiber system.2.We construct a fiber-based Mach-Zender interferometer(MZI)to estimate random signals.The MZI is composed by two 50/50 fiber beam splitters,two fiber PZT phase modulators and two electro-optical modulators(EOM).One MZI input port injects an amplitude modulated beam,while the other port injects a vacuum state.The random signal is imposed on one arm of the MZI by an EOM,which interferes with the signal of the other arm and is received by balanced detectors.The detectors’DC output signal is used to lock the low-frequency loop and suppress environmental disturbance.After demodulated and amplified,the AC signal enters the filter estimation loop,and the PID,as the feedback estimator,impose its output estimated signal on the other arm of the MZI to improve the measurement accuracy.This system is used to track the random phase signals accurately and has potential use in the fiber sensing system. |
