Quantum Enhanced Optical Phase Estimation With A Squeezed State

Metrology is a comprehensive subject that studies measurement and measurement error.With the rapid development of quantum mechanics and the constant improvement of quantum resources,quantum metrology is a new developed subject because of the combination of metrology and quantum mechanics at the micro level and has been developed rapidly in recent decades.The research goal of quantum metrology is to realize the measurement of physical parameters with high resolution and sensitivity.The theory of quantum mechanics is used to describe the physical system in order to achieve higher measurement accuracy than the classical measurement.Precision measurement of physical quantities is fundamental to scientific and technological progress,and quantum mechanic plays a central role in this challenge.On the one hand,the inevitable statistical error because of the vacuum fluctuation of quantized electromagnetic field limits the measurement accuracy.Quantum mechanic gives a limit for parameter measurement accuracy that cannot be broken by classical metrology,which is so-called standard quantum limit(SQL).On the other hand,some nonclassical characteristics of quantum mechanic,such as coherence,entanglement and squeezing,can be used to break through the standard quantum limit and realize quantum enhanced measurement.Phase estimation protocol provides a fundamental benchmark for quantum metrology and it is a powerful measurement strategy to perform accurate measurements of various physical quantities including length,velocity and displacements.The core problem is to obtain high estimation accuracy and sensitivity with fixed resources(photon/measurement sample number).Due to the inexistence of the phase Hermitian operator,the true value of phase cannot be directly measured.A general method is to find an observable operator associated with phase,such as field-or intensity-based quantities by interferometric devices,and then deduce the phase indirectly according to the measurement results.This indirect measurement process for the value of phase shift is called phase estimation.Quantum phase estimation is the phase estimation protocol with quantum resources,and it can provide a measuring method of phase shift with precision superior to the SQL due to the application of nonclassical states.A squeezed vacuum state,whose variance in one quadrature is lower than the corresponding SQL,has been pointed out as a sensitive resource for quantum phase estimation and the estimation accuracy is directly influenced by the properties of the squeezed state.The main research content during my Ph.D period is quantum enhanced optical phase estimation with a squeezed state.The research is started from the quantum resource for quantum phase estimation.Firstly,the frequency and intensity noise of the laser are optimized,and the squeezed state which can work stably for a long time is generated.And then the generated stable squeezed state is used as the probe beam for quantum phase estimation,a simple and stable scheme of quantum phase estimation with squeezed state has been realized.Based on the deterministic advantage of continuous-variable non-classical field,the scheme has a broad application in the field of quantum metrology.The main contents of the doctoral dissertation:1.Improvement of the intensity noise and frequency stabilization of Nd:YAP laser with an ultra-low expansion Fabry-Perot cavity.A spherical high finesse(50000)ultra-low expansion Fabry-Perot cavity is selected as the reference cavity of the laser.By using an acousto-optic modulator(AOM)as the fast feedback actuator to improve the response bandwidth of the locking system,an special-designed cascade Pound-Drever-Hall technique is realized to lock the laser to the ultra-stable F-P cavity.The frequency drift of the laser is suppressed to 7.72 MHz in 4 hours,and the noise level of the laser is simultaneously reduced to the quantum noise limit in the frequency below 300 k Hz.The improvement of frequency and intensity noise of the laser has been completed.2.The quantum enhancement phase estimation is realized experimentally by using the generated stable squeezed.The previously optimized laser are used as the injected seed beams and the pump beam of an efficient nondegenerate optical parametric amplifier(NOPA)with a wedged KTP crystal,which can realize type-II noncritical phase matching without walk-off effect.And then the squeezed state which can work stably for a long time is generated.The generated squeezed state acquires an unknown phase shift and then is combined with a strong local oscillator beam at a 50/50 beam splitter(BS)for homodyne measurement to obtain the quadrature component associated with the phase shift.The true value of the phase can be inferred by Bayesian inference from the homodyne measurements,and then a simple and stable scheme of quantum phase estimation has been realized.We experimentally implement the phase estimation accuracy can be superior to the standard quantum limit with squeezed state at a given photon number.The squeezed pure state behaves as the optimal resource to reach quantum Cramér-Rao bound(QCRB).The creative works are as follows:1.By adding an AOM as the fast feedback actuator,an special-designed cascade Pound-Drever-Hall technique is utilized to lock the laser to a high finesse F-P cavity.The improvement of frequency and intensity noise of the laser has been realized.2.A simple and stable experimental scheme of high precision phase estimation is realized with the generated squeezed state by combining balanced homodyne detection and Bayesian inference,the estimation accuracy can be superior to the standard quantum limit and the squeezed pure state behaves as the optimal resource to reach QCRB.