Study On Signal-to-noise Ratio And Detection Limit Of Weak Measurement In Noise Environment

Weak measurement,as one of the indirect measurement,has been widely applied to observe the effect of puny measurement to different felds in recent years.because its weak value is much larger than the eigenvalue of system observable.Such as optical precision measurement and gravity wave detection.However,there is some noise in the measurement inevitablely.Therefore,it's a high-profile subject that how to suppress the impact of noise on the measurement effectively and improve signal-to-noise ratio and detection limit.Obviously,it is necessary to know what noise affects the measurement in the system if you want to improve the measurement by suppressing noise.For optical weak measurement system,it'is widely considered that.shot noise is the dominant noise affecting the measurement.However,it is not clear the influence of frequency noise,another basic noise of system,is pivotal or not.We research influence of various noise to signal-to-noise ratio and detection limit quantitatively in the mirrors displacement measurement of Mach-Zehnder interferometer so as to explain the influence of the frequency noise is critical and promote further improvement on measurement.In addition,in order to further develop the optical precision measurement,we also research the improvement quantitatively when both input ports of MZ interferometer entering the squeezed light field.The main contents of this paper are as follows:The first chapter mainly introduces the research background and purposes of the paper.The research status of weak measurement in optical interferometer,research progress of weak measurement in noisy environment and the frameworks and main contents of paper are introducted briefly.The second chapter mainly introduces the related basic theory of this paper and the principle of realizing quantum weak measurement in MZ interferometer.Such as the related concept of quantum measurement and weak measurement,light field of different quantum state.the principle and specific derivation process of re-alizing weak measurement and replacing momentum with frequency displacenment as measurement signal in MZ interferometer.The third chapter research the influence of different,noise on the signal-to-noise and the detection limit in the measurement of the mirror displacement in the MZ interferometer.We discover the effect of radiation pressure from input light on this measurement is negligible,and the weaker measurement strength of the weak measurement,the higher success rate of postselection and the more effective information will detect,and also propose the noise affecting measurement not noly shot noise but also frequency noise are nonnegligible.When considering combined effects of two kinds of noise,the detection limit is more precise by forty-eight percent than consideration of shot noise only.In addition,the total number of photons at tlhe exit ports,the measurement signal and the frequency noise remain constant when the both input ports of MZ interferometer entering the squeezed light field.But the shot noise is compressed by a factor of e-2rs,the signal-to-noise ratio improved by a factor of about ers,and the detection limit improved by a factor of e-rs.The greater squeezing factor,the more obvious improvenent will obtain.The fourth chapter is the summary and outlook to this paper.We hope that we could suppress even eliminate the frequency noise by modulating input state of system and measurement device on the basis of this paper and could achieve higher quality quantum measurement.