Laser Frequency Noise And Clock-jitter Noise Reduction By Using Time Delay Interferometry Technique

Space-borne gravitational wave（GW）detection will open a new window in the lower frequency band from 0.1 m Hz to 1 Hz,which cannot be accessed for the ground-based GW detector due to the Earth’s seismic and gravity-gradient noises.Because of the lower-frequency spectrum range,space-borne GW detectors could provide a wealth of information to study the highly energetic cosmic events.In general,the space-borne GW detectors measure the Doppler shifts（5-20 MHz）in a giant laser interferometer,and subsequently the GW signal can be picked out via a series of data post processing.Due to their extremely small amplitudes(about 10^-20/Hz^1/2)in the science band,the noise management and reduction is of key importance for the successful observation of GWs.Today,the state of the art of the pre-stabilized laser can reach the level of 10^-13/Hz^1/2 in the interested band,7 orders of magnitude above the requirement.In the ground-based GW detectors,the laser phase noise can be real-time cancelled out with the help of the equal-arm configuration in the Michelson interferometer.However,it is rather difficult to fly an equal-arm constellation in the space all the time.Technique of time delay interferometry（TDI）has been therefore proposed and developed to solve this great challenge.In TDI,multi data streams are time shifted to align the laser phase noise precisely,giving rise to a virtual equal-arm interferometer,and the laser phase noise can be effectively removed through the linear combinations.Another significant noise is the clock noise introduced when counting the various frequency offsets.To date,the best performance of the clock is at the level of 10^-17/Hz^1/2,3 orders of magnitude above the requirement.Recently,time delay interferometry with the simultaneous reduction of laser phase noise and clock noise has been progressing at a rapid pace.This Ph D thesis focuses on the reduction strategies and algorithms of the two noises,laser phase noise and clock noise,and consists of three specific parts.1.A variety of alternative combinations are found to identify different GW signals and instrument noise,by combining the geometric TDI with the ternary-symbolic formulas algorithm.2.A general algorithm for the clock noise reduction is proposed using various TDI combinations and the sideband modulation technique.The clock noise can be reduced to be below the second-order commutator term of the time delay operator.3.By solving the limitation of specific TDI combination and decomposing the signal and noise in one single data stream,the sensitivity functions for arbitrary TDI combinations is analytically evaluated under the metric theory of gravity,which can be used to see the detection limit for different combinations of TDI.Our work can offer a theoretical reference for the sensitivity functions and the noise reduction in the space-borne GW detectors.