Precision Temperature Control In Laser Frequency Stabilization

Narrow-linewidth lasers with high frequency stability play important roles in various research fields of precision measurements such as precision spectroscopy,optical frequency standards,and gravitational-wave detection.Locking the laser frequency to the resonances of high-finesse optical cavity by the Pound-Drever-Hall(PDH)locking technique can obtain a narrow-linewidth laser with high frequency stability.In the PDH stabilization scheme,the frequency stability of the cavity-stabilized laser largely depends on the length stability of the optical reference cavity.The temperature stabiliy of the reference cavity is an important factor which affects the length stability of the reference cavity and therefore has an effect on the frequency stability of the frequency-stabilized laser.To minimize the effect of the cavity's temperature fluctuations on the frequency stability of the frequency-stabilized laser,we focus on improving the temperature stability of the reference cavity in this thesis.Firstly,using the vaccum chamber housing the reference cavity as the temperature cotrol plant,we measure and analyze the individual and the overall open-loop response of the temperature control system.The analysis lays a foundation for the subsequent noise analysis of the same system,and for the construction of a two-stage temperature control system of the 20 cm reference cavity in the laser frequency stabilization system.The performance of the temperature control system is optimized in terms of the step response of the system,providing the basis of the response analysis of the system.The main purpose of the response analysis of the system is to optimize its performance.The stability of the temperature control system is investigated primarily from a knowledge of the open-loop response of the system.In order to investigate the factors that limit the control accuracy of the home-made temperature controller circuit,the noise analysis of the temperature control system is carried out in this thesis.For this purpose,we establish the noise model of the temperature control system,then quantitatively analyze the contributions of a variety of noise sources to the temperature noise,and identify the main source of the temperature noise.A home-made "noninverting amplifier"temperature controller and an improved "instrumentation amplifier" temperature controller based on the former are used for the temperature control of the vacuum chamber.Meanwhile,we measure and analyze the temperature noises of both temperature control systems,validating the noise model of the temperature control system.The analysis reveals that the in-loop temperature noises of both kinds of temperature control systems are eventually limited by the residual ambient temperature noise due to the limited loop gain.The out-of-loop temperature noise of the "noninverting amplifier" temperature control system is ultimately limited by the output noise of the sigle-arm resistance bridge,whereas the out-of-loop temperature noise of the "instrumentation amplifier" temperature control system is limited by the output noise of the Wheatstone bridge and the noise of the instrumentation amplifier.In addition,we briefly discuss the measures that can be adopted to further improve the performance of the thermal control system.Based on the above work,we develop a two-stage temperature control system for the temperature stabilization of the 20-cm reference cavity used in the laser stabilization system.First of all,the cylinder and two covers of the vacuum chamber housing the 20-cm reference cavity are independently temperature stabilized by three"Instrumentation Amplifier" temperature controller circuit.And then the entire vacuum system is placed in the home-made thermostat for the implementation of the second-stage temperature control.When the two-stage temperature control system works properly,we make long-term measurements of the temperature fluctuations of the environment,the air inside the thermostat,and different locations on the vacuum chamber with free running thermistors.During the 21-days measurement period,the room temperature fluctuates by about 0.45 ?,the temperature fluctuation of the air in the thermostat is about 4 mK,and the temperature fluctuations of different locations on the vacuum chamber are within 0.2 mK.Through the analysis,it is found that the two-stage temperature control system has at least 2200 times attenuation to the ambient temperature noise in the Fourier frequency range of 10-6 Hz?10-3Hz.In order to further improve the temperature stability of the reference cavity,we reduce the rate of the heat transfer between the vacuum chamber and the reference cavity by palcing two layers of thermal shields inside the vaccum chamber.To estimate the temperature evolution of the reference cavity,we establish a model that describes the heat transfer among the vacuum chamber,the thermal shields and the cavity.Meanwhile,we operate the reference cavity at its coefficient of of thermal expansion(CTE)null temperature,which can effectively reduce the sensitivity of the cavity length to the temperature fluctuation.According to the heat transfer model,we estimate the temperature stability of the cavity from the temperature fluctuation of the vacuum chamber,and the evaluate the resultant fractional frequency stability.For the temperture offset from the CTE point of the cavity |?T|?0.2 K,the cavity temperature fluctuation induced fractional frequency instability is less than the thermal noise limit(2.12×10-16)of the cavity for times scales shorter than 104 s,indicating that the thermal instability of the cavity is not a limiting factor for the laser frequency stability.