高精度冷原子重力仪噪声与系统误差研究
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摘要
近二十年来,基于原子干涉的新型惯性传感器得到飞速发展,譬如原子重力仪、原子陀螺仪、原子重力梯度仪等。这些传感器的高稳定性、高灵敏度、高重复率以及潜在的高精度引起了人们的广泛关注,它们在基础科学和应用科学都有着非常广阔的应用前景。早期的原子重力仪体积庞大,只能在实验室环境下工作,人们一直尝试设计紧凑的、可移动的小型化原子重力仪。小型化的原子重力仪可以广泛应用于地球物理、资源勘探、地震研究、重力勘察和惯性导航等领域。最近,随着新技术的快速发展,小型化的原子重力仪不再是遥不可及的东西,目前它们的性能已经可以和传统最好的惯性传感器相媲美。未来,这些小型化的仪器将用在可移动的平台上进行重力测量,譬如飞机、车辆、舰艇甚至卫星。
最近,我们设计并实现了一台高精度的原子重力仪。本论文讨论该重力仪的实验实现过程,并对其主要的噪声源和系统误差进行了详细分析。原子重力仪的主要噪声源包括后向反射镜振动噪声、拉曼光相位噪声、量子极限噪声、探测噪声、拉曼光光强噪声等,其中后向反射镜振动噪声和拉曼光相位噪声是主要的噪声源。系统误差主要包括二阶塞曼频移、射频信号引起的相移、单光子光移、双光子光移、科里奥利力引起的相移及拉曼光波前弯曲引起的相移等等,我们将在文中一一叙述。
目前,在脉冲间隔时间T等于60ms且重复率为2.2Hz的情况下,该重力仪的测量灵敏度可达1.1×10-8g@200s,在此基础上,我们利用该重力仪连续测量了128小时的潮汐信号。另外,我们的原子重力仪还测量了2013年发生的巴基斯坦地震产生的完整地震波信号,这个信号与传统地震仪测量到的地震波信号非常吻合。最后,实验上还测量了本地绝对重力加速度值gabs=(9.793346±2)m/s2,测量精度约1×10-7g。该重力仪目前的性能可以满足大多数重力测量实际应用的要求,为实用型小型化原子重力仪的实现奠定了良好基础。下面对论文各章的主要内容进行介绍：
第一章介绍了原子重力仪的研究背景。首先阐述了重力测量的历史及现状,并比较了几种重力仪的性能。另外,讨论了高精度重力仪在诸多领域的应用前景,并介绍了原子重力仪的最新进展情况。
第二章阐述了原子重力仪的理论基础。首先引入受激拉曼跃迁理论,解释双光子跃迂和共振条件,并介绍实现原子物质波分束与合束的拉曼脉冲。随后介绍三脉冲原子干涉仪,并推导原子物质波包在两条干涉路径上积累的位相差,得到它与重力加速度g的关系。最后,引入干涉仪灵敏度函数为分析原子重力仪噪声做准备。
第三章主要描述了原子重力仪的实验实现过程。先介绍主要的实验装置,包括光学系统、真空系统、磁场系统以及计算机控制系统。然后,简单介绍原子干涉的实验步骤,包括冷原子团制备、选态、干涉仪构建、归一化探测。最后给出实验的结果,主要包括重力测量的灵敏度及精度、长时间潮汐监测信号、绝对重力加速度值以及地震波信号等。
第四章分析了原子重力仪主要的噪声源。首先介绍原子重力仪信噪比评估方法,推导条纹信噪比与重力测量分辨率之间的关系。然后研究干涉条纹斜坡上的相位灵敏度,认识幅度噪声和相位噪声。最后分析原子重力仪主要的噪声源,包括振动噪声、拉曼光相位噪声、量子极限噪声、探测噪声、拉曼光光强噪声等。
第五章评估了原子重力仪的系统误差。首先引入系统误差评估方法,按照是否与拉曼光波矢方向有关分离出各个系统误差。通过不同测量配置方法可以提取固定的系统误差,并评估其大小。最后介绍环境引起的重力加速度变化,并讨论其对绝对重力加速度值评估的影响。
第六章总结了原子重力仪的实验结果及目前存在的问题,并对其未来的前景作了展望。
Over the last twenty years, the novel inertial sensors based on atom interferometer have a rapid development, such as atom gravimeter, atom gyroscope, atom gravity gradiometer. They have attracted worldwide attentions due to their remarkable stability, high sensitivity, high repetition rate and potentially high accuracy. They could be widely applied in the field of the fundamental science and practical research. The previous atom gravimeters could only operate in the laboratories due to their bulk volume. Lots of efforts have been made to simplify the laboratory-based experimental apparatus so as to build compact and transportable atom gravimeter. Such mobile devices are of great use for a wide range, such as geophysics, resource exploration, seismic studies, gravimeter survey, inertial navigation and so on. Recently, the mobile atomic gravimeter has become a reality as the rapid development of the new technologies; and the performances could be comparable with the best classical gravimeter. In the future, they may be installed in the mobile platforms, such as the plane, truck, warship, and even satellite.
Recently, we have designed and realized a high precision atom gravimeter. This thesis focuses on the details of the experiment, and the analysis of the main noise sources and the systematic errors. The main noise sources include the vibration noise of the retro-reflection mirror, the phase noise of the Raman beams, the shot noise, the detection noise, the intensity noise of the Raman beams and so on. Among them, the vibration noise and the phase noise of the Raman beams are dominant. The systematic errors consist of the quadratic Zeeman shift, rf shift, one-photon light shift, two-photon light shift, the phase shift due to Coriolis force and the wave-front distortions of the Raman beams and so on, we will discuss them one by one in this thesis.
Currently, with the interrogation time2T=120ms and the repetition rate2.2Hz, a sensitivity of1.1×10-8g@200s has been reached in our experiment. The tidal phenomenon is observed by monitoring the local gravity continuously over128h based on our atom gravimeter. Moreover, a whole seismic wave occurred in Pakistan was recorded in great detail with our atom gravimeter and the results are compared with that recorded by a traditional seismic detector, which coincide with each other very well. Finally, the absolute gravity value of our laboratory has been measured to be (9.793346±2)m/s2, the uncertainty of measurement is about1×10-7g. The current performance of our gravimeter could meet themost of the field applications. It could be a useful reference for designing the transportable atom gravimeters. The outlines of the chapter of this thesis list as follows:
In the first chapter, the background of the atomic gravimeter is introduced. Firstly, we describe the history and development status of gravity measurement and give the comparison of the performance of several gravimeters. Besides, some discussions on the application prospect of the high precision gravimeter are made. The latest progress on atomic gravimeter is reviewed.
In the second chapter, the basic theory of atomic gravimeter has been presented. Firstly, the theory of stimulated Raman transition is introduced so that the two-photon transition and the resonant condition could be explained. The Raman pulse used for separating and recombining the atomic wave package are introduced. Then, the atom interferometer realized by three Raman pulses is introduced. The phase accumulated along the two different interference paths is deduced. The relationship between the phase and the gravitational acceleration g is obtained. Finally, the sensitivity function of atom interferometer is introduced, which will be useful for the analysis of the noises source of atomic gravimeter.
In the third chapter, the experimental realization of our atomic gravimeter is described. We first introduce the apparatus, which include the optical system, the vacuum chamber, the magnetic field system, the vibration isolation system, the computer control system and the electronic system. Then, the experimental steps are reviewed, which include the preparation of the cold atoms, states selection, the sequence of three Raman pulse, the normalized detection system. Finally, the main experimental results are given, including the sensitivity and accuracy of the gravity measurement, the long-term gravity monitoring, the measurement of the absolute gravity value, the detection of the seismic wave and so on.
In the fourth chapter, the main noise sources of atomic gravimeter have been analyzed. We first introduce the evaluation method of the signal to noise, and deduce the relationship between the SNR and the resolution of gravity measurement. Then, the sensitivity at the slope of interference fringe is investigated so that the amplitude noise and the phase noise are recognized. In the end, we analyzed the main noise source of atomic gravimeter, which include the vibration noise, the phase noise of Raman beam, the shot noise, the detection noise, the intensity noise of the Raman pulses, and so on.
In the fifth chapter, the systematic errors of atomic gravimeter are evaluated. At first, the evaluation method of the systematic error is presented; the different systematic phase shifts could be extracted by inversing the Raman wave vector to measure the fringes. Benefit from the different configurations of measurement, the amplitude of the phase shifts could be obtained. Finally, the variation of gravity acceleration due to the environmental effects is introduced and their impacts on gravity measurements are discussed.
In the sixth chapter, the main experimental results and the existed problems have been summarized; the prospect of the future atomic gravimeter is shown.
最近,我们设计并实现了一台高精度的原子重力仪。本论文讨论该重力仪的实验实现过程,并对其主要的噪声源和系统误差进行了详细分析。原子重力仪的主要噪声源包括后向反射镜振动噪声、拉曼光相位噪声、量子极限噪声、探测噪声、拉曼光光强噪声等,其中后向反射镜振动噪声和拉曼光相位噪声是主要的噪声源。系统误差主要包括二阶塞曼频移、射频信号引起的相移、单光子光移、双光子光移、科里奥利力引起的相移及拉曼光波前弯曲引起的相移等等,我们将在文中一一叙述。
目前,在脉冲间隔时间T等于60ms且重复率为2.2Hz的情况下,该重力仪的测量灵敏度可达1.1×10-8g@200s,在此基础上,我们利用该重力仪连续测量了128小时的潮汐信号。另外,我们的原子重力仪还测量了2013年发生的巴基斯坦地震产生的完整地震波信号,这个信号与传统地震仪测量到的地震波信号非常吻合。最后,实验上还测量了本地绝对重力加速度值gabs=(9.793346±2)m/s2,测量精度约1×10-7g。该重力仪目前的性能可以满足大多数重力测量实际应用的要求,为实用型小型化原子重力仪的实现奠定了良好基础。下面对论文各章的主要内容进行介绍：
第一章介绍了原子重力仪的研究背景。首先阐述了重力测量的历史及现状,并比较了几种重力仪的性能。另外,讨论了高精度重力仪在诸多领域的应用前景,并介绍了原子重力仪的最新进展情况。
第二章阐述了原子重力仪的理论基础。首先引入受激拉曼跃迁理论,解释双光子跃迂和共振条件,并介绍实现原子物质波分束与合束的拉曼脉冲。随后介绍三脉冲原子干涉仪,并推导原子物质波包在两条干涉路径上积累的位相差,得到它与重力加速度g的关系。最后,引入干涉仪灵敏度函数为分析原子重力仪噪声做准备。
第三章主要描述了原子重力仪的实验实现过程。先介绍主要的实验装置,包括光学系统、真空系统、磁场系统以及计算机控制系统。然后,简单介绍原子干涉的实验步骤,包括冷原子团制备、选态、干涉仪构建、归一化探测。最后给出实验的结果,主要包括重力测量的灵敏度及精度、长时间潮汐监测信号、绝对重力加速度值以及地震波信号等。
第四章分析了原子重力仪主要的噪声源。首先介绍原子重力仪信噪比评估方法,推导条纹信噪比与重力测量分辨率之间的关系。然后研究干涉条纹斜坡上的相位灵敏度,认识幅度噪声和相位噪声。最后分析原子重力仪主要的噪声源,包括振动噪声、拉曼光相位噪声、量子极限噪声、探测噪声、拉曼光光强噪声等。
第五章评估了原子重力仪的系统误差。首先引入系统误差评估方法,按照是否与拉曼光波矢方向有关分离出各个系统误差。通过不同测量配置方法可以提取固定的系统误差,并评估其大小。最后介绍环境引起的重力加速度变化,并讨论其对绝对重力加速度值评估的影响。
第六章总结了原子重力仪的实验结果及目前存在的问题,并对其未来的前景作了展望。
Over the last twenty years, the novel inertial sensors based on atom interferometer have a rapid development, such as atom gravimeter, atom gyroscope, atom gravity gradiometer. They have attracted worldwide attentions due to their remarkable stability, high sensitivity, high repetition rate and potentially high accuracy. They could be widely applied in the field of the fundamental science and practical research. The previous atom gravimeters could only operate in the laboratories due to their bulk volume. Lots of efforts have been made to simplify the laboratory-based experimental apparatus so as to build compact and transportable atom gravimeter. Such mobile devices are of great use for a wide range, such as geophysics, resource exploration, seismic studies, gravimeter survey, inertial navigation and so on. Recently, the mobile atomic gravimeter has become a reality as the rapid development of the new technologies; and the performances could be comparable with the best classical gravimeter. In the future, they may be installed in the mobile platforms, such as the plane, truck, warship, and even satellite.
Recently, we have designed and realized a high precision atom gravimeter. This thesis focuses on the details of the experiment, and the analysis of the main noise sources and the systematic errors. The main noise sources include the vibration noise of the retro-reflection mirror, the phase noise of the Raman beams, the shot noise, the detection noise, the intensity noise of the Raman beams and so on. Among them, the vibration noise and the phase noise of the Raman beams are dominant. The systematic errors consist of the quadratic Zeeman shift, rf shift, one-photon light shift, two-photon light shift, the phase shift due to Coriolis force and the wave-front distortions of the Raman beams and so on, we will discuss them one by one in this thesis.
Currently, with the interrogation time2T=120ms and the repetition rate2.2Hz, a sensitivity of1.1×10-8g@200s has been reached in our experiment. The tidal phenomenon is observed by monitoring the local gravity continuously over128h based on our atom gravimeter. Moreover, a whole seismic wave occurred in Pakistan was recorded in great detail with our atom gravimeter and the results are compared with that recorded by a traditional seismic detector, which coincide with each other very well. Finally, the absolute gravity value of our laboratory has been measured to be (9.793346±2)m/s2, the uncertainty of measurement is about1×10-7g. The current performance of our gravimeter could meet themost of the field applications. It could be a useful reference for designing the transportable atom gravimeters. The outlines of the chapter of this thesis list as follows:
In the first chapter, the background of the atomic gravimeter is introduced. Firstly, we describe the history and development status of gravity measurement and give the comparison of the performance of several gravimeters. Besides, some discussions on the application prospect of the high precision gravimeter are made. The latest progress on atomic gravimeter is reviewed.
In the second chapter, the basic theory of atomic gravimeter has been presented. Firstly, the theory of stimulated Raman transition is introduced so that the two-photon transition and the resonant condition could be explained. The Raman pulse used for separating and recombining the atomic wave package are introduced. Then, the atom interferometer realized by three Raman pulses is introduced. The phase accumulated along the two different interference paths is deduced. The relationship between the phase and the gravitational acceleration g is obtained. Finally, the sensitivity function of atom interferometer is introduced, which will be useful for the analysis of the noises source of atomic gravimeter.
In the third chapter, the experimental realization of our atomic gravimeter is described. We first introduce the apparatus, which include the optical system, the vacuum chamber, the magnetic field system, the vibration isolation system, the computer control system and the electronic system. Then, the experimental steps are reviewed, which include the preparation of the cold atoms, states selection, the sequence of three Raman pulse, the normalized detection system. Finally, the main experimental results are given, including the sensitivity and accuracy of the gravity measurement, the long-term gravity monitoring, the measurement of the absolute gravity value, the detection of the seismic wave and so on.
In the fourth chapter, the main noise sources of atomic gravimeter have been analyzed. We first introduce the evaluation method of the signal to noise, and deduce the relationship between the SNR and the resolution of gravity measurement. Then, the sensitivity at the slope of interference fringe is investigated so that the amplitude noise and the phase noise are recognized. In the end, we analyzed the main noise source of atomic gravimeter, which include the vibration noise, the phase noise of Raman beam, the shot noise, the detection noise, the intensity noise of the Raman pulses, and so on.
In the fifth chapter, the systematic errors of atomic gravimeter are evaluated. At first, the evaluation method of the systematic error is presented; the different systematic phase shifts could be extracted by inversing the Raman wave vector to measure the fringes. Benefit from the different configurations of measurement, the amplitude of the phase shifts could be obtained. Finally, the variation of gravity acceleration due to the environmental effects is introduced and their impacts on gravity measurements are discussed.
In the sixth chapter, the main experimental results and the existed problems have been summarized; the prospect of the future atomic gravimeter is shown.
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