应用于光钟的镱原子激光冷却和囚禁的理论研究
|
摘要
原子光钟是基础物理研究和频率标准这一古老研究领域的重要研究课题。这一研究能够成为当前一个热点的主要原因是微波原子钟的发展已经遇到瓶颈。而光钟由于采用频率更高的光频,因此是下一代高精度原子钟的公认的发展方向。经过一段时间的发展,目前光钟的发展方向主要定位在单离子钟和光晶格钟。最新型的单个离子光钟已经成功实现了～10-18的分数频率不确定度,并成功运用于基础物理常数变化的测定和相对论物理的检验,将基础物理常数变化限制在一个更小的范围。然而根据量子理论,离子钟将最终受限制于量子投影噪声。减小量子投影噪声的一个重要途径就是增加被测原子或离子的数量。受库仑相互作用的影响,离子阱中的离子数量很难再增加。而光晶格钟秉承了离子钟的优点同时又可以提高量子吸收器的数量,其量子投影噪声大大减小,精度将有望超过离子钟,因此光晶格钟是目前一个热门的研究方向。镱原子光钟是光晶格钟的方向之一。而光晶格钟的一个核心问题就是如何获得对外界干扰免疫的时钟跃迁,目前通用的做法是利用激光冷却与囚禁技术来实现。
激光冷却与囚禁镱原子复杂而锁碎,涉及到方方面面的问题,小到一个控制电路的设计与实现,大到一台激光器的设计以及冷却与囚禁光学系统的设计与实现。由于是从无到有的建设冷镱原子系统,我们当前需要解决的有三个问题。第一个问题是,高效率的冷却激光光源的设计与实现。尽管目前多种方案可以获得冷却激光,然而冷却激光的方案还在探索和发展之中。激光功率和效率的提高将直接改善冷却的效果,同时简化系统。第二个问题是,在锶原子建立在交际跃迁上的磁光阱可以将锶原子冷却到多普勒冷却极限以下,而对于镱原子交际跃迁磁光阱冷却获得的温度远远大于多普勒冷却极限温度。第三个问题是,目前已经实现的镱原子光晶格钟的频率评估发现,原子之间的碰撞频移还很大,其中一个影响就是镱原子的温度还不够低。同时单个离子光钟成功的经验表明把原子冷却到振动基态对抑制原子钟的不确定度是十分重要的。
本论文针对以上三个问题展开深入研究。论文的第一章简单介绍了原子钟到光钟的发展过程,以及光钟关键技术的原理,总结了镱原子光晶格钟的在国际上的发展状况,介绍了冷镱原子与光钟的关系以及镱原子冷却的基本原理。
第二章我们研究了如何使用二次谐波产生技术高效产生一级冷却激光光源的问题。我们首先推导了在双轴晶体中二次谐波产生功率与基频激光的聚焦,走离效应,相位匹配等因素的关系,最后得到一个二次谐波产生功率表达式。我们将这个表达式应用于分析三硼酸锉晶体倍频797.822 nm激光的优化设计。我们首先计算出晶体的相位匹配条件以及相关晶体参数,然后利用二次谐波产生功率表达式计算出最佳二次谐波产生所需的光束条件。根据这些条件我们设计了用于增强基波光强的谐振腔。考虑到各种因素之后,我们预测按照这个方案可以获得180 mW的一级冷却激光,对应于37%的转化效率。
第三章我们研究了如何使用二次谐波产生技术在实验室高效产生二级冷却激光光源。第一。我们研究了光纤激光到波导倍频器的激光耦合问题。通过实验探索我们找出来一种由光纤准直器和准直透镜组成的光学耦合系统其耦合效率可以比常用的显微物镜光纤耦合系统高出10%以上。第二,我们研究了光波导的中二次谐波产生与基波的偏振以及波导的温度等条件的关系,并找出了光波导的最佳工作条件。第三,我们研究了光波导绿光输出的光束准直问题,通过实验探索我们找到由显微物镜和透镜组成的光学准直系统可以获得M2<1.1的光束质量。第四,我们对实验中测量到的波纹状温度调节曲线进行了研究,经过理论分析我们发现这种波纹状的温度调节曲线是由于波导的光学非均匀性造成。我们同时研究了光学非均匀性对二次谐波转化效率的影响。第五,我们研究了在高基波功率时,二次谐波功率与理论预测值相比出现下降的问题。通过模拟,我们发现这种下降分两个过程,第一个过程是吸收造成的下降,第二个过程是吸收以及其引起的温度改变造成的下降。
第四章我们研究了一级磁光阱冷却和二级磁光阱冷却的多普勒冷却机制。第一,我们研究了一级磁光阱冷却的动力学特性和热力学特性,并解释了此前的一级磁光阱冷却的结果。第二,我们研究了二级磁光阱的动力学特性和热力学特性,通过分析我们发现在二级磁光阱的多普勒冷却机制根据动力学特性可以分为两种情况,第一是重力可以忽略的情况,第二种是重力需要考虑的情况。在这两种情况下,其热力学特性也不同。根据分析结果我们计算了原子温度和磁光阱参数的关系。
第五章我们研究了钟频光位移的抑制的物理机制和冷镱原子的控制系统。第一,我们从微扰理论出发推导出原子在光场作用下的极化率公式并根据光位移的表达式我们初步计算了镱原子的最佳波长。同时,我们还计算了一维和三维光晶格的囚禁势。第二,我们研究了如何在实现对冷却系统实行一体化的控制。在声光调制器,机械开关等控制执行元件的基础上,我们利用多功能数据采集卡以及相关软件平台设计了一套有机的控制系统。
第六章我们研究了在磁光阱多普勒冷却的基础上进一步将镱原子温度冷却到更低并最终将原子冷却到运动零点能的冷却方案。第一,我们介绍了镱原子在光晶格中的相互作用机制,以及其对光晶格原子钟的不确定度的影响。第二,我们介绍了边带冷却的原理以及使用钟频跃迁进行边带的物理机制。第三,我们首先介绍了拉曼跃迁的原理,接下来我们研究了如何通过最佳波长光晶格产生拉曼耦合以及使用拉曼耦合进行边带冷却的方案。根据分析结果,我们预测这种冷却方案可以将原子冷却到运动基态,温度可以冷却到1μK以下。这种边带冷却技术和绝热冷却技术结和可以应用于光晶格钟。
最后在第七章中,我们对本文主要研究工作进行了概括性总结,并在此基础上,对未来的发展进行了展望。
Study on optical atomic clocks is a hot topic in the field of fundamental physics and frequency metrology as the fractional frequency uncertainty of the microwave atomic clock is approaching the quantum projection noise limit. The need of more accurate atomic clocks for testing the fundamental physical problem such as measuring variation of fundamental constants, testing the relativity theory is very urgent. With the rapid progress in space science and technology, the current atomic clocks also can not fulfill the requirements. As the optical frequency is around several orders of magnitude higher than the microwave frequency, the fractional frequency uncertainty of the optical clock may be much smaller than that of the microwave clock. Therefore, the optical clock is considered as the candidate of the next generation frequency standards. The state-of-art single ion optical clock has achieved the fractional frequency uncertainty on the order of 10-18 and it has been used for testing the variation of fundamental constants and the theory of relativity. The variation of fundamental constants has been restricted in a very small range. However, the single ion optical clock will be limited by quantum projection noise according to the quantum theory. An important way to reduce the quantum projection noise is to increase the number of quantum absorbers. In the ion traps, the number of ions is limited by the coulomb repulsion. The optical lattice clock inherits the merits of the ion clock and the number of quantum absorbers can be greatly increased. The optical lattice clock may surpass the ion clock in the future. Therefore, considerable strides have been taken recently toward this kind of optical clocks. Ytterbium lattice clock is one kind of the lattice clocks. Currently, a key issue of the optical lattice clock is how to make the clock line immune to the environment perturbations. Improving the methods of cooling and trapping of ultracold Ytterbium atoms is the major solution.
Cooling and trapping Ytterbium atoms is a complex work. Many problems need to be solved from a control circuit to a laser and the cooling and trapping optical systems. Currently, we need to solve three problems. The first one is designing and constructing highly efficient and compact laser sources for laser cooling and trapping. Increasing the efficiency of the laser and making it smaller can improve the cooling results and simplify the system. The second one is that the final temperature of the second stage Doppler cooling of Ytterbium is much higher than the Doppler cooling limit. The magneto-optical trap on the intercombination transition of strontium can cool the temperature of strontium atoms down to the Doppler cooling limit. However, the final temperature of magneto-optical trap on the intercombination transition of Ytterbium is much higher than the Doppler cooling limit. The third one is cooling the Ytterbium atoms to zero-point energy of motion. Recent frequency evaluation of the Ytterbium atomic clock indicates that density related frequency shift is one of the major sources of the systematic uncertainties. Cooling the temperature of Ytterbium is one way to reduce the density shift. The success of the single ion clock shows that cooling the Ytterbium atoms down the zero-point energy of motion is very important for the high accuracy optical clock.
We investigate the three problems in this thesis. In chapter 1, we briefly introduce the development of atomic clocks from micro-wave to optical wave and the basic principle of key technology of optical clocks. We introduce the development of the Ytterbium atomic clock and summarize the current state of it. We briefly describe the relation of the cold Ytterbium between the optical clocks and the principle of slowing and cooling Ytterbium atoms.
In chapter 2, we investigate how to efficiently generate the first stage Doppler cooling laser source. Firstly, we calculate the relation of second harmonic power between the focusing of fundamental wave, the walk off effects and the phase matching and obtain an expression of the second harmonic power. Then we use it for optimizing the second harmonic generation of a diode laser at 797.822 nm in a LiNbO3 crystal. Firstly, we calculate the phase matching condition and the relating crystal parameters. Then, we use the expression of the second harmonic power for calculating the optimal condition of the fundamental beam. According to the optimal condition, we design the resonator for enhancing the fundamental wave. According to this scheme, we can obtain more than 180 mW second harmonic power which corresponding to the conversion efficiency of 37%.
In chapter 3, we investigate how to efficiently generate the second stage Doppler cooling laser source. Firstly, we study the coupling of the fiber laser output into the waveguide. After the experimental investigation, we find an efficient coupling optical system which is consisted of two fiber collimators and two collimating lenses. The coupling efficiency is about 10% higher than that of the objective lens coupling system. Secondly, we investigate the dependence of the second harmonic generation conversion efficiency on the fundamental light polarization and the waveguide temperature. Thirdly, we study the collimating of the green light. We can obtain a beam quality of M2≤1.1 with an objective lens and a focusing lens. Fourthly, we analyze the asymmetric ripples in the temperature tuning curve measured in this experiment. The result shows that the asymmetric ripple is mainly caused by the optical inhomogeneities. Fifthly, we study the second harmonic generation at high fundamental power. The experimental results show that there is an efficiency drop at the high fundamental powers. Through simulations, we find that the loss can be divided into two stages. In the first stage, the loss is dominated by the absorption. In the second stage, the loss is a combined effect of the absorption and the thermal dephasing.
In chapter 4, we study the Doppler cooling mechanism of the 1st stage and the 2nd stage magneto-optical trap. Firstly, we study the mechanical and the thermal dynamical properties of the 1st stage magneto-optical trap and interpret the previous reported experimental results. Secondly, we study the mechanical and the thermal dynamical properties of the 2nd stage magneto-optical trap. The result shows that the 2nd stage magneto-optical trap has to be attributed to two cases according to their mechanical properties. In the first case, the influence of the gravity can be neglected. In the second case, the influence of the gravity can not be neglected. The thermal properties are also different in the two cases. According to the result, we calculate the dependence of the temperature of atoms on the magneto-optical trap parameters.
In chapter 5, we study the physical mechanism of the cancellation of the light shift of the clock transition and the control of the cooling and trapping of Ytterbium. Firstly, we derive the formula of light induced polarizability and calculate the "magic wavelength" of Ytterbium lattice clock. Meanwhile, we calculate the optical potential of the one dimension and the three dimensional optical lattices. Secondly, we study how to control the cooling and trapping organically. We integrate the action components with the multifunction data acquisition card and the corresponding software platform.
In chapter 6. we study how to cooling the Ytterbium atoms to a lower temperature on the basis of the Doppler cooling in magneto-optical trap and eventually cool the atoms down to the zero-point energy of motion. Firstly, we introduce the interaction of the Ytterbium atoms in the optical lattice and it influence on the optical clock. Secondly, we introduce the principle of the sideband cooling and the physic mechanism of it. Thirdly, we introduce the principle of the Raman transition and study the sideband cooling of the Ytterbium atoms down to the zero-point energy of motion with it. According to the analysis, the temperature of the Ytterbium atoms can be cooled down to 1μK. Combined the sideband cooling and adiabatic cooling, the optical lattice clock can be greatly improved.
In chapter 7, we summarize the work in this thesis and propose possible developments in the future.
激光冷却与囚禁镱原子复杂而锁碎,涉及到方方面面的问题,小到一个控制电路的设计与实现,大到一台激光器的设计以及冷却与囚禁光学系统的设计与实现。由于是从无到有的建设冷镱原子系统,我们当前需要解决的有三个问题。第一个问题是,高效率的冷却激光光源的设计与实现。尽管目前多种方案可以获得冷却激光,然而冷却激光的方案还在探索和发展之中。激光功率和效率的提高将直接改善冷却的效果,同时简化系统。第二个问题是,在锶原子建立在交际跃迁上的磁光阱可以将锶原子冷却到多普勒冷却极限以下,而对于镱原子交际跃迁磁光阱冷却获得的温度远远大于多普勒冷却极限温度。第三个问题是,目前已经实现的镱原子光晶格钟的频率评估发现,原子之间的碰撞频移还很大,其中一个影响就是镱原子的温度还不够低。同时单个离子光钟成功的经验表明把原子冷却到振动基态对抑制原子钟的不确定度是十分重要的。
本论文针对以上三个问题展开深入研究。论文的第一章简单介绍了原子钟到光钟的发展过程,以及光钟关键技术的原理,总结了镱原子光晶格钟的在国际上的发展状况,介绍了冷镱原子与光钟的关系以及镱原子冷却的基本原理。
第二章我们研究了如何使用二次谐波产生技术高效产生一级冷却激光光源的问题。我们首先推导了在双轴晶体中二次谐波产生功率与基频激光的聚焦,走离效应,相位匹配等因素的关系,最后得到一个二次谐波产生功率表达式。我们将这个表达式应用于分析三硼酸锉晶体倍频797.822 nm激光的优化设计。我们首先计算出晶体的相位匹配条件以及相关晶体参数,然后利用二次谐波产生功率表达式计算出最佳二次谐波产生所需的光束条件。根据这些条件我们设计了用于增强基波光强的谐振腔。考虑到各种因素之后,我们预测按照这个方案可以获得180 mW的一级冷却激光,对应于37%的转化效率。
第三章我们研究了如何使用二次谐波产生技术在实验室高效产生二级冷却激光光源。第一。我们研究了光纤激光到波导倍频器的激光耦合问题。通过实验探索我们找出来一种由光纤准直器和准直透镜组成的光学耦合系统其耦合效率可以比常用的显微物镜光纤耦合系统高出10%以上。第二,我们研究了光波导的中二次谐波产生与基波的偏振以及波导的温度等条件的关系,并找出了光波导的最佳工作条件。第三,我们研究了光波导绿光输出的光束准直问题,通过实验探索我们找到由显微物镜和透镜组成的光学准直系统可以获得M2<1.1的光束质量。第四,我们对实验中测量到的波纹状温度调节曲线进行了研究,经过理论分析我们发现这种波纹状的温度调节曲线是由于波导的光学非均匀性造成。我们同时研究了光学非均匀性对二次谐波转化效率的影响。第五,我们研究了在高基波功率时,二次谐波功率与理论预测值相比出现下降的问题。通过模拟,我们发现这种下降分两个过程,第一个过程是吸收造成的下降,第二个过程是吸收以及其引起的温度改变造成的下降。
第四章我们研究了一级磁光阱冷却和二级磁光阱冷却的多普勒冷却机制。第一,我们研究了一级磁光阱冷却的动力学特性和热力学特性,并解释了此前的一级磁光阱冷却的结果。第二,我们研究了二级磁光阱的动力学特性和热力学特性,通过分析我们发现在二级磁光阱的多普勒冷却机制根据动力学特性可以分为两种情况,第一是重力可以忽略的情况,第二种是重力需要考虑的情况。在这两种情况下,其热力学特性也不同。根据分析结果我们计算了原子温度和磁光阱参数的关系。
第五章我们研究了钟频光位移的抑制的物理机制和冷镱原子的控制系统。第一,我们从微扰理论出发推导出原子在光场作用下的极化率公式并根据光位移的表达式我们初步计算了镱原子的最佳波长。同时,我们还计算了一维和三维光晶格的囚禁势。第二,我们研究了如何在实现对冷却系统实行一体化的控制。在声光调制器,机械开关等控制执行元件的基础上,我们利用多功能数据采集卡以及相关软件平台设计了一套有机的控制系统。
第六章我们研究了在磁光阱多普勒冷却的基础上进一步将镱原子温度冷却到更低并最终将原子冷却到运动零点能的冷却方案。第一,我们介绍了镱原子在光晶格中的相互作用机制,以及其对光晶格原子钟的不确定度的影响。第二,我们介绍了边带冷却的原理以及使用钟频跃迁进行边带的物理机制。第三,我们首先介绍了拉曼跃迁的原理,接下来我们研究了如何通过最佳波长光晶格产生拉曼耦合以及使用拉曼耦合进行边带冷却的方案。根据分析结果,我们预测这种冷却方案可以将原子冷却到运动基态,温度可以冷却到1μK以下。这种边带冷却技术和绝热冷却技术结和可以应用于光晶格钟。
最后在第七章中,我们对本文主要研究工作进行了概括性总结,并在此基础上,对未来的发展进行了展望。
Study on optical atomic clocks is a hot topic in the field of fundamental physics and frequency metrology as the fractional frequency uncertainty of the microwave atomic clock is approaching the quantum projection noise limit. The need of more accurate atomic clocks for testing the fundamental physical problem such as measuring variation of fundamental constants, testing the relativity theory is very urgent. With the rapid progress in space science and technology, the current atomic clocks also can not fulfill the requirements. As the optical frequency is around several orders of magnitude higher than the microwave frequency, the fractional frequency uncertainty of the optical clock may be much smaller than that of the microwave clock. Therefore, the optical clock is considered as the candidate of the next generation frequency standards. The state-of-art single ion optical clock has achieved the fractional frequency uncertainty on the order of 10-18 and it has been used for testing the variation of fundamental constants and the theory of relativity. The variation of fundamental constants has been restricted in a very small range. However, the single ion optical clock will be limited by quantum projection noise according to the quantum theory. An important way to reduce the quantum projection noise is to increase the number of quantum absorbers. In the ion traps, the number of ions is limited by the coulomb repulsion. The optical lattice clock inherits the merits of the ion clock and the number of quantum absorbers can be greatly increased. The optical lattice clock may surpass the ion clock in the future. Therefore, considerable strides have been taken recently toward this kind of optical clocks. Ytterbium lattice clock is one kind of the lattice clocks. Currently, a key issue of the optical lattice clock is how to make the clock line immune to the environment perturbations. Improving the methods of cooling and trapping of ultracold Ytterbium atoms is the major solution.
Cooling and trapping Ytterbium atoms is a complex work. Many problems need to be solved from a control circuit to a laser and the cooling and trapping optical systems. Currently, we need to solve three problems. The first one is designing and constructing highly efficient and compact laser sources for laser cooling and trapping. Increasing the efficiency of the laser and making it smaller can improve the cooling results and simplify the system. The second one is that the final temperature of the second stage Doppler cooling of Ytterbium is much higher than the Doppler cooling limit. The magneto-optical trap on the intercombination transition of strontium can cool the temperature of strontium atoms down to the Doppler cooling limit. However, the final temperature of magneto-optical trap on the intercombination transition of Ytterbium is much higher than the Doppler cooling limit. The third one is cooling the Ytterbium atoms to zero-point energy of motion. Recent frequency evaluation of the Ytterbium atomic clock indicates that density related frequency shift is one of the major sources of the systematic uncertainties. Cooling the temperature of Ytterbium is one way to reduce the density shift. The success of the single ion clock shows that cooling the Ytterbium atoms down the zero-point energy of motion is very important for the high accuracy optical clock.
We investigate the three problems in this thesis. In chapter 1, we briefly introduce the development of atomic clocks from micro-wave to optical wave and the basic principle of key technology of optical clocks. We introduce the development of the Ytterbium atomic clock and summarize the current state of it. We briefly describe the relation of the cold Ytterbium between the optical clocks and the principle of slowing and cooling Ytterbium atoms.
In chapter 2, we investigate how to efficiently generate the first stage Doppler cooling laser source. Firstly, we calculate the relation of second harmonic power between the focusing of fundamental wave, the walk off effects and the phase matching and obtain an expression of the second harmonic power. Then we use it for optimizing the second harmonic generation of a diode laser at 797.822 nm in a LiNbO3 crystal. Firstly, we calculate the phase matching condition and the relating crystal parameters. Then, we use the expression of the second harmonic power for calculating the optimal condition of the fundamental beam. According to the optimal condition, we design the resonator for enhancing the fundamental wave. According to this scheme, we can obtain more than 180 mW second harmonic power which corresponding to the conversion efficiency of 37%.
In chapter 3, we investigate how to efficiently generate the second stage Doppler cooling laser source. Firstly, we study the coupling of the fiber laser output into the waveguide. After the experimental investigation, we find an efficient coupling optical system which is consisted of two fiber collimators and two collimating lenses. The coupling efficiency is about 10% higher than that of the objective lens coupling system. Secondly, we investigate the dependence of the second harmonic generation conversion efficiency on the fundamental light polarization and the waveguide temperature. Thirdly, we study the collimating of the green light. We can obtain a beam quality of M2≤1.1 with an objective lens and a focusing lens. Fourthly, we analyze the asymmetric ripples in the temperature tuning curve measured in this experiment. The result shows that the asymmetric ripple is mainly caused by the optical inhomogeneities. Fifthly, we study the second harmonic generation at high fundamental power. The experimental results show that there is an efficiency drop at the high fundamental powers. Through simulations, we find that the loss can be divided into two stages. In the first stage, the loss is dominated by the absorption. In the second stage, the loss is a combined effect of the absorption and the thermal dephasing.
In chapter 4, we study the Doppler cooling mechanism of the 1st stage and the 2nd stage magneto-optical trap. Firstly, we study the mechanical and the thermal dynamical properties of the 1st stage magneto-optical trap and interpret the previous reported experimental results. Secondly, we study the mechanical and the thermal dynamical properties of the 2nd stage magneto-optical trap. The result shows that the 2nd stage magneto-optical trap has to be attributed to two cases according to their mechanical properties. In the first case, the influence of the gravity can be neglected. In the second case, the influence of the gravity can not be neglected. The thermal properties are also different in the two cases. According to the result, we calculate the dependence of the temperature of atoms on the magneto-optical trap parameters.
In chapter 5, we study the physical mechanism of the cancellation of the light shift of the clock transition and the control of the cooling and trapping of Ytterbium. Firstly, we derive the formula of light induced polarizability and calculate the "magic wavelength" of Ytterbium lattice clock. Meanwhile, we calculate the optical potential of the one dimension and the three dimensional optical lattices. Secondly, we study how to control the cooling and trapping organically. We integrate the action components with the multifunction data acquisition card and the corresponding software platform.
In chapter 6. we study how to cooling the Ytterbium atoms to a lower temperature on the basis of the Doppler cooling in magneto-optical trap and eventually cool the atoms down to the zero-point energy of motion. Firstly, we introduce the interaction of the Ytterbium atoms in the optical lattice and it influence on the optical clock. Secondly, we introduce the principle of the sideband cooling and the physic mechanism of it. Thirdly, we introduce the principle of the Raman transition and study the sideband cooling of the Ytterbium atoms down to the zero-point energy of motion with it. According to the analysis, the temperature of the Ytterbium atoms can be cooled down to 1μK. Combined the sideband cooling and adiabatic cooling, the optical lattice clock can be greatly improved.
In chapter 7, we summarize the work in this thesis and propose possible developments in the future.
引文
[1]S. A.Diaddams. J. C. Bergquist, S. R. Jefferts. and C. W. Oates, Science,306, 1318(2004).
[2]L. Essen, and J. V. L. Parry, Nature,176,280 (1955).
[3]Patrick Gill,Metrologia,42, S125 (2005).
[4]R. Wynands, and S. Weyers,42, S64 (2005).
[5]D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jefferts, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and D. J. Wineland, J. Res. Natl. Inst. Stand. Technol.106,47 (2001).
[6]V G Pal'chikov, Yu S Domnin, and A V Novoselov, J. Opt. B:Quantum Semiclass. Opt.5. S131 (2003).
[7]N. F. Ramsey. Phys. Today,33,25 (1980).
[8]Jacques Vanier, and Claude Metrologia,42, S31 (2005).
[9]J. R. Zacharias Phys. Rev.94,751 (1954).
[10]M. Kasevich, E. Riis, S. Chu, and R. Devoe, Phys. Rev. Lett.63,612 (1989).
[11]K. B. Davis, M.-O. Mcwcs, M. R. Andrews, N. J. Van Dreuten, D. S. Durfcc, D. M. Kurn, and W. Ketterle, Phys.Rev. Lett.75,3969(1995).
[12]M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science,269,198(1995).
[13]B. DeMarco, and D. S. Jin, Science,285,1703(1999).
[14]M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, Nature,435,1047 (2005).
[15]Theodor W. Hansch, Rev. Mod. Phys.78,1297(2005).
[16]John L. Hall, Rev. Mod. Phys.78,1279(2005).
[17]Stenger, J. H. Schnatz. C. Tamm. and H. R. Telle, Phys. Rev. Lett.88, 073601(2002).
[18]Zimmermann. M. Ch. Gohle, R. Holzwarth, Th. Udem, and T. W. Hansch Opt. Lett.29,310(2004).
[19]Steven T. Cundiff. and Jun Ye Rev. Mod. Phys.75,325(2003).
[20]Long-Sheng Ma. Zhiyi bi. Albrecht Bartels. Lennart Robertsson. Massimo Zucco Robert S. Windeler, Guodo Wilpers. Chris Oates. Leo Hollberg, and Scott A. Diddams Science,303,1843 (2004).
[21]G. Wilpers, T. Binnewies, C. Degenhardt, U. Sterr. J. Helmcke, and F. Riehle Phys. Rev. Lett.89,230801 (2002).
[22]Jean-Philippe Uzan Rev. Mod. Phys.75,403 (2003).
[23]Th. Udem, R. Holzwarth, and T. W. Hansch, Nature,416,233 (2002)
[24]Masao Takamoto, Feng-Lei Hong, Ryoichi Higashi, and Hidetoshi Katori, Nature, 435,321(2005)
[25]Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. L. Yudin Phys. Rev. Lett.96,083002 (2006).
[26]L. Yi, S. Mejri, J. J. McFerran, Y. Le Coq, and S. Bize Phys. Rev. Lett.106, 073005(2011)
[27]T. Rosenband, P. O. Schmidt, D. B. Hume, W. M. Itano, T. M. Fortier, J. E. Stalnaker, K. Kim, S. A. Diddams, J. C. J. Koelemeij, J. C. Bergquist, and D. J. Wineland Phys. Rev. Lett.98,220801 (2007)
[28]Claude N. Cohen-Tannoudji, and William D. Phillips Phys. Today,43,33 (1990).
[29]H. J. Metcalf, and P. Van der Straten J. Opt. Soc. Am. B.20,887 (2003).
[30]D. J. Wineland, and Wayne M. Itano Phys. Rev. A.20,1521 (1979).
[31]William D. Phillips, Rev. Mod. Phys.70,721 (1998).
[32]D. J. Wineland, Wayne M. Itano, J. C. Bergquist, and Randall G. Hulet Phys. Rev. A 36,2220 (1987).
[33]C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband Phys. Rev. Lett.104, (070802).
[34]Immanuel Bloch, Jean Dalibard, and Wilhelm Zwerger Rev. Mod. Phys.80,885 (2008)
[35]Tetsuya Ido, and Hidetoshi Katori Phys. Rev. Lett.90,053001 (2003).
[36]R.J. Rufac, B. C. Young, J. A. Beal, W. M. Itano, D. J. Wineland, and J. C. Bergquist Phys. Rev. Lett.85,2462 (2000).
[37]S. A. Diddams. Th. Udem, J. C. Bergquist. E. A. Curtis. R. E. Drullinger. L. Hollberg. W. M. Itano. W. D. Lee, C. W. Oates. K. R. Vogel. and D. J. Wineland. Science,293,825(2001).
[38]B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist. Phys. Rev. Lett.82, 3799(1999).
[39]R. H. Dicke, Phys. Rev.89,472 (1953).
[40]H. Stoehr. F. Mensing, J. Helmcke, and U. Sterr, Opt. Lett.31,736 (2006).
[41]A. D. Ludlow, X. Huang, M. Notcutt, T. Zanon-Willette. S. M. Foreman. M. M. Boyd, S. Blatt, and J. Ye, Opt. Lett.32,641 (2007).
[42]J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hansch Phys. Rev. A. 77,053809(2008).
[43]Uwe Sterr, and Christian Lisdat Nature. Phys 5,382 (2009).
[44]W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan. D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland Phys. Rev. A.47,3554 (1993).
[45]Santarelli, Ph. Laurent, P. Lemonde and A. Clairon, A. G. Mann. S. Chang, A. N. Luiten, and C. Salomon Phys. Rev. Lett.82,4619 (1999).
[46]Martin M. Boyd, Andrew D. Ludlow, Sebastian Blatt, Seth M. Foreman, Tetsuya Ido, Tanya Zelevinsky, and Jun Ye Phys. Rev. Lett.98,083002 (2007).
[47]Masao Takamoto, and Hidetoshi Katori Phys. Rev. Lett.91,223001 (2003).
[48]Martin M. Boyd, Tanya Zelevinsky, Andrew D. Ludlow, Sebastian Blatt, Tetsuya Ido, and Jun Ye, Science,314,1430 (2006).
[49]Tomoya Akatsuka, Masao Takamoto, and Hidetoshi Katori, Phys. Rev. A.81, 023402(2010).
[50]N. D. Lemke, A. D. Ludlow, Z. W. Barber, T. M. Fortier, S. A. Diddams, Y. Jiang, S. R. Jefferts, T. P. Heavner, T. E. Parker, and C. W. Oates Phys. Rev. Lett.103, 063001 (2009).
[51]C. W. Hoyt, Z. W. Barber. C. W. Oates, T. M. Fortier, S. A. Diddams. and L. Hollberg Phys. Rev. Lett.95,083003 (2005).
[52]N. Poli, Z. W. Barber, N. D. Lemke, C. W. Oates, L. S. Ma, J. E. Stalnaker. T. M. Fortier. S. A. Diddams. L. Hollberg. J. C. Bergquist. A. Brusch. S. Jefferts, T. M. Heavner. and T. Parker Phys. Rev. A 77,050501 (2008).
[53]K. Honda. Y. Takahashi. T. Kuwamoto. M. Fujimoto. K. Toyoda. K. Ishikawa. and T. Yabuzaki Phys. Rev. A 59, R934 (1999).
[54]T. Kuwamoto, K. Honda. Y. Takahashi. and T. Yabuzaki Phys. Rev. A 60, R745 (1999).
[55]Yosuke Takasu. Kenichi Maki. Kaduki Komori. Tetsushi Takano, Kazuhito Honda, Mitsutaka Kumakura. Tsutomu Yabuzaki and Yoshiro Takahashi, Phys. Rev. Lett.91,040404 (2003).
[56]Chang Yong Park and Tai Hyun Yoon, Phys. Rev. A 68,055401 (2003).
[57]S. G. Porsev, A. Drevianko. and E. N. Fortson. Phys. Rev. A 69,021403 (R) (2004).
[58]Tao Hong, Claire Cremer, Warren Nagourney, and E. N. Fortson Phys. Rev. Lett. 94,050801 (2005).
[59]A. V. Taichenachev, V. I. Yudin, C. W. Oates, C. W. Hoyt, Z. W. Barber, and L. Hollberg Phys. Rev. Lett 96,083001 (2006).
[60]Z. W. Barber, J. E. Stalnaker, N. D. Lemke, N. Poli, C. W. Oates, T. M. Fortier, S. A. Diddams, L. Hollberg, C. W. Hoyt, A. V. Taichenachev, and V. I. Yudin Phys. Rev. Lett.100,103002(2008).
[61]W. Demtroder, Laser spectroscopy:basic concepts and instrumentation (Springer-verlag,2003)
[62]W. Phillips and H. Metcalf, Phys. Rev. Lett.48,596 (1982).
[63]P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, J. Opt. Soc. Am. B.6,2083(1989).
[64]E. Raab, M. Prentisss, A. Cable, S. Chu, and D. Pritchard, Phys. Rev. Lett.59, 2631 (1987).
[65]Charra, F., Gurzadyan. G.:A-D. Nelson. D. F. (ed.). SpringerMaterials-The Landolt-Bornstein Database.
[66]Fabrizio Villa, Antonino Chiummo, Elisabeth Giacobino, and Alberto Bramati, J. Opt. Soc. Am. B 24,576 (2007).
[67]P. A. Franken. A. E. Hill. C. W. Peters and G. Weinreich. Phys. Rev. Lett.7,118 (1961).
[68]G. D. Boyd and D. A. Kleinman. J. Appl. Lett.39,3597 (1968).
[69]B. Beier. D. Woll, M. Scheldt. K-J. Boller and R. Wallenstein. Appl. Phys. Lett. 21,315(1997).
[70]D. A. Kleinman. Phys. Rev.128,1761 (1962).
[71]F Brehat and B Wyncke J. Phys. B:At. Mol. Opt. Phys.22,1891 (1989).
[72]P. Kerkoc. R. T. Bailey. F. R. Cruickshank and D. Pugh, J. Opt. Soc. Am. B.15, 428(1998).
[73]M. A. Dreger. and J. H. Erkkila, Opt. Lett.17,787 (1992).
[74]J. Hald, Opt. Commun.197,169(2001).
[75]J. Q. Yao and Theodore S. Fahlen, J. Appl. Phys.55,65(1984).
[76]K. Kato. IEEE J. Quantum Electron.30,2950(1994).
[77]M.V.Hobden, J. Appl. Phys.38,4365 (1967).
[78]H. Kogelnik, and T. Li, Appl. Opt.5,1550 (1966).
[79]A. Ashkin, G, D.Boyd, and J. M. Dziedzic, IEEE J. Quantum Electron.2,109 (1966).
[80]Joseph T. Verdeyen, Laser electronics (Prentice Hall,1995)
[81]R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B.31,97(1983)
[82]T. W. Hansch and B. Couillaud, Opt. Commun.35,441 (1980).
[83]Z. Y. Ou, S. F. Pereira, E. S. Polzik, and H. J. Kimble, Opt. Lett.17,640 (1992).
[84]D.Woll, B.Beier, K.-J. Boller, and R.wallenstein M.Hagberg and S.O'Brien, Opt. Lett.24,691 (1999).
[85]Tomoya Sugita, Kiminori Mizuuchi, Yasuo Kitaoka, and Kazuhisa Yamamoto, Opt. Lett.24,1590(1999).
[86]Andreas Jechow. Danilo Skoczowsky and Ralf Menzel, Opt. Express.15,6976 (2007).
[87]Krishnan R. Parameswaran, Jonathan R. Kurz, Rostislav V. Roussev, and Martin M.Fejer, Opt. Lett.27,43 (2002).
[88]Krishnan R. Parameswaran. Roger K.Route. Jonathan R. Kurz. Rostislav V. Roussev. and Martin M. Fejer, Masatoshi Fujimura, Opt. Lett.27,179 (2002).
[89]Martin M. Fejer. G. A. Magel. Dieter H. Jundt. and Robert L. Byer. IEEE J. Quantum Electron.28,2631 (1992).
[90]K. Furukawa, K. Kitamura, A. Alexandrovski, R. K. Route and M M. Fejer, G. Foulon, Appl. Phys. Lett.78,1970 (2001).
[91]A.Bouchier, G. Lucas-Lecliu, P. Georges and J. M. Maillard, Opt. Express.13, 6974 (2005).
[92]F. R. Nash, G. D.Boyd, M.Sargent, and P. M. Bridenbaugh, J. Appl. Phys.41, 2564(1970).
[93]M. L. Bortz, S. J. Field, M. M. Fejer, D. W. Nam, R. G. Waarts, and D. F. Welch, IEEE J. Quantum Electron.30,2953 (1994).
[94]Sten Helmfrid and Gunnar Arvidson, J. Opt. Soc. Am. B.8,797 (1991).
[95]Yeung Lak Lee, Yong-Chul Noh, Changsoo Jung, Tae Jun Yu, Bong-Ahn Yu, Kyunghwan Oh, Appl. Phys. Lett.86,011104 (2004).
[96]O. Gayer, Z. Sacks, E. Galun, A. Arie, Appl. Phys. B 91343 (2008)
[97]Sten Helmfrid, Gunnar Arvidsson, and Jonas Webjorn, J. Opt. Soc. Am. B.10, 222(1992).
[98]P. F. Hu, T. C. Chong, L. P. Shi, W. X. Hou, Optical and Quantum Electronics,31, 337-349(1999)
[99]Oleg A. Louchev, Nan Ei Yu, Sunao Kurimura, and Kenji Kitamura, Appl. Phys. Lett.87,131101(2005).
[100]D. Eimerl, IEEE J. Quantum Electron.23,2238-2251 (1987).
[101]B. M. Jin, I. W. Kim, W. B. White, A. S. Bhalla, Mater. Lett.30,385-388 (1997).
[102]R. K. Choubey, P. Sen, P. K. Sen, R. Bhatt, S. Kar. V. Shukla, K. S. Bartwal, Opt. Mater,28,467(2006).
[103]Charra, F., Gurzadyan, G.:A-D. Nelson, D. F. (ed.). SpringerMaterials-The Landolt-Bornstein Database.
[104]Laszlo. Palfalvi, Gabor Almasi, Janos Hebling Agnes peter and Katalin Polgar, Appl. Phys. Lett.80,2245 (2002).
[105]C. J. Foot. Atomic physics (Oxford University Press 2005)
[106]F. Diedrich. J. C. Bergquist, Wayne M. Itano. and D. J. Wineland Phys. Rev. Lett.62,403(1989)
[107]Steven Chu, Rev. Mod. Phys.70,685(1998).
[108]Claude N. Cohen-Tannoudji, Rev. Mod. Phys.70,707(1998).
[109]William D. Philips, Rev. Mod. Phys.70,721(1998).
[110]Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee. D. M. Kurn and W. Ketterle Phys. Rev. Lett.75,3969 (1995).
[111]Thomas H. Lofus, Tetsuya Ido, Martin M. Boyd, Andrew D. Ludlow and Jun Ye, Phys. Rev. Lett.70,063413 (2004).
[112]Xinye Xu, Thomas H. Loftus, Matthew J. Smith, John L. Hall. Alan Gallagher and Jun Ye, Phys. Rev. A.66,011401(R) (2002).
[113]R. Maruyama. R. H. Wynar, M. V. Romalis, A. Andalkar. M. D. Swallows, C. E. Person and E. N. Fortson, Phys. Rev. A.68,011403(R)(2003).
[114]Gribakin. G. F. and V. V. Flambaum, Phys. Rev. A.48,546(1993).
[115]L. D. Landau and E. M. Lifshitz, Quantum Mechanics:non-relativistic theory (Elsevier 1965).
[116]Kurt Gibble, Phys. Rev. Lett.103,113202 (2009).
[117]Peter J. Martin, Bruce G. Oldaker, Andrew H. Miklich, and David E. Pritchard, Phys. Rev. Lett.60,515 (1988)
[118]Campbell G K, Boyd M M, Thomsen J W, Martin M J, Blatt S. Swallows M D, Nicholson T L, Fortier T, Oates C W, Diddams S A, Lemke N D, Naidom P, Juloenne P, Ye Jun and Ludlow A D, Science,324,360 (2009).
[119]C. W. Hoyt, Z. W. Barber. C. W. Oates, T. M. Fortier, S. A. Diddams, and L. Hollberg, Phys. Rev. Lett.95,083003 (2005).
[120]Reichenbach Iris and Deutsch Ivan H, Phys. Rev. Lett.99,123001 (2007).
[121]杨福家,原子物理学,(高等教育出版社2006)
[122]Haman S E, Haycock D L, Klose G, Pax P H, Deutsch I H and Jessen P S. Phys. Rev. Lett.80,4149(1998).
[123]Vuletic Valadan. Chin Cheng. Kerman Andrew J. and Chu Steven Phys. Rev. Lett.81,5768(1998).
[124]Deutsch Ivan H and Jessen Poul S. Phys. Rev. A.57,1972(1998).
[125]Ludlow Andrew D. Boyd Martin. M. Zelevinsky Tanya. Foreman Seth M. Blatt Sebastian. Notcutt Mark, Ido Tetsuya and Ye Jun. Phys. Rev. Lett.96, 033003 (2006).
[2]L. Essen, and J. V. L. Parry, Nature,176,280 (1955).
[3]Patrick Gill,Metrologia,42, S125 (2005).
[4]R. Wynands, and S. Weyers,42, S64 (2005).
[5]D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jefferts, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and D. J. Wineland, J. Res. Natl. Inst. Stand. Technol.106,47 (2001).
[6]V G Pal'chikov, Yu S Domnin, and A V Novoselov, J. Opt. B:Quantum Semiclass. Opt.5. S131 (2003).
[7]N. F. Ramsey. Phys. Today,33,25 (1980).
[8]Jacques Vanier, and Claude Metrologia,42, S31 (2005).
[9]J. R. Zacharias Phys. Rev.94,751 (1954).
[10]M. Kasevich, E. Riis, S. Chu, and R. Devoe, Phys. Rev. Lett.63,612 (1989).
[11]K. B. Davis, M.-O. Mcwcs, M. R. Andrews, N. J. Van Dreuten, D. S. Durfcc, D. M. Kurn, and W. Ketterle, Phys.Rev. Lett.75,3969(1995).
[12]M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science,269,198(1995).
[13]B. DeMarco, and D. S. Jin, Science,285,1703(1999).
[14]M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, Nature,435,1047 (2005).
[15]Theodor W. Hansch, Rev. Mod. Phys.78,1297(2005).
[16]John L. Hall, Rev. Mod. Phys.78,1279(2005).
[17]Stenger, J. H. Schnatz. C. Tamm. and H. R. Telle, Phys. Rev. Lett.88, 073601(2002).
[18]Zimmermann. M. Ch. Gohle, R. Holzwarth, Th. Udem, and T. W. Hansch Opt. Lett.29,310(2004).
[19]Steven T. Cundiff. and Jun Ye Rev. Mod. Phys.75,325(2003).
[20]Long-Sheng Ma. Zhiyi bi. Albrecht Bartels. Lennart Robertsson. Massimo Zucco Robert S. Windeler, Guodo Wilpers. Chris Oates. Leo Hollberg, and Scott A. Diddams Science,303,1843 (2004).
[21]G. Wilpers, T. Binnewies, C. Degenhardt, U. Sterr. J. Helmcke, and F. Riehle Phys. Rev. Lett.89,230801 (2002).
[22]Jean-Philippe Uzan Rev. Mod. Phys.75,403 (2003).
[23]Th. Udem, R. Holzwarth, and T. W. Hansch, Nature,416,233 (2002)
[24]Masao Takamoto, Feng-Lei Hong, Ryoichi Higashi, and Hidetoshi Katori, Nature, 435,321(2005)
[25]Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. L. Yudin Phys. Rev. Lett.96,083002 (2006).
[26]L. Yi, S. Mejri, J. J. McFerran, Y. Le Coq, and S. Bize Phys. Rev. Lett.106, 073005(2011)
[27]T. Rosenband, P. O. Schmidt, D. B. Hume, W. M. Itano, T. M. Fortier, J. E. Stalnaker, K. Kim, S. A. Diddams, J. C. J. Koelemeij, J. C. Bergquist, and D. J. Wineland Phys. Rev. Lett.98,220801 (2007)
[28]Claude N. Cohen-Tannoudji, and William D. Phillips Phys. Today,43,33 (1990).
[29]H. J. Metcalf, and P. Van der Straten J. Opt. Soc. Am. B.20,887 (2003).
[30]D. J. Wineland, and Wayne M. Itano Phys. Rev. A.20,1521 (1979).
[31]William D. Phillips, Rev. Mod. Phys.70,721 (1998).
[32]D. J. Wineland, Wayne M. Itano, J. C. Bergquist, and Randall G. Hulet Phys. Rev. A 36,2220 (1987).
[33]C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband Phys. Rev. Lett.104, (070802).
[34]Immanuel Bloch, Jean Dalibard, and Wilhelm Zwerger Rev. Mod. Phys.80,885 (2008)
[35]Tetsuya Ido, and Hidetoshi Katori Phys. Rev. Lett.90,053001 (2003).
[36]R.J. Rufac, B. C. Young, J. A. Beal, W. M. Itano, D. J. Wineland, and J. C. Bergquist Phys. Rev. Lett.85,2462 (2000).
[37]S. A. Diddams. Th. Udem, J. C. Bergquist. E. A. Curtis. R. E. Drullinger. L. Hollberg. W. M. Itano. W. D. Lee, C. W. Oates. K. R. Vogel. and D. J. Wineland. Science,293,825(2001).
[38]B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist. Phys. Rev. Lett.82, 3799(1999).
[39]R. H. Dicke, Phys. Rev.89,472 (1953).
[40]H. Stoehr. F. Mensing, J. Helmcke, and U. Sterr, Opt. Lett.31,736 (2006).
[41]A. D. Ludlow, X. Huang, M. Notcutt, T. Zanon-Willette. S. M. Foreman. M. M. Boyd, S. Blatt, and J. Ye, Opt. Lett.32,641 (2007).
[42]J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hansch Phys. Rev. A. 77,053809(2008).
[43]Uwe Sterr, and Christian Lisdat Nature. Phys 5,382 (2009).
[44]W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan. D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland Phys. Rev. A.47,3554 (1993).
[45]Santarelli, Ph. Laurent, P. Lemonde and A. Clairon, A. G. Mann. S. Chang, A. N. Luiten, and C. Salomon Phys. Rev. Lett.82,4619 (1999).
[46]Martin M. Boyd, Andrew D. Ludlow, Sebastian Blatt, Seth M. Foreman, Tetsuya Ido, Tanya Zelevinsky, and Jun Ye Phys. Rev. Lett.98,083002 (2007).
[47]Masao Takamoto, and Hidetoshi Katori Phys. Rev. Lett.91,223001 (2003).
[48]Martin M. Boyd, Tanya Zelevinsky, Andrew D. Ludlow, Sebastian Blatt, Tetsuya Ido, and Jun Ye, Science,314,1430 (2006).
[49]Tomoya Akatsuka, Masao Takamoto, and Hidetoshi Katori, Phys. Rev. A.81, 023402(2010).
[50]N. D. Lemke, A. D. Ludlow, Z. W. Barber, T. M. Fortier, S. A. Diddams, Y. Jiang, S. R. Jefferts, T. P. Heavner, T. E. Parker, and C. W. Oates Phys. Rev. Lett.103, 063001 (2009).
[51]C. W. Hoyt, Z. W. Barber. C. W. Oates, T. M. Fortier, S. A. Diddams. and L. Hollberg Phys. Rev. Lett.95,083003 (2005).
[52]N. Poli, Z. W. Barber, N. D. Lemke, C. W. Oates, L. S. Ma, J. E. Stalnaker. T. M. Fortier. S. A. Diddams. L. Hollberg. J. C. Bergquist. A. Brusch. S. Jefferts, T. M. Heavner. and T. Parker Phys. Rev. A 77,050501 (2008).
[53]K. Honda. Y. Takahashi. T. Kuwamoto. M. Fujimoto. K. Toyoda. K. Ishikawa. and T. Yabuzaki Phys. Rev. A 59, R934 (1999).
[54]T. Kuwamoto, K. Honda. Y. Takahashi. and T. Yabuzaki Phys. Rev. A 60, R745 (1999).
[55]Yosuke Takasu. Kenichi Maki. Kaduki Komori. Tetsushi Takano, Kazuhito Honda, Mitsutaka Kumakura. Tsutomu Yabuzaki and Yoshiro Takahashi, Phys. Rev. Lett.91,040404 (2003).
[56]Chang Yong Park and Tai Hyun Yoon, Phys. Rev. A 68,055401 (2003).
[57]S. G. Porsev, A. Drevianko. and E. N. Fortson. Phys. Rev. A 69,021403 (R) (2004).
[58]Tao Hong, Claire Cremer, Warren Nagourney, and E. N. Fortson Phys. Rev. Lett. 94,050801 (2005).
[59]A. V. Taichenachev, V. I. Yudin, C. W. Oates, C. W. Hoyt, Z. W. Barber, and L. Hollberg Phys. Rev. Lett 96,083001 (2006).
[60]Z. W. Barber, J. E. Stalnaker, N. D. Lemke, N. Poli, C. W. Oates, T. M. Fortier, S. A. Diddams, L. Hollberg, C. W. Hoyt, A. V. Taichenachev, and V. I. Yudin Phys. Rev. Lett.100,103002(2008).
[61]W. Demtroder, Laser spectroscopy:basic concepts and instrumentation (Springer-verlag,2003)
[62]W. Phillips and H. Metcalf, Phys. Rev. Lett.48,596 (1982).
[63]P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, J. Opt. Soc. Am. B.6,2083(1989).
[64]E. Raab, M. Prentisss, A. Cable, S. Chu, and D. Pritchard, Phys. Rev. Lett.59, 2631 (1987).
[65]Charra, F., Gurzadyan. G.:A-D. Nelson. D. F. (ed.). SpringerMaterials-The Landolt-Bornstein Database.
[66]Fabrizio Villa, Antonino Chiummo, Elisabeth Giacobino, and Alberto Bramati, J. Opt. Soc. Am. B 24,576 (2007).
[67]P. A. Franken. A. E. Hill. C. W. Peters and G. Weinreich. Phys. Rev. Lett.7,118 (1961).
[68]G. D. Boyd and D. A. Kleinman. J. Appl. Lett.39,3597 (1968).
[69]B. Beier. D. Woll, M. Scheldt. K-J. Boller and R. Wallenstein. Appl. Phys. Lett. 21,315(1997).
[70]D. A. Kleinman. Phys. Rev.128,1761 (1962).
[71]F Brehat and B Wyncke J. Phys. B:At. Mol. Opt. Phys.22,1891 (1989).
[72]P. Kerkoc. R. T. Bailey. F. R. Cruickshank and D. Pugh, J. Opt. Soc. Am. B.15, 428(1998).
[73]M. A. Dreger. and J. H. Erkkila, Opt. Lett.17,787 (1992).
[74]J. Hald, Opt. Commun.197,169(2001).
[75]J. Q. Yao and Theodore S. Fahlen, J. Appl. Phys.55,65(1984).
[76]K. Kato. IEEE J. Quantum Electron.30,2950(1994).
[77]M.V.Hobden, J. Appl. Phys.38,4365 (1967).
[78]H. Kogelnik, and T. Li, Appl. Opt.5,1550 (1966).
[79]A. Ashkin, G, D.Boyd, and J. M. Dziedzic, IEEE J. Quantum Electron.2,109 (1966).
[80]Joseph T. Verdeyen, Laser electronics (Prentice Hall,1995)
[81]R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B.31,97(1983)
[82]T. W. Hansch and B. Couillaud, Opt. Commun.35,441 (1980).
[83]Z. Y. Ou, S. F. Pereira, E. S. Polzik, and H. J. Kimble, Opt. Lett.17,640 (1992).
[84]D.Woll, B.Beier, K.-J. Boller, and R.wallenstein M.Hagberg and S.O'Brien, Opt. Lett.24,691 (1999).
[85]Tomoya Sugita, Kiminori Mizuuchi, Yasuo Kitaoka, and Kazuhisa Yamamoto, Opt. Lett.24,1590(1999).
[86]Andreas Jechow. Danilo Skoczowsky and Ralf Menzel, Opt. Express.15,6976 (2007).
[87]Krishnan R. Parameswaran, Jonathan R. Kurz, Rostislav V. Roussev, and Martin M.Fejer, Opt. Lett.27,43 (2002).
[88]Krishnan R. Parameswaran. Roger K.Route. Jonathan R. Kurz. Rostislav V. Roussev. and Martin M. Fejer, Masatoshi Fujimura, Opt. Lett.27,179 (2002).
[89]Martin M. Fejer. G. A. Magel. Dieter H. Jundt. and Robert L. Byer. IEEE J. Quantum Electron.28,2631 (1992).
[90]K. Furukawa, K. Kitamura, A. Alexandrovski, R. K. Route and M M. Fejer, G. Foulon, Appl. Phys. Lett.78,1970 (2001).
[91]A.Bouchier, G. Lucas-Lecliu, P. Georges and J. M. Maillard, Opt. Express.13, 6974 (2005).
[92]F. R. Nash, G. D.Boyd, M.Sargent, and P. M. Bridenbaugh, J. Appl. Phys.41, 2564(1970).
[93]M. L. Bortz, S. J. Field, M. M. Fejer, D. W. Nam, R. G. Waarts, and D. F. Welch, IEEE J. Quantum Electron.30,2953 (1994).
[94]Sten Helmfrid and Gunnar Arvidson, J. Opt. Soc. Am. B.8,797 (1991).
[95]Yeung Lak Lee, Yong-Chul Noh, Changsoo Jung, Tae Jun Yu, Bong-Ahn Yu, Kyunghwan Oh, Appl. Phys. Lett.86,011104 (2004).
[96]O. Gayer, Z. Sacks, E. Galun, A. Arie, Appl. Phys. B 91343 (2008)
[97]Sten Helmfrid, Gunnar Arvidsson, and Jonas Webjorn, J. Opt. Soc. Am. B.10, 222(1992).
[98]P. F. Hu, T. C. Chong, L. P. Shi, W. X. Hou, Optical and Quantum Electronics,31, 337-349(1999)
[99]Oleg A. Louchev, Nan Ei Yu, Sunao Kurimura, and Kenji Kitamura, Appl. Phys. Lett.87,131101(2005).
[100]D. Eimerl, IEEE J. Quantum Electron.23,2238-2251 (1987).
[101]B. M. Jin, I. W. Kim, W. B. White, A. S. Bhalla, Mater. Lett.30,385-388 (1997).
[102]R. K. Choubey, P. Sen, P. K. Sen, R. Bhatt, S. Kar. V. Shukla, K. S. Bartwal, Opt. Mater,28,467(2006).
[103]Charra, F., Gurzadyan, G.:A-D. Nelson, D. F. (ed.). SpringerMaterials-The Landolt-Bornstein Database.
[104]Laszlo. Palfalvi, Gabor Almasi, Janos Hebling Agnes peter and Katalin Polgar, Appl. Phys. Lett.80,2245 (2002).
[105]C. J. Foot. Atomic physics (Oxford University Press 2005)
[106]F. Diedrich. J. C. Bergquist, Wayne M. Itano. and D. J. Wineland Phys. Rev. Lett.62,403(1989)
[107]Steven Chu, Rev. Mod. Phys.70,685(1998).
[108]Claude N. Cohen-Tannoudji, Rev. Mod. Phys.70,707(1998).
[109]William D. Philips, Rev. Mod. Phys.70,721(1998).
[110]Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee. D. M. Kurn and W. Ketterle Phys. Rev. Lett.75,3969 (1995).
[111]Thomas H. Lofus, Tetsuya Ido, Martin M. Boyd, Andrew D. Ludlow and Jun Ye, Phys. Rev. Lett.70,063413 (2004).
[112]Xinye Xu, Thomas H. Loftus, Matthew J. Smith, John L. Hall. Alan Gallagher and Jun Ye, Phys. Rev. A.66,011401(R) (2002).
[113]R. Maruyama. R. H. Wynar, M. V. Romalis, A. Andalkar. M. D. Swallows, C. E. Person and E. N. Fortson, Phys. Rev. A.68,011403(R)(2003).
[114]Gribakin. G. F. and V. V. Flambaum, Phys. Rev. A.48,546(1993).
[115]L. D. Landau and E. M. Lifshitz, Quantum Mechanics:non-relativistic theory (Elsevier 1965).
[116]Kurt Gibble, Phys. Rev. Lett.103,113202 (2009).
[117]Peter J. Martin, Bruce G. Oldaker, Andrew H. Miklich, and David E. Pritchard, Phys. Rev. Lett.60,515 (1988)
[118]Campbell G K, Boyd M M, Thomsen J W, Martin M J, Blatt S. Swallows M D, Nicholson T L, Fortier T, Oates C W, Diddams S A, Lemke N D, Naidom P, Juloenne P, Ye Jun and Ludlow A D, Science,324,360 (2009).
[119]C. W. Hoyt, Z. W. Barber. C. W. Oates, T. M. Fortier, S. A. Diddams, and L. Hollberg, Phys. Rev. Lett.95,083003 (2005).
[120]Reichenbach Iris and Deutsch Ivan H, Phys. Rev. Lett.99,123001 (2007).
[121]杨福家,原子物理学,(高等教育出版社2006)
[122]Haman S E, Haycock D L, Klose G, Pax P H, Deutsch I H and Jessen P S. Phys. Rev. Lett.80,4149(1998).
[123]Vuletic Valadan. Chin Cheng. Kerman Andrew J. and Chu Steven Phys. Rev. Lett.81,5768(1998).
[124]Deutsch Ivan H and Jessen Poul S. Phys. Rev. A.57,1972(1998).
[125]Ludlow Andrew D. Boyd Martin. M. Zelevinsky Tanya. Foreman Seth M. Blatt Sebastian. Notcutt Mark, Ido Tetsuya and Ye Jun. Phys. Rev. Lett.96, 033003 (2006).