超窄线宽激光及其在光钟中的应用
|
摘要
超窄线宽稳频激光器在科学研究与技术领域中有着重要且广泛的应用,如光原子钟、高分辨激光光谱、低噪声微波信号产生、基本物理常数测量和基础物理验证等。
在光原子钟研究中,这种窄线宽稳频激光器被称为“本地振荡器”(LO),用该激光探测装载在光晶格中的冷原子或被囚禁的单冷离子,可获得线宽超窄且频率极稳定的跃迁谱线(称为钟跃迁谱线),并用该跃迁谱线对本振激光频率实现精密锁定,从而建成高稳定度和高精度的光学频率标准或光钟。降低本振激光的频率噪声和提高其频率稳定度将有助于增加本振激光探测原子的时间,从而提高探测钟跃迁谱线的分辨率,同时减小Dick效应对光钟频率稳定性的影响,进而提高光原子钟的频率稳定度。目前,基于中性原子光钟的频率稳定度在很大程度上受限于本振激光的频率噪声。因此,降低窄线宽激光的频率噪声对光原子钟及其它应用具有至关重要的作用。
为了获得高稳定且频率噪声极低的激光,通常采用Pound-Drever-Hall (PDH)技术将激光的频率精密锁定在超稳定光学参考谐振腔的谐振频率上。本论文首先简要介绍了PDH技术的原理,分析了该稳频技术中各种噪声对稳频的影响。当系统具有高信噪比的鉴频信号和高精度的频率控制系统时,激光的频率稳定度在很大程度上取决于参考腔长度的稳定性。因此,本论文还讨论了提高光学参考腔长度稳定性的方法,如采用各种隔离环境噪声的措施来减小外界环境对腔长的影响,并讨论分析了垂直、水平和环形三种腔体结构和支撑方式,使得光学谐振腔具有“振动免疫”的特点。在实验上,我们将光学谐振腔放置在精密温度控制的高真空室内,并采取隔振、隔音措施,大大提高了光学谐振腔的长度稳定性。同时,结合激光功率精密控制技术和光纤位相噪声消除技术,通过高精密伺服控制系统,实现将激光频率锁定在超稳腔的谐振频率上。经测量比对,窄线宽稳频激光的频率特性都已接近参考腔的热噪声极限。其中,两台1064nm稳频激光的线宽达到1Hz(分辨率0.25Hz)、频率不稳定度达到1.7×10-15(1秒平均时间)；578m窄线宽激光器的线宽达到0.25Hz(分辨率85mHz),在1-10秒的平均时间内频率不稳定度达到≤3×10"16。
为了进一步验证窄线宽稳频激光的性能,本文还将研制的578nm低噪声窄线宽激光应用于镱原子光钟实验。用该激光探测囚禁在光晶格中的冷镱(Yb)原子,观察到镱原子钟跃迁谱线宽度为1Hz(跃迁频率为518THz),其品质因子>5×1014；本论文通过降低LO激光频率噪声、提高激光频率稳定度,延长了激光对原子的探测时间,从而减小了Dick效应对光钟频率稳定性的影响,提高了光钟的频率稳定度。实验测量显示,光钟的频率不稳定度达到了5×10-16/(?)τ(τ为平均时间),这是目前已报道的光钟频率稳定性最好的结果。
最后,论文展望了进一步改善窄线宽稳频激光器性能的方案,着重讨论了减小参考谐振腔热噪声影响的方法,同时还介绍了产生窄线宽激光的其它方法及发展前景。论文的最后还讨论了通过进一步提高窄线宽稳频激光器性能、并积极采取其它有效的实验方案来减小Dick效应对光钟频率稳定性的影响,从而进一步提高光钟的频率稳定性。
Spectrally narrow, ultrastable lasers have a variety of important applications such as optical atomic clocks, high-resolution laser spectroscopy, generation of low phase noise microwave signals, measurements of fundamental physical constants and tests of fundamental physics.
In one of its important applications, optical atomic clocks, a narrow linewidth laser source with high frequency stability, called the local oscillator (LO), probes cold atoms in optical lattice sites or a trapped single ion to resolve an ultra-narrow highly-stable transition (clock transition), which is used as a feedback signal to control the frequency of the LO. The frequency stability of optical atomic clocks depends on the frequency noise and frequency stability of the LO, which enables high frequency resolution and a reduced Dick effect, resulting partly from longer interaction time with atoms. In fact the performance of state-of-the-art optical clocks based on neutral atoms is usually limited by an imperfect local oscillator. Improving local oscillator thus plays a critical role in optical atomic clocks as well as its other applications.
To suppress the frequency noise and improve the frequency stability, a laser is usually frequency-stabilized to an ultra-stable optical reference cavity by the Pound-Drever-Hall (PDH) technique. This thesis first gives a brief introduction to the PDH technique, including a variety of noise sources that might limit the performance of ultrastable lasers. Assuming a good signal-to-noise ratio (SNR) and a tight phase lock, we find that the laser frequency stability depends on the length stability of the reference cavities. Here I discuss how we improve the length stability of reference cavities, including the shape and support configuration of the reference cavities for vibration insensitivity and isolation from environmental vibration and acoustic noise. Experimentally, I show how we realized ultrastable reference cavities (two1064nm cavities and two578nm cavities) based on vacuum chambers, precision temperature control and acoustic isolation. Lasers stabilized to these cavities have almost reached to the thermal noise limit for these reference cavities. Two1064nm lasers have achieved a linewidth of1Hz (RBW=0.25Hz) and fractional frequency instability of1.7×10-15at an averaging time of1s. The resulting stabilized578nm laser is measured to have a linewidth of0.25Hz (RBW=85mHz) and fractional frequency instability of≤3×10-16at an averaging time of1-10s, a result that advances the state-of-the-art for laser stabilization.
To further characterize the performance of the ultra-stable narrow-linewidth lasers, the578nm laser was used to probe the clock transition of cold ytterbium (Yb) atoms trapped in optical lattice sites. We resolved an atomic spectrum with spectral linewidth1Hz, corresponding to a line quality factor of>5×1014at a transition frequency of518THz. With the stable laser source and the signal to noise ratio afforded by the Yb optical clock, we dramatically reduced the key instability limitations of the clock, and made measurements consistent with a clock instability of5×10-16/√τ, the lowest recorded for an atomic clock.
Further improvements of ultrastable lasers, especially reducing the thermal noise limit of the reference cavities, are discussed. Alternative methods to generate narrow linewidth laser light are also introduced. As an application to optical clocks, improvements on the LO directly reduce the Dick-effect of optical atomic clocks, which is the main limitation of the frequency stability of state-of-the-art optical atomic clocks. Therefore, I also consider ways to reduce the Dick effect limitation as a means toward even more stable optical clocks.
在光原子钟研究中,这种窄线宽稳频激光器被称为“本地振荡器”(LO),用该激光探测装载在光晶格中的冷原子或被囚禁的单冷离子,可获得线宽超窄且频率极稳定的跃迁谱线(称为钟跃迁谱线),并用该跃迁谱线对本振激光频率实现精密锁定,从而建成高稳定度和高精度的光学频率标准或光钟。降低本振激光的频率噪声和提高其频率稳定度将有助于增加本振激光探测原子的时间,从而提高探测钟跃迁谱线的分辨率,同时减小Dick效应对光钟频率稳定性的影响,进而提高光原子钟的频率稳定度。目前,基于中性原子光钟的频率稳定度在很大程度上受限于本振激光的频率噪声。因此,降低窄线宽激光的频率噪声对光原子钟及其它应用具有至关重要的作用。
为了获得高稳定且频率噪声极低的激光,通常采用Pound-Drever-Hall (PDH)技术将激光的频率精密锁定在超稳定光学参考谐振腔的谐振频率上。本论文首先简要介绍了PDH技术的原理,分析了该稳频技术中各种噪声对稳频的影响。当系统具有高信噪比的鉴频信号和高精度的频率控制系统时,激光的频率稳定度在很大程度上取决于参考腔长度的稳定性。因此,本论文还讨论了提高光学参考腔长度稳定性的方法,如采用各种隔离环境噪声的措施来减小外界环境对腔长的影响,并讨论分析了垂直、水平和环形三种腔体结构和支撑方式,使得光学谐振腔具有“振动免疫”的特点。在实验上,我们将光学谐振腔放置在精密温度控制的高真空室内,并采取隔振、隔音措施,大大提高了光学谐振腔的长度稳定性。同时,结合激光功率精密控制技术和光纤位相噪声消除技术,通过高精密伺服控制系统,实现将激光频率锁定在超稳腔的谐振频率上。经测量比对,窄线宽稳频激光的频率特性都已接近参考腔的热噪声极限。其中,两台1064nm稳频激光的线宽达到1Hz(分辨率0.25Hz)、频率不稳定度达到1.7×10-15(1秒平均时间)；578m窄线宽激光器的线宽达到0.25Hz(分辨率85mHz),在1-10秒的平均时间内频率不稳定度达到≤3×10"16。
为了进一步验证窄线宽稳频激光的性能,本文还将研制的578nm低噪声窄线宽激光应用于镱原子光钟实验。用该激光探测囚禁在光晶格中的冷镱(Yb)原子,观察到镱原子钟跃迁谱线宽度为1Hz(跃迁频率为518THz),其品质因子>5×1014；本论文通过降低LO激光频率噪声、提高激光频率稳定度,延长了激光对原子的探测时间,从而减小了Dick效应对光钟频率稳定性的影响,提高了光钟的频率稳定度。实验测量显示,光钟的频率不稳定度达到了5×10-16/(?)τ(τ为平均时间),这是目前已报道的光钟频率稳定性最好的结果。
最后,论文展望了进一步改善窄线宽稳频激光器性能的方案,着重讨论了减小参考谐振腔热噪声影响的方法,同时还介绍了产生窄线宽激光的其它方法及发展前景。论文的最后还讨论了通过进一步提高窄线宽稳频激光器性能、并积极采取其它有效的实验方案来减小Dick效应对光钟频率稳定性的影响,从而进一步提高光钟的频率稳定性。
Spectrally narrow, ultrastable lasers have a variety of important applications such as optical atomic clocks, high-resolution laser spectroscopy, generation of low phase noise microwave signals, measurements of fundamental physical constants and tests of fundamental physics.
In one of its important applications, optical atomic clocks, a narrow linewidth laser source with high frequency stability, called the local oscillator (LO), probes cold atoms in optical lattice sites or a trapped single ion to resolve an ultra-narrow highly-stable transition (clock transition), which is used as a feedback signal to control the frequency of the LO. The frequency stability of optical atomic clocks depends on the frequency noise and frequency stability of the LO, which enables high frequency resolution and a reduced Dick effect, resulting partly from longer interaction time with atoms. In fact the performance of state-of-the-art optical clocks based on neutral atoms is usually limited by an imperfect local oscillator. Improving local oscillator thus plays a critical role in optical atomic clocks as well as its other applications.
To suppress the frequency noise and improve the frequency stability, a laser is usually frequency-stabilized to an ultra-stable optical reference cavity by the Pound-Drever-Hall (PDH) technique. This thesis first gives a brief introduction to the PDH technique, including a variety of noise sources that might limit the performance of ultrastable lasers. Assuming a good signal-to-noise ratio (SNR) and a tight phase lock, we find that the laser frequency stability depends on the length stability of the reference cavities. Here I discuss how we improve the length stability of reference cavities, including the shape and support configuration of the reference cavities for vibration insensitivity and isolation from environmental vibration and acoustic noise. Experimentally, I show how we realized ultrastable reference cavities (two1064nm cavities and two578nm cavities) based on vacuum chambers, precision temperature control and acoustic isolation. Lasers stabilized to these cavities have almost reached to the thermal noise limit for these reference cavities. Two1064nm lasers have achieved a linewidth of1Hz (RBW=0.25Hz) and fractional frequency instability of1.7×10-15at an averaging time of1s. The resulting stabilized578nm laser is measured to have a linewidth of0.25Hz (RBW=85mHz) and fractional frequency instability of≤3×10-16at an averaging time of1-10s, a result that advances the state-of-the-art for laser stabilization.
To further characterize the performance of the ultra-stable narrow-linewidth lasers, the578nm laser was used to probe the clock transition of cold ytterbium (Yb) atoms trapped in optical lattice sites. We resolved an atomic spectrum with spectral linewidth1Hz, corresponding to a line quality factor of>5×1014at a transition frequency of518THz. With the stable laser source and the signal to noise ratio afforded by the Yb optical clock, we dramatically reduced the key instability limitations of the clock, and made measurements consistent with a clock instability of5×10-16/√τ, the lowest recorded for an atomic clock.
Further improvements of ultrastable lasers, especially reducing the thermal noise limit of the reference cavities, are discussed. Alternative methods to generate narrow linewidth laser light are also introduced. As an application to optical clocks, improvements on the LO directly reduce the Dick-effect of optical atomic clocks, which is the main limitation of the frequency stability of state-of-the-art optical atomic clocks. Therefore, I also consider ways to reduce the Dick effect limitation as a means toward even more stable optical clocks.
引文
[1]A. L. Schawlow, C. H. Townes. Infrared and optical masers [J]. Phys. Rev., 1958,112:1940-1949.
[2]G. R. Hanes, K. M. Baird, J. De Remigis. Stability, reproducibility, and absolute wavelength of a 633-nm He-Ne laser stabilized to an iodine hyperfine component [J].Appl. Opt.,1973,12:1600-1605.
[3]S. Picard et. al. Comparison of127I2-stabilized frequency-doubled Nd:YAG lasers at the Bureau International des Poids et Mesures [J]. Appl. Opt.,2003, 42:1019-1028.
[4]J. L. Hall et. al. Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser [J]. IEEE Trans. Instrum. Meas.,1999,48:583-586.
[5]T. J. Quinn. International report:Practical realization of the definition of the metre (1997) [J]. Metrologia,1999,36:211-244.
[6]R. L. Barger, M. S. Sorem, J. L. Hall. Frequency stabilization of a cw dye laser [J]. Appl. Phys. Lett.,1973,22:573-575.
[7]R. W. P. Drever et. al. Laser phase and frequency stabilization using an optical resonator [J]. Appl. Phys. B,1983,31:97-105.
[8]M. M. Boyd et. al. Optical atomic coherence at the 1-second time scale [J]. Science,2006,314:1430-1433.
[9]A. D. Ludlow et al. Sr lattice clock at 1×1016 fractional uncertainty by remote optical evaluation with a Ca clock [J]. Science,2008,319:1805-1808.
[10]T. Rosenband et al. Frequency ratio of Al+ and Hg+ single-ion optical clocks; Metrology at the 17th decimal place [J]. Science,2008,319:1808-1812.
[11]F. Acernese et al. The Virgo status [J]. Class. Quantum Grav.,2006,23: S635.
[12]S. J. Waldman et al. Status of LIGO at the start of the fifth science run [J]. Class. Quantum Grav.,2006,23:S653.
[13]J. Millo et al. Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock [J]. Appl. Phys. lett.,2009,94:141105-141103.
[14]A. Bartels, et. al. Femtosecond laser based synthesis of Ultrastable microwave signals from optical frequency references [J]. Opt. Lett.,2005,30: 667-669.
[15]T. M. Fortier et. al. Generation of ultrastable microwaves via optical frequency division [J]. Nature Photonics,2011,5:425-429.
[16]H. Muller et. al. Tests of relativity by complementary rotating Michelson-Morley experiments [J]. Phys. Rev. Lett.,2007,99:050401.
[17]S. G. Turyshev. Experimental tests of general relativity:Recent progress and future directions [J]. Physics-Uspekhi,2009,52:1-28.
[18]S. Grop et. al.10 GHz cryocooled sapphire oscillator with extremely low phase noise [J]. Electron. Lett.,2010,46:420-421.
[19]J. A. Scheer, J. Kurtz. Coherent radar performance estimation [M]. Artech House,1993.
[20]P. W. Juodawlkis et. al. Optically sampled analog-to-digital converters [J]. IEEE Trans. Micro. Theo. Tech.,2001,49:1840-1853.
[21]S. Doeleman. Frequency standards and metrology:proceedings of the 7th symposium [M]. World Scientific,2009.
[22]S. Weyers et. al. Reaching the quantum limit in a fountain clock using a microwave oscillator phase locked to an ultrastable laser [J]. Phys. Rev. A, 2009,79:031803.
[23]J. Levine. Introduction to time and frequency metrology [J]. Rev. Sci. Instrum.,1999,70:2567-2596.
[24]A. D. Ludlow. The strontium optical lattice clock:optical spectroscopy with sub-hertz accuracy [D]. U.S.:JILA,2008.
[25]C. W. Chou, et. al. Frequency comparison of two high-accuracy Al+ optical clocks [J]. Phys. Rev. Lett.,2010,104:070802.
[26]N. D. Lemke, et. al. Spin-1/2 optical lattice clock [J]. Phys. Rev. Lett.,2009, 103:063001.
[27]S. Bize, et. al. Advances in atomic fountains [J]. Compt. Rend. Phys.,2004, 5:829-843.
[28]T. P. Heavener, et. al. Recent improvements in NIST-F1 and a resulting accuracy of δf/f=0.61×10-15 [J]. IEEE Trans. Instrum. & Meas.,2005,54: 842.
[29]V. Gerginov, et. al. Uncertainty evaluation of the caesium fountain clock PTB-CSF2 [J]. Metrologia,2010,47:65.
[30]C. Vian, et. al. BNM-SYRTE fountains:recent results [J]. IEEE Trans. Instrum. Meas.,2005,54:833-836.
[31]L. Hollberg, et. al. Optical frequency/wavelength references [J]. J. Phys. B: Mol. Opt. Phys.,2005,38:S469-495.
[32]T. C. Li, et. al. Improvements and new evaluation of NIM4 caesium fountain clock at NIM in 2005-2006 [J]. Chinese Phys. Lett.,2007,24:1177.
[33]E. Peik, et. al. Limit on the present temporal variation of the fine structure constant [J]. Phys. Rev. Lett.,2004,93:170801.
[34]M. Fischer, et. al. New limits on the drift of fundamental constants from laboratory measurements [J]. Phys. Rev. Lett.,2004,92:230802.
[35]T. M. Fortier, et. al. Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance [J]. Phys. Rev. Lett.,2007,98:070801.
[36]S. N. Lea. Limits to time variation of fundamental constants from comparisons of atomic frequency standards [J]. Rep. Pro. Phys.,2007,70: 1473-1523.
[37]C. W. Chou, et. al. Optical clocks and relativity [J]. Science,2010,329: 1630-1633.
[38]S. Reynaud, C. Satomon, P. Wolf. Testing general relativity with atomic clocks [J]. Space Sci. Rev.,2009,148:233-247.
[39]S. Bize, et al. Cold atom clocks and applications [J]. J. Phys. B-Atomic Molecular and Optical Physics,2005,38:S449.
[40]P. Gill, et al. Optical atomic clocks for space [R]. National Physical Laboratory technical supporting document NO.21641,2008.
[41]A. Bauch. Caesium atomic clocks:function, performance and applications, Measurement [J]. Science & Technology,2003,14:1159.
[42]T. Udem, et al. Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser [J]. Phys. Rev. Lett.,2001,86: 4996-4999.
[43]G. J. Dick. Local oscillator induced instabilities in trapped ion frequency standards [C]. Proc. Precise Time and Time Interval Meeting,1987,133-147.
[44]G. Santarelli, et. al. Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator [J]. IEEE Trans. Ultra. Ferro. Freq. Cont.,1998,45:887-894.
[45]A. Quessada, et. al. The Dick effect for an optical frequency standard [J]. J. Opt. B:Quantum Semiclass. Opt.,2003,5:S150-153.
[46]L. S. Ma. Optical atomic clocks:from dream to reality [J]. Opt. Photon. News,2007,18:42-47.
[47]S. A Diddams, et. al. Standards of time and frequency at the outset of the 21st century [J]. Science,2004,306:1318-1324.
[48]S. A Diddams, et. al. An optical clock based on a single trapped 199Hg+ion [J]. Science,2001,293:825-828.
[49]M. Takamoto, et. al. An optical lattice clock [J]. Nature,2005,435:321-324.
[50]R. L. Targat, et. al. Accurate optical lattice clock with 87Sr atoms [J]. Phys. Rev. Lett.,2006,97:130801.
[51]Z. W. Barber, et. al. Optical lattice induced light shifts in an Yb atomic clock [J]. Phys. Rev. Lett.,2008,100:103002.
[52]T. Kohno, et. al. One-dimensional optical lattice clock with a fermionic 171Yb isotope [J]. Appl. Phys. Exp.,2009,2:072501.
[53]X. Y. Xu, et. al. Laser cooling and trapping of ytterbium atoms [J]. Front. Phys. Chinese,2009,4:160-164.
[54]C. W. Oates, E. A. Curtis, L. Hollberg. Improved short-term stability of optical frequency standards:approaching 1 Hz in 1 s with the Ca standard at 657 nm [J]. Opt. Lett.,2000,25:1603-1605.
[55]G. Wilpers, et. al. Optical clock with ultracold neutral atoms [J]. Phys. Rev. Lett.,2002,89:230801.
[56]M. Petersen, et. al. Doppler-free spectroscopy of the 1S0-3P0 optical clock transition in laser-cooled fermionic isotopes of neutral mercury [J]. Phys. Rev. Lett.,2008,101:183004.
[57]H. Hachisu, et. al. Trapping of neutral mercury atoms and prospects for optical lattice clocks [J]. Phys. Rev. Lett.,2008,100:053001.
[58]J. J. McFerran, et. al. Sub-Doppler cooling of fermionic Hg isotopes in a magneto-optical trap [J]. Opt. Lett.,201035:3078-3080.
[59]W. G. Rellergert, et. al. Constraining the evolution of the fundamental constants with a solid-state optical frequency reference based on the 229Th nucleus [J]. Phys. Rev. Lett.,2010,104:200802.
[60]H. S. Margolis, et. al. Hertz-level measurement of the optical clock frequency in a single 88Sr+ion [J]. Science,2004,306:1355-1358.
[61]P. Dube, et. al. Electric quadrupole shift cancellation in single-ion optical frequency standards [J]., Phys. Rev. Lett.,2005,95:033001.
[62]K. Hosaka, et. al. Frequency measurement of the 2S1/2-2Fy/2 electric octupole transition in a single 171Yb+ ion [J]. Phys. Rev. A,2009,79:033403.
[63]T. Schneider, E. Peik, Chr. Tamm. Sub-hertz optical frequency comparisons between two trapped 171Yb+ ions [J]. Phys. Rev. Lett.,2005,94:230801.
[64]J. V. Zanthier, et. al. Absolute frequency measurement of the In+ clock transition with a mode-locked laser [J]. Opt. Lett.,2000,25:1729-1731.
[65]Th. Becker, et. al. High-resolution spectroscopy of a single In+ ion:Progress towards an optical frequency standard [J]. Phys. Rev. A,2001,63:051802.
[66]C. Champenois, et. al. Evaluation of the ultimate performances of a Ca+ single-ion frequency standard [J]. Phys. Lett. A,2004,331:298-311.
[67]M. Chwalla, et. al. Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition [J]. Phys. Rev. Lett.,2009,102:023002.
[68]B. Guo et. al. Measurement of secular motion frequency in miniature Paul trap to ascertain the stability parameters [J]. Chinese Phys. Lett.,2010,27: 013202.
[69]J. L. Hall. Nobel lecture:defining and measuring optical frequencies [J]. Rev. Mod. Phys.,2006,78:1279-1295.
[70]T. W. Hansch. Nobel lecture:passion for precision [J]. Rev. Mod. Phys., 2006,78:1297-1309.
[71]H. Schnatz et. al. First phase-coherent frequency measurement of visible radiation [J]. Phys. Rev. Lett.,1996,76:18-21.
[72]L. S. Ma et. al. Optical frequency synthesis and comparison with uncertainty at the 10-19 level [J]. Science,2004,303:1843-1845.
[73]L. S. Ma, et. al. Delivering the same optical frequency at two places:accurate cancellation of phase noise introduced by an optical fiber or other time-varying path [J]. Opt. Lett.,1994,19:1777-1779.
[74]网页[EB/OL].http://www.corning.com/docs/specialtymaterials/pisheets/UleBro91106.pdf.
[75]B. C. Young et. al. Visible lasers with subhertz linewidths [J]. Phys. Rev. Lett,1999,82:3799-3802.
[76]M. Notcutt et. al. Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity [J]. Opt. Lett.,2005,30: 1815-1817.
[77]M. Notcutt et. al. Mounting system for optical frequency reference cavities [P]. U.S. Patent:7469454.B2,2008.
[78]A. D. Ludlow et. al. Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1×10-15 [J]. Opt. Lett.,2007,32:641-643.
[79]J. Alnis et. al. Subhertz linewidth diode lasers by stabilization to vibrationally and thermal compensated ultralow-expansion glass Fabry-Perot cavities [J]. Phys. Rev. A,2008,77:053809.
[80]Y. Y. Jiang et. al. Two-hertz-linewidth Nd:YAG lasers at 1064 nm stabilized to vertically mounted ultra-stable cavities [J]. Chin. Phys. B,2008,17: 2152-2155.
[81]Y. Y. Jiang et. al. Nd:YAG lasers at 1064 nm with 1-Hz linewidth [J]. Appl. Phys. B,2010,98:61-67.
[82]L. S. Chen et. al. Vibration-induced elastic deformation of Fabry-Perot cavities [J]. Phys. Rev. A,2006,74:053801.
[83]H. Stoehr et. al. Diode laser with 1 Hz linewidth [J]. Opt. Lett.,2006,31: 736-738.
[84]T. Nazarova et. al. Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser [J]. Appl. Phys. B,2006,83:531-536.
[85]S. A. Webster et. al. Vibration insensitive optical cavity [J]. Phys. Rev. A, 2007,75:011801R.
[86]J. Millo, et. al. Ultrastable lasers based on vibration insensitive cavities [J]. Phys. Rev. A,2009,79:053829.
[87]A. Abramovici, et. al. LIGO:the laser interferometer gravitational-wave observatory [J]. Science,1992,256:325-333.
[88]P. R. Saulson. Fundamentals of interferometric gravitational wave detectors [M]. World Scientific,1994.
[89]E. D. Black. Notes on thermal noise, with a bibliography [R]. LIGO Technical Note:LIGO-T03142-01-R,2004.
[90]K. Numata, A. Kemery, J. Camp. Thermal-noise limit in the frequency stabilization of lasers with rigid cavities [J]. Phys. Rev. Lett.,2004,93: 250602.
[91]S. A. Webster, et. al. Thermal-noise-limited optical cavity [J]. Phys. Rev. A, 2008,77; 033847.
[92]M. Notcutt, et. al. Contribution of thermal noise to frequency stability of rigid optical cavity via Hertz-linewidth lasers [J]. Phys. Rev. A,2006,73: 031804.
[93]E. D. Black. An introduction to Pound-Drever-Hall laser frequency stabilization [J]. Am. J. Phys.,2001,69:79-87.
[94]网页[EB/OL]. http://search.newport.com/?q=*&x2=sku&q2=1801-FS-M.
[95]E. A. Whittaker, M. Gehrtz, G. C. Bjorklund. Residual amplitude modulation in laser electro-optic phase modulation [J]. J. Opt. Soc. Am. B,1985,2: 1320-1326.
[96]E. A. Whittaker, et. al. Reduction of residual amplitude modulation in frequency-modulation spectroscopy by using harmonic frequency modulation [J]. J. Opt. Soc. Am. B,1988,5:1253-1256.
[97]N. C. Wong, J. L. Hall. Servo control of amplitude modulation in frequency-modulation spectroscopy:demonstration of shot-noise-limited detection [J]. J. Opt. Soc. Am. B,1985,2:1527-1533.
[98]Y. H. Chen, et. al. Suppression of residual amplitude modulation in electro-optical phase modulators using Fabry-Perot cavity [J]. Acta Optica Sinica,2007,27:1-6.
[99]M. Notcutt, et. al. Temperature compensation for cryogenic cavity stabilized lasers [J]. J. Phys. D:Appl. Phys.,1995,28:1807-1810.
[100]R. W. Fox. Temperature analysis of low-expansion Fabry-Perot cavities [J]. Opt. Exp.,2009,17:15023-15031.
[101]T. Legero, T. Kessler, U. Sterr. Tuning the thermal expansion properties of optical reference cavities with fused silica mirrors [J]. J. Opt. Soc. Am. B, 2010,27:914-919.
[102]Y. Jiang, et. al. Making optical atomic clocks more stable with 10-16-level laser stabilization [J]. Nature Photonics,2011,5:158-161.
[103]F. J. Raab, S. E. Whitcomb. Technical Report:LIGO-T920004-00-R [R], 1992.
[104]J. Hough et al. The Detection of Gravitational Waves [M]. Cambridge University Press,1991.
[105]J. Miao, et. al. Vibration insensitive optical ring cavity [J]. Chin. Phys. B, 2009,18:2334-2339.
[106]J. L. Hall, J. Ye, L. S. Ma. Measurement of mirror birefringence at the sub-ppm level:Proposed application to a test of QED [J]. Phys. Rev. A,2000, 62:013815.
[107]P. Barriga, et. al. Self-compensation of astigmatism in mode-cleaners for advanced interferometers [J].J. Phys.,2006,32:457-463.
[108]T. Skettrup. Rectangular laser resonators with astigmatic compensation [J]. J. Opt. A:Pure Appl. Opt.,2005,7:645-654.
[109]Y. Levin. Fluctuation-dissipation theorem for the thermo-refractive noise [J]. Phys. Lett. A,2008,372:1941-1944.
[110]V. B. Braginsky, M. L. Gorodetsky, S. P. Vyatchanin. Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae [J]. Phys. Lett.A,1999,264:1-10.
[111]M. Cerdonio, et. al. Thermoelastic effects at low temperatures and quantum limits in displacement measurements [J]. Phys. Rev. D,2001,63:082003.
[112]M. De Rosa, et. al. Experimental measurement of the dynamic photothermal effect in Fabry-Perot cavities for gravitational wave detectors [J]. Phys. Rev. Lett.,2002,89:237402.
[113]P. R. Saulson. Thermal noise in mechanical experiments [J]. Phys. Rev. D, 1990,42:2437-2445.
[114]V. B. Braginsky, S. P. Vyatchanin. Thermodynamical fluctuations in optical mirror coatings [J]. Phys. Lett. A,2003,312:244-255.
[115]J. P. Richard, J. J. Hamilton. Cryogenic monocrystalline silicon Fabry-Perot cavity for the stabilization of laser frequency [J]. Rev. Sci. Instrum.,1991,62: 2375-2378.
[116]T. Kessler, et. al. A sub-40 mHz linewidth laser based on a silicon single-crystal optical cavity [J]. arXiv:1112.3854vl,2012.
[117]G. M. Harry, et. al. Titania-doped tantala/silica coatings for gravitational-wave detection [J]. Class. Quantum Grav.,2007,24:405-415.
[118]Characterization of frequency and phase noise [R]. Report 580 of the International Radio Consultative Committee,1986,142-150.
[119]H. G. Lu, et. al. Measurement of reflectivity of optical mirrors using laser phase modulation and finesse of Fabry-Perot cavity [J]. Chin. J. Lasers, 2006,33:1675-1679.
[120]J. Ye. Ultrasensitive high resolution laser spectroscopy and its application to optical frequency standards [D].US:JILA,1997.
[121]J. Ye, J. L. Hall. Cavity ringdown heterodyne spectroscopy:High sensitivity with microwatt light power [J]. Phys. Rev. A,2000,61:061802.
[122]J. J. Scherer, et. al. Cavity ringdown laser absorption spectroscopy:history development and application to pulsed molecular beams [J]. Chem. Rev., 1997,97:25.
[123]M. J. Lawrence, et. al. Dynamic response of a Fabry-Perot interferometer [J]. J. Opt. Soc. Am. B,1999,16:523-532.
[124]H. Q. Chen, et. al. Optical-heterodyne cavity-ring-down spectroscopy with 1-Hz-linewidth laser [J].. in preparation.
[125]C. J. Hood, et. al. Characterization of high-finesse mirrors:Loss, phase shifts, and mode structure in an optical cavity [J]. Phys. Rev. A,2001,64:033804.
[126]M. Zhu, J. L. Hall. Stabilization of optical phase/frequency of a laser system: application to a commercial dye laser with an external stabilizer [J]. J. Opt. Soc. Am. B,1993,10:802-816.
[127]J. L. Hall, M. Zhu. An Introduction to Phase-Stable Optical Sources [C]. International School of Physics Enrico Fermi, Course CXVIII, Laser Manipulation of Atoms and Ions, edited by E. Arimondo, W. Phillips, and S. F. (North Holland, ADDRESS),1992,671-702.
[128]D. W. Allan. Time And Frequency (Time-Domain) Characterization, Estimation, And Prediction Of Precision Clocks And Oscillators [J]. IEEE Trans. Ultrasonic Ferro.& Freq. Ctrl.,1987,34:647-654.
[129]W. J. Riley. Handbook of frequency stability analysis [R]. U.S.:NIST Special Publication,1065,2008.
[130]R. Santra, K. V. Christ, C. H. Greene. Properties of metastable alkaline-earth-metal atoms calculated using an accurate effective core potential [J]. Phys. Rev. A,2004,69:042510.
[131]Z. W. Barber, et. al. Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice [J]. Phys. Rev. Lett.,2006, 96:083002.
[132]R. Santra, et. al. High-accuracy optical clock via three-level coherence in neutral bosonic 88Sr [J]. Phys. Rev. Lett.,2005,94:173002.
[133]E. L. Raab, et. al. Trapping of neutral sodium atoms with radiation Pressure [J]. Phys. Rev. Lett.,1987,59:2631.
[134]H. J. Metcalf, P.V. D. Straten. Laser cooling and trapping [M]. Springer, 1999.
[135]Z. Barber. Ytterbium optical lattice clock [D]. U.S.:JILA,2007.
[136]R. H. Dicke. The effect of collisions upon the Doppler width of spectral Lines [J]. Phys. Rev.,1953,89:472.
[137]J. C. Bergquist, et. al. Observation of quantum jumps in a single atom [J]. Phys. Rev. Lett.,1986,57:1699.
[138]A. D. Ludlow, et. al. Cold collision shift cancelation and inelastic scattering in a Yb optical lattice clock [J]. Phys. Rev. A,2011,84:052724.
[139]N. D. Lemke, et. al. p-wave cold collisions in an optical lattice clock [J]. Phys. Rev. Lett.,2011,107:103902.
[140]W. M. Itano el. al. Quantum projection noise:Population fluctuations in two-level systems [J]. Phys. Rev. A,1993,47:3554-3570.
[141]C. W. Oates et. al. Stable laser system for probing the clock transition at 578 nm in neutral ytterbium [C]. Proc.2007 IEEE Int. Freq. Cont. Symp.,2007, 1274-1277.
[142]K. Yamamoto, et. al. Measurement of the mechanical loss of a cooled reflective coating for gravitational wave detection [J]. Phys. Rev. D,2006, 74:022002.
[143]G. M. Harry, et. al. Thermal noise from optical coatings in gravitational wave detectors [J]. Appl. Opt.,2006,45:1569-1574.
[144]Ch. Comtet, et. al. Reduction of tantala mechanical losses in coatings for the next generation of VIRGO and LIGO interferometric gravitational waves detectors [EB/OL]. http://hal.in2p3.fr/in2p3-00177578/en/,2007.
[145]J. Agresti, et. al. Optimized multilayer dielectric mirror coatings for gravitational wave interferometers [R]. LIGO Tech. No. LIGO-P060027-00-Z,2006.
[146]S. Gossler, et. al. Coating-free mirrors for high precision interferometric experiments [J]. Phys. Rev. A,2007,76:053810.
[147]P. S. Johnston, K. K. Lehmann. Cavity enhanced absorption spectroscopy using a broadband prism cavity and a supercontinuum source [J]. Opt. Exp., 2008,16:15013-15023.
[148]H. J. Kimble, et. al. Optical interferometers with reduced sensitivity to thermal noise [J]. Phys. Rev. Lett.,2008,101:260602.
[149]C. H. Metzger, K. Karrai. Cavity cooling of a microlever [J]. Nature,2004, 432:1002-1005.
[150]S. Gigan, et. al. Self-cooling of micromirror by radiation pressure [J]. Nature, 2006,444:67-70.
[151]O. Arcizet, et. al. Radiation-pressure cooling and optomechanical instability of a micromirror [J]. Nature,2006,444:71-74.
[152]D. Kleckner, D. Bouwmeester. Sub-Kelvin optical cooling of a micromechanical resonator [J]. Nature,2006,444:75-78.
[153]J. L. Hall et. al. Measurement of mirror birefringence at the sub-ppm level: Proposed application to a test of QED [J]. Phys. Rev. A,2000,62:013815.
[154]D. Herriott, et. al. Off-axis paths in spherical mirror interferometers [J]. Appl. Opt,1964,3:523-526.
[155]D. Budker, et. al. Obtaining frequency markers of variable separation with a spherical mirror Fabry-Perot interferometer [J]. Rev. Sci. Instr.,2000,71: 2984-2987.
[156]P. B. Sellin, et. al. Programmable frequency reference for subkilohertz laser stabilization by use of persistent spectral hole burning [J]. Opt. Lett.,1999, 24:1038-1040.
[157]N. M. Trickland, et. al. Laser frequency stabilization using regenerative spectral hole burning [J]. Phys. Rev. B,2000,62:1473-1476.
[158]B. Julsgaard, et. al. Understanding laser stabilization using spectral hole burning [J]. Opt. Exp.,2007,15:11444-11465.
[159]M. J. Thorpe, et. al. Frequency-stabilization to 6×10-16 via spectral-hole burning [J]. Nature Photonics,2011,5:688-693.
[160]Q. F. Chen, et. al. Spectrally narrow, long-term stable optical frequency reference based on a Eu3+:Y2SiO5 crystal at cryogenic temperature [J]. Phys. Rev. Lett,2011,107:223202.
[161]M. J. Martin, et. al. Extreme non-linear response of ultra-narrow optical transitions in cavity QED for laser stabilization [J]. arXiv:1105.2373vl, 2011.
[162]F. Kefelian, et. al. Ultralow-frequency-noise stabilization of a laser by locking to an optical fiber-delay line [J]. Opt. Lett.,2009,34:914-916.
[163]M. Kasevich, et. al. poster presentation [C]. International Conference on Laser Spectroscopy,2007.
[164]J. Lodewyck, et. al. Nondestructive measurement of the transition probability in a Sr optical lattice clock [J]. Phys. Rev. A,2009,79:061401.
[165]M. Takamoto, T. Takano, H. Katori. Frequency comparison of optical lattice clocks beyond the Dick limit [J]. Nature Photonics,2011,5:288-292.
[2]G. R. Hanes, K. M. Baird, J. De Remigis. Stability, reproducibility, and absolute wavelength of a 633-nm He-Ne laser stabilized to an iodine hyperfine component [J].Appl. Opt.,1973,12:1600-1605.
[3]S. Picard et. al. Comparison of127I2-stabilized frequency-doubled Nd:YAG lasers at the Bureau International des Poids et Mesures [J]. Appl. Opt.,2003, 42:1019-1028.
[4]J. L. Hall et. al. Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser [J]. IEEE Trans. Instrum. Meas.,1999,48:583-586.
[5]T. J. Quinn. International report:Practical realization of the definition of the metre (1997) [J]. Metrologia,1999,36:211-244.
[6]R. L. Barger, M. S. Sorem, J. L. Hall. Frequency stabilization of a cw dye laser [J]. Appl. Phys. Lett.,1973,22:573-575.
[7]R. W. P. Drever et. al. Laser phase and frequency stabilization using an optical resonator [J]. Appl. Phys. B,1983,31:97-105.
[8]M. M. Boyd et. al. Optical atomic coherence at the 1-second time scale [J]. Science,2006,314:1430-1433.
[9]A. D. Ludlow et al. Sr lattice clock at 1×1016 fractional uncertainty by remote optical evaluation with a Ca clock [J]. Science,2008,319:1805-1808.
[10]T. Rosenband et al. Frequency ratio of Al+ and Hg+ single-ion optical clocks; Metrology at the 17th decimal place [J]. Science,2008,319:1808-1812.
[11]F. Acernese et al. The Virgo status [J]. Class. Quantum Grav.,2006,23: S635.
[12]S. J. Waldman et al. Status of LIGO at the start of the fifth science run [J]. Class. Quantum Grav.,2006,23:S653.
[13]J. Millo et al. Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock [J]. Appl. Phys. lett.,2009,94:141105-141103.
[14]A. Bartels, et. al. Femtosecond laser based synthesis of Ultrastable microwave signals from optical frequency references [J]. Opt. Lett.,2005,30: 667-669.
[15]T. M. Fortier et. al. Generation of ultrastable microwaves via optical frequency division [J]. Nature Photonics,2011,5:425-429.
[16]H. Muller et. al. Tests of relativity by complementary rotating Michelson-Morley experiments [J]. Phys. Rev. Lett.,2007,99:050401.
[17]S. G. Turyshev. Experimental tests of general relativity:Recent progress and future directions [J]. Physics-Uspekhi,2009,52:1-28.
[18]S. Grop et. al.10 GHz cryocooled sapphire oscillator with extremely low phase noise [J]. Electron. Lett.,2010,46:420-421.
[19]J. A. Scheer, J. Kurtz. Coherent radar performance estimation [M]. Artech House,1993.
[20]P. W. Juodawlkis et. al. Optically sampled analog-to-digital converters [J]. IEEE Trans. Micro. Theo. Tech.,2001,49:1840-1853.
[21]S. Doeleman. Frequency standards and metrology:proceedings of the 7th symposium [M]. World Scientific,2009.
[22]S. Weyers et. al. Reaching the quantum limit in a fountain clock using a microwave oscillator phase locked to an ultrastable laser [J]. Phys. Rev. A, 2009,79:031803.
[23]J. Levine. Introduction to time and frequency metrology [J]. Rev. Sci. Instrum.,1999,70:2567-2596.
[24]A. D. Ludlow. The strontium optical lattice clock:optical spectroscopy with sub-hertz accuracy [D]. U.S.:JILA,2008.
[25]C. W. Chou, et. al. Frequency comparison of two high-accuracy Al+ optical clocks [J]. Phys. Rev. Lett.,2010,104:070802.
[26]N. D. Lemke, et. al. Spin-1/2 optical lattice clock [J]. Phys. Rev. Lett.,2009, 103:063001.
[27]S. Bize, et. al. Advances in atomic fountains [J]. Compt. Rend. Phys.,2004, 5:829-843.
[28]T. P. Heavener, et. al. Recent improvements in NIST-F1 and a resulting accuracy of δf/f=0.61×10-15 [J]. IEEE Trans. Instrum. & Meas.,2005,54: 842.
[29]V. Gerginov, et. al. Uncertainty evaluation of the caesium fountain clock PTB-CSF2 [J]. Metrologia,2010,47:65.
[30]C. Vian, et. al. BNM-SYRTE fountains:recent results [J]. IEEE Trans. Instrum. Meas.,2005,54:833-836.
[31]L. Hollberg, et. al. Optical frequency/wavelength references [J]. J. Phys. B: Mol. Opt. Phys.,2005,38:S469-495.
[32]T. C. Li, et. al. Improvements and new evaluation of NIM4 caesium fountain clock at NIM in 2005-2006 [J]. Chinese Phys. Lett.,2007,24:1177.
[33]E. Peik, et. al. Limit on the present temporal variation of the fine structure constant [J]. Phys. Rev. Lett.,2004,93:170801.
[34]M. Fischer, et. al. New limits on the drift of fundamental constants from laboratory measurements [J]. Phys. Rev. Lett.,2004,92:230802.
[35]T. M. Fortier, et. al. Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance [J]. Phys. Rev. Lett.,2007,98:070801.
[36]S. N. Lea. Limits to time variation of fundamental constants from comparisons of atomic frequency standards [J]. Rep. Pro. Phys.,2007,70: 1473-1523.
[37]C. W. Chou, et. al. Optical clocks and relativity [J]. Science,2010,329: 1630-1633.
[38]S. Reynaud, C. Satomon, P. Wolf. Testing general relativity with atomic clocks [J]. Space Sci. Rev.,2009,148:233-247.
[39]S. Bize, et al. Cold atom clocks and applications [J]. J. Phys. B-Atomic Molecular and Optical Physics,2005,38:S449.
[40]P. Gill, et al. Optical atomic clocks for space [R]. National Physical Laboratory technical supporting document NO.21641,2008.
[41]A. Bauch. Caesium atomic clocks:function, performance and applications, Measurement [J]. Science & Technology,2003,14:1159.
[42]T. Udem, et al. Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser [J]. Phys. Rev. Lett.,2001,86: 4996-4999.
[43]G. J. Dick. Local oscillator induced instabilities in trapped ion frequency standards [C]. Proc. Precise Time and Time Interval Meeting,1987,133-147.
[44]G. Santarelli, et. al. Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator [J]. IEEE Trans. Ultra. Ferro. Freq. Cont.,1998,45:887-894.
[45]A. Quessada, et. al. The Dick effect for an optical frequency standard [J]. J. Opt. B:Quantum Semiclass. Opt.,2003,5:S150-153.
[46]L. S. Ma. Optical atomic clocks:from dream to reality [J]. Opt. Photon. News,2007,18:42-47.
[47]S. A Diddams, et. al. Standards of time and frequency at the outset of the 21st century [J]. Science,2004,306:1318-1324.
[48]S. A Diddams, et. al. An optical clock based on a single trapped 199Hg+ion [J]. Science,2001,293:825-828.
[49]M. Takamoto, et. al. An optical lattice clock [J]. Nature,2005,435:321-324.
[50]R. L. Targat, et. al. Accurate optical lattice clock with 87Sr atoms [J]. Phys. Rev. Lett.,2006,97:130801.
[51]Z. W. Barber, et. al. Optical lattice induced light shifts in an Yb atomic clock [J]. Phys. Rev. Lett.,2008,100:103002.
[52]T. Kohno, et. al. One-dimensional optical lattice clock with a fermionic 171Yb isotope [J]. Appl. Phys. Exp.,2009,2:072501.
[53]X. Y. Xu, et. al. Laser cooling and trapping of ytterbium atoms [J]. Front. Phys. Chinese,2009,4:160-164.
[54]C. W. Oates, E. A. Curtis, L. Hollberg. Improved short-term stability of optical frequency standards:approaching 1 Hz in 1 s with the Ca standard at 657 nm [J]. Opt. Lett.,2000,25:1603-1605.
[55]G. Wilpers, et. al. Optical clock with ultracold neutral atoms [J]. Phys. Rev. Lett.,2002,89:230801.
[56]M. Petersen, et. al. Doppler-free spectroscopy of the 1S0-3P0 optical clock transition in laser-cooled fermionic isotopes of neutral mercury [J]. Phys. Rev. Lett.,2008,101:183004.
[57]H. Hachisu, et. al. Trapping of neutral mercury atoms and prospects for optical lattice clocks [J]. Phys. Rev. Lett.,2008,100:053001.
[58]J. J. McFerran, et. al. Sub-Doppler cooling of fermionic Hg isotopes in a magneto-optical trap [J]. Opt. Lett.,201035:3078-3080.
[59]W. G. Rellergert, et. al. Constraining the evolution of the fundamental constants with a solid-state optical frequency reference based on the 229Th nucleus [J]. Phys. Rev. Lett.,2010,104:200802.
[60]H. S. Margolis, et. al. Hertz-level measurement of the optical clock frequency in a single 88Sr+ion [J]. Science,2004,306:1355-1358.
[61]P. Dube, et. al. Electric quadrupole shift cancellation in single-ion optical frequency standards [J]., Phys. Rev. Lett.,2005,95:033001.
[62]K. Hosaka, et. al. Frequency measurement of the 2S1/2-2Fy/2 electric octupole transition in a single 171Yb+ ion [J]. Phys. Rev. A,2009,79:033403.
[63]T. Schneider, E. Peik, Chr. Tamm. Sub-hertz optical frequency comparisons between two trapped 171Yb+ ions [J]. Phys. Rev. Lett.,2005,94:230801.
[64]J. V. Zanthier, et. al. Absolute frequency measurement of the In+ clock transition with a mode-locked laser [J]. Opt. Lett.,2000,25:1729-1731.
[65]Th. Becker, et. al. High-resolution spectroscopy of a single In+ ion:Progress towards an optical frequency standard [J]. Phys. Rev. A,2001,63:051802.
[66]C. Champenois, et. al. Evaluation of the ultimate performances of a Ca+ single-ion frequency standard [J]. Phys. Lett. A,2004,331:298-311.
[67]M. Chwalla, et. al. Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition [J]. Phys. Rev. Lett.,2009,102:023002.
[68]B. Guo et. al. Measurement of secular motion frequency in miniature Paul trap to ascertain the stability parameters [J]. Chinese Phys. Lett.,2010,27: 013202.
[69]J. L. Hall. Nobel lecture:defining and measuring optical frequencies [J]. Rev. Mod. Phys.,2006,78:1279-1295.
[70]T. W. Hansch. Nobel lecture:passion for precision [J]. Rev. Mod. Phys., 2006,78:1297-1309.
[71]H. Schnatz et. al. First phase-coherent frequency measurement of visible radiation [J]. Phys. Rev. Lett.,1996,76:18-21.
[72]L. S. Ma et. al. Optical frequency synthesis and comparison with uncertainty at the 10-19 level [J]. Science,2004,303:1843-1845.
[73]L. S. Ma, et. al. Delivering the same optical frequency at two places:accurate cancellation of phase noise introduced by an optical fiber or other time-varying path [J]. Opt. Lett.,1994,19:1777-1779.
[74]网页[EB/OL].http://www.corning.com/docs/specialtymaterials/pisheets/UleBro91106.pdf.
[75]B. C. Young et. al. Visible lasers with subhertz linewidths [J]. Phys. Rev. Lett,1999,82:3799-3802.
[76]M. Notcutt et. al. Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity [J]. Opt. Lett.,2005,30: 1815-1817.
[77]M. Notcutt et. al. Mounting system for optical frequency reference cavities [P]. U.S. Patent:7469454.B2,2008.
[78]A. D. Ludlow et. al. Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1×10-15 [J]. Opt. Lett.,2007,32:641-643.
[79]J. Alnis et. al. Subhertz linewidth diode lasers by stabilization to vibrationally and thermal compensated ultralow-expansion glass Fabry-Perot cavities [J]. Phys. Rev. A,2008,77:053809.
[80]Y. Y. Jiang et. al. Two-hertz-linewidth Nd:YAG lasers at 1064 nm stabilized to vertically mounted ultra-stable cavities [J]. Chin. Phys. B,2008,17: 2152-2155.
[81]Y. Y. Jiang et. al. Nd:YAG lasers at 1064 nm with 1-Hz linewidth [J]. Appl. Phys. B,2010,98:61-67.
[82]L. S. Chen et. al. Vibration-induced elastic deformation of Fabry-Perot cavities [J]. Phys. Rev. A,2006,74:053801.
[83]H. Stoehr et. al. Diode laser with 1 Hz linewidth [J]. Opt. Lett.,2006,31: 736-738.
[84]T. Nazarova et. al. Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser [J]. Appl. Phys. B,2006,83:531-536.
[85]S. A. Webster et. al. Vibration insensitive optical cavity [J]. Phys. Rev. A, 2007,75:011801R.
[86]J. Millo, et. al. Ultrastable lasers based on vibration insensitive cavities [J]. Phys. Rev. A,2009,79:053829.
[87]A. Abramovici, et. al. LIGO:the laser interferometer gravitational-wave observatory [J]. Science,1992,256:325-333.
[88]P. R. Saulson. Fundamentals of interferometric gravitational wave detectors [M]. World Scientific,1994.
[89]E. D. Black. Notes on thermal noise, with a bibliography [R]. LIGO Technical Note:LIGO-T03142-01-R,2004.
[90]K. Numata, A. Kemery, J. Camp. Thermal-noise limit in the frequency stabilization of lasers with rigid cavities [J]. Phys. Rev. Lett.,2004,93: 250602.
[91]S. A. Webster, et. al. Thermal-noise-limited optical cavity [J]. Phys. Rev. A, 2008,77; 033847.
[92]M. Notcutt, et. al. Contribution of thermal noise to frequency stability of rigid optical cavity via Hertz-linewidth lasers [J]. Phys. Rev. A,2006,73: 031804.
[93]E. D. Black. An introduction to Pound-Drever-Hall laser frequency stabilization [J]. Am. J. Phys.,2001,69:79-87.
[94]网页[EB/OL]. http://search.newport.com/?q=*&x2=sku&q2=1801-FS-M.
[95]E. A. Whittaker, M. Gehrtz, G. C. Bjorklund. Residual amplitude modulation in laser electro-optic phase modulation [J]. J. Opt. Soc. Am. B,1985,2: 1320-1326.
[96]E. A. Whittaker, et. al. Reduction of residual amplitude modulation in frequency-modulation spectroscopy by using harmonic frequency modulation [J]. J. Opt. Soc. Am. B,1988,5:1253-1256.
[97]N. C. Wong, J. L. Hall. Servo control of amplitude modulation in frequency-modulation spectroscopy:demonstration of shot-noise-limited detection [J]. J. Opt. Soc. Am. B,1985,2:1527-1533.
[98]Y. H. Chen, et. al. Suppression of residual amplitude modulation in electro-optical phase modulators using Fabry-Perot cavity [J]. Acta Optica Sinica,2007,27:1-6.
[99]M. Notcutt, et. al. Temperature compensation for cryogenic cavity stabilized lasers [J]. J. Phys. D:Appl. Phys.,1995,28:1807-1810.
[100]R. W. Fox. Temperature analysis of low-expansion Fabry-Perot cavities [J]. Opt. Exp.,2009,17:15023-15031.
[101]T. Legero, T. Kessler, U. Sterr. Tuning the thermal expansion properties of optical reference cavities with fused silica mirrors [J]. J. Opt. Soc. Am. B, 2010,27:914-919.
[102]Y. Jiang, et. al. Making optical atomic clocks more stable with 10-16-level laser stabilization [J]. Nature Photonics,2011,5:158-161.
[103]F. J. Raab, S. E. Whitcomb. Technical Report:LIGO-T920004-00-R [R], 1992.
[104]J. Hough et al. The Detection of Gravitational Waves [M]. Cambridge University Press,1991.
[105]J. Miao, et. al. Vibration insensitive optical ring cavity [J]. Chin. Phys. B, 2009,18:2334-2339.
[106]J. L. Hall, J. Ye, L. S. Ma. Measurement of mirror birefringence at the sub-ppm level:Proposed application to a test of QED [J]. Phys. Rev. A,2000, 62:013815.
[107]P. Barriga, et. al. Self-compensation of astigmatism in mode-cleaners for advanced interferometers [J].J. Phys.,2006,32:457-463.
[108]T. Skettrup. Rectangular laser resonators with astigmatic compensation [J]. J. Opt. A:Pure Appl. Opt.,2005,7:645-654.
[109]Y. Levin. Fluctuation-dissipation theorem for the thermo-refractive noise [J]. Phys. Lett. A,2008,372:1941-1944.
[110]V. B. Braginsky, M. L. Gorodetsky, S. P. Vyatchanin. Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae [J]. Phys. Lett.A,1999,264:1-10.
[111]M. Cerdonio, et. al. Thermoelastic effects at low temperatures and quantum limits in displacement measurements [J]. Phys. Rev. D,2001,63:082003.
[112]M. De Rosa, et. al. Experimental measurement of the dynamic photothermal effect in Fabry-Perot cavities for gravitational wave detectors [J]. Phys. Rev. Lett.,2002,89:237402.
[113]P. R. Saulson. Thermal noise in mechanical experiments [J]. Phys. Rev. D, 1990,42:2437-2445.
[114]V. B. Braginsky, S. P. Vyatchanin. Thermodynamical fluctuations in optical mirror coatings [J]. Phys. Lett. A,2003,312:244-255.
[115]J. P. Richard, J. J. Hamilton. Cryogenic monocrystalline silicon Fabry-Perot cavity for the stabilization of laser frequency [J]. Rev. Sci. Instrum.,1991,62: 2375-2378.
[116]T. Kessler, et. al. A sub-40 mHz linewidth laser based on a silicon single-crystal optical cavity [J]. arXiv:1112.3854vl,2012.
[117]G. M. Harry, et. al. Titania-doped tantala/silica coatings for gravitational-wave detection [J]. Class. Quantum Grav.,2007,24:405-415.
[118]Characterization of frequency and phase noise [R]. Report 580 of the International Radio Consultative Committee,1986,142-150.
[119]H. G. Lu, et. al. Measurement of reflectivity of optical mirrors using laser phase modulation and finesse of Fabry-Perot cavity [J]. Chin. J. Lasers, 2006,33:1675-1679.
[120]J. Ye. Ultrasensitive high resolution laser spectroscopy and its application to optical frequency standards [D].US:JILA,1997.
[121]J. Ye, J. L. Hall. Cavity ringdown heterodyne spectroscopy:High sensitivity with microwatt light power [J]. Phys. Rev. A,2000,61:061802.
[122]J. J. Scherer, et. al. Cavity ringdown laser absorption spectroscopy:history development and application to pulsed molecular beams [J]. Chem. Rev., 1997,97:25.
[123]M. J. Lawrence, et. al. Dynamic response of a Fabry-Perot interferometer [J]. J. Opt. Soc. Am. B,1999,16:523-532.
[124]H. Q. Chen, et. al. Optical-heterodyne cavity-ring-down spectroscopy with 1-Hz-linewidth laser [J].. in preparation.
[125]C. J. Hood, et. al. Characterization of high-finesse mirrors:Loss, phase shifts, and mode structure in an optical cavity [J]. Phys. Rev. A,2001,64:033804.
[126]M. Zhu, J. L. Hall. Stabilization of optical phase/frequency of a laser system: application to a commercial dye laser with an external stabilizer [J]. J. Opt. Soc. Am. B,1993,10:802-816.
[127]J. L. Hall, M. Zhu. An Introduction to Phase-Stable Optical Sources [C]. International School of Physics Enrico Fermi, Course CXVIII, Laser Manipulation of Atoms and Ions, edited by E. Arimondo, W. Phillips, and S. F. (North Holland, ADDRESS),1992,671-702.
[128]D. W. Allan. Time And Frequency (Time-Domain) Characterization, Estimation, And Prediction Of Precision Clocks And Oscillators [J]. IEEE Trans. Ultrasonic Ferro.& Freq. Ctrl.,1987,34:647-654.
[129]W. J. Riley. Handbook of frequency stability analysis [R]. U.S.:NIST Special Publication,1065,2008.
[130]R. Santra, K. V. Christ, C. H. Greene. Properties of metastable alkaline-earth-metal atoms calculated using an accurate effective core potential [J]. Phys. Rev. A,2004,69:042510.
[131]Z. W. Barber, et. al. Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice [J]. Phys. Rev. Lett.,2006, 96:083002.
[132]R. Santra, et. al. High-accuracy optical clock via three-level coherence in neutral bosonic 88Sr [J]. Phys. Rev. Lett.,2005,94:173002.
[133]E. L. Raab, et. al. Trapping of neutral sodium atoms with radiation Pressure [J]. Phys. Rev. Lett.,1987,59:2631.
[134]H. J. Metcalf, P.V. D. Straten. Laser cooling and trapping [M]. Springer, 1999.
[135]Z. Barber. Ytterbium optical lattice clock [D]. U.S.:JILA,2007.
[136]R. H. Dicke. The effect of collisions upon the Doppler width of spectral Lines [J]. Phys. Rev.,1953,89:472.
[137]J. C. Bergquist, et. al. Observation of quantum jumps in a single atom [J]. Phys. Rev. Lett.,1986,57:1699.
[138]A. D. Ludlow, et. al. Cold collision shift cancelation and inelastic scattering in a Yb optical lattice clock [J]. Phys. Rev. A,2011,84:052724.
[139]N. D. Lemke, et. al. p-wave cold collisions in an optical lattice clock [J]. Phys. Rev. Lett.,2011,107:103902.
[140]W. M. Itano el. al. Quantum projection noise:Population fluctuations in two-level systems [J]. Phys. Rev. A,1993,47:3554-3570.
[141]C. W. Oates et. al. Stable laser system for probing the clock transition at 578 nm in neutral ytterbium [C]. Proc.2007 IEEE Int. Freq. Cont. Symp.,2007, 1274-1277.
[142]K. Yamamoto, et. al. Measurement of the mechanical loss of a cooled reflective coating for gravitational wave detection [J]. Phys. Rev. D,2006, 74:022002.
[143]G. M. Harry, et. al. Thermal noise from optical coatings in gravitational wave detectors [J]. Appl. Opt.,2006,45:1569-1574.
[144]Ch. Comtet, et. al. Reduction of tantala mechanical losses in coatings for the next generation of VIRGO and LIGO interferometric gravitational waves detectors [EB/OL]. http://hal.in2p3.fr/in2p3-00177578/en/,2007.
[145]J. Agresti, et. al. Optimized multilayer dielectric mirror coatings for gravitational wave interferometers [R]. LIGO Tech. No. LIGO-P060027-00-Z,2006.
[146]S. Gossler, et. al. Coating-free mirrors for high precision interferometric experiments [J]. Phys. Rev. A,2007,76:053810.
[147]P. S. Johnston, K. K. Lehmann. Cavity enhanced absorption spectroscopy using a broadband prism cavity and a supercontinuum source [J]. Opt. Exp., 2008,16:15013-15023.
[148]H. J. Kimble, et. al. Optical interferometers with reduced sensitivity to thermal noise [J]. Phys. Rev. Lett.,2008,101:260602.
[149]C. H. Metzger, K. Karrai. Cavity cooling of a microlever [J]. Nature,2004, 432:1002-1005.
[150]S. Gigan, et. al. Self-cooling of micromirror by radiation pressure [J]. Nature, 2006,444:67-70.
[151]O. Arcizet, et. al. Radiation-pressure cooling and optomechanical instability of a micromirror [J]. Nature,2006,444:71-74.
[152]D. Kleckner, D. Bouwmeester. Sub-Kelvin optical cooling of a micromechanical resonator [J]. Nature,2006,444:75-78.
[153]J. L. Hall et. al. Measurement of mirror birefringence at the sub-ppm level: Proposed application to a test of QED [J]. Phys. Rev. A,2000,62:013815.
[154]D. Herriott, et. al. Off-axis paths in spherical mirror interferometers [J]. Appl. Opt,1964,3:523-526.
[155]D. Budker, et. al. Obtaining frequency markers of variable separation with a spherical mirror Fabry-Perot interferometer [J]. Rev. Sci. Instr.,2000,71: 2984-2987.
[156]P. B. Sellin, et. al. Programmable frequency reference for subkilohertz laser stabilization by use of persistent spectral hole burning [J]. Opt. Lett.,1999, 24:1038-1040.
[157]N. M. Trickland, et. al. Laser frequency stabilization using regenerative spectral hole burning [J]. Phys. Rev. B,2000,62:1473-1476.
[158]B. Julsgaard, et. al. Understanding laser stabilization using spectral hole burning [J]. Opt. Exp.,2007,15:11444-11465.
[159]M. J. Thorpe, et. al. Frequency-stabilization to 6×10-16 via spectral-hole burning [J]. Nature Photonics,2011,5:688-693.
[160]Q. F. Chen, et. al. Spectrally narrow, long-term stable optical frequency reference based on a Eu3+:Y2SiO5 crystal at cryogenic temperature [J]. Phys. Rev. Lett,2011,107:223202.
[161]M. J. Martin, et. al. Extreme non-linear response of ultra-narrow optical transitions in cavity QED for laser stabilization [J]. arXiv:1105.2373vl, 2011.
[162]F. Kefelian, et. al. Ultralow-frequency-noise stabilization of a laser by locking to an optical fiber-delay line [J]. Opt. Lett.,2009,34:914-916.
[163]M. Kasevich, et. al. poster presentation [C]. International Conference on Laser Spectroscopy,2007.
[164]J. Lodewyck, et. al. Nondestructive measurement of the transition probability in a Sr optical lattice clock [J]. Phys. Rev. A,2009,79:061401.
[165]M. Takamoto, T. Takano, H. Katori. Frequency comparison of optical lattice clocks beyond the Dick limit [J]. Nature Photonics,2011,5:288-292.