-
介绍了喷泉频标的原理与发展.喷泉频标是一项近20年来发展起来的原子钟技术，它以激光冷却技术为基础，利用该技术实现了冷原子介质的俘获与上抛.冷原子介质在上抛下落过程中首先完成原子态制备，然后两次通过微波谐振腔实现Ramsey作用，在两次作用之间原子经历自由演化，最后原子经过探测区，通过双能级荧光探测法探测原子跃迁概率得到鉴频的Ramsey干涉条纹，并实现频率锁定，其中心条纹的线宽在1 Hz左右.频率稳定度和频率不确定度是喷泉频标的两个重要指标.影响喷泉钟频率稳定度的因素主要有量子投影噪声和电子学噪声，目前喷泉钟的短期稳定度为 (10-13–10-14)τ-1/2，长期稳定度在 10-16–10-17量级.喷泉频标的频率不确定度主要受二阶塞曼频移、黑体辐射频移、冷原子碰撞频移以及与微波相关的频移等的影响.目前喷泉钟的不确定度在小的10-16量级.作为基准频标，喷泉钟的工作介质主要是133Cs，87Rb.国际各大计量机构都研制了喷泉频标，它在各地协调世界时的建立、国际原子时的校准等方面发挥着越来越重要的作用.此外，喷泉频标还用于研究高精度时频基准和时间比对链路、验证基本物理理论等.The principle and development of fountain frequency standard are introduced in this paper. Fountain frequency standard is an atomic clock technology developed in recent 20 years. It is based on laser cooling technology, and realizes the trapping and projection of the cold atom medium with laser cooling technology. In the process of launching upward and falling back, the cold atom medium first completes the preparation of atomic state, then passes through the microwave cavity twice to achieve the Ramsey interaction; between the two interactions it undergoes free evolution, and finally the Ramsey interference fringes are obtained by detecting the atomic interference probability with the two-level fluorescence detection method in the detection region, and the frequency is locked with a line width of the central fringe being about 1 Hz. The stability and uncertainty of the frequency are two important indexes of the fountain frequency standard. The factors influencing the stability of the fountain clock frequency mainly are quantum projection noise and electronic noise. At present, the short term stability of the fountain clock is (10-13-10-14)τ-1/2, and the long term stability is (10-16-10-17). The frequency uncertainty of the fountain frequency standard is mainly influenced by the two-order Zeeman frequency shift, the blackbody radiation frequency shift, the cold atom collisional frequency shift, and the frequency shift relating to the microwave. The uncertainty of the fountain clock is around 10-16 currently. As a reference frequency standard, the working media of the fountain clock mainly are 133Cs and 87Rb. All international metrology institutions have been developing the fountain frequency standard, and it plays a more and more important role in establishing the coordinated universal time and the calibration of the international atomic time. In addition, the fountain frequency standards are also used to study high-precision time-frequency reference and time comparison chain, and verify basic physical theories.
-
Keywords:
- fountain frequency standard /
- Ramsey effect /
- stability /
- uncertainty
[1] Bureau International des Poids et Mesures https://www.bipm.org/metrology/time-frequency/units.html [2014]
[2] Lemonde P, Laurent P, Santarelli G, Abgrall M, Sortais Y, Bize S, Nicolas C, Zhang S, Clairon A, Dimarcq N, Petit P, Mann A G, Luiten A N, Chang S, Salomon C 2001 (Luiten A N ed) Frequency Measurement and Control: Advanced Techniques and Future Trends (Berlin, Heidelberg: Springer Berlin Heidelberg) pp131-153
[3] Metcalf J H, van der Straten P 1999 Laser Cooling and Trapping (Berlin, Heidelberg: Springer Berlin Heidelberg) pp71-175
[4] Chu S 1998 Rev. Mod. Phys. 70 685
[5] Cohen-Tannoudji C 1998 Rev. Mod. Phys. 70 707
[6] Phillips D W 1998 Rev. Mod. Phys. 70 721
[7] Kasevich A M, Riis E, Chu S, Devoe G R 1989 Phys. Rev. Lett. 63 612
[8] Gibble K, Chu S 1993 Phys. Rev. Lett. 70 1771
[9] Clairon A, Salomon C, Guellati S, Phillips D W 1991 Europhys. Lett. 16 165
[10] Lett D P, Watts N R, Westbrook I C, Phillips D W, Gould L P, Metcalf J H 1988 Phys. Rev. Lett. 61 169
[11] Dalibard J, Cohen-Tannoudji C 1989 J. Opt. Soc. Am. B 6 2023
[12] Clarion A, Laurent P, Stantarelli G, Ghezali S, Lea S, Bahoura M 1995 IEEE Trans. Instrum. Meas. 44 128
[13] Clarion A, Stantarelli G, Laurent P, Ghezali S, Lea S, Bahoura M, Simon E, Weyers S, Szymaniec K 1996 Proceedings of Fifth Symposium on Frequency Standards and Metrology Woods Hole, USA, October 15-19, 1995 p49
[14] Bize S 2001 Ph. D. Dissertation (Paris: Bureau National de Métrologie)
[15] Vian C, Rosenbusch P, Marion H, Bize S, Cacciapuoti L, Zhang S, Abgrall M 2005 IEEE Trans. Instrum. Meas. 54 833
[16] Jefferts S R, Shirley J, Parker T E, Heavner T P, Meekhof D M, Nelson C, Levi F, Costanzo G, de Marchi A, Drullinger R, Hollberg L, Lee W D, Walls F L 2002 Metrologia 39 321
[17] Heavner T P, Jefferts S R, Donley E A, Shirley J H, Parker T E 2005 Metrologia 42 411
[18] Ekstrom C, Peil S, Swanson T, Crane S 2009 Frequency Standards and Metrology: Proceedings of the 7th Symposium Pacific Grove, USA, October 5-11, 2008 p308
[19] Peil S, Crane S, Hanssen J, Swanson T B 2011 Proceedings of Frequency Control and the European Frequency and Time Forum San Francisco, USA, May 2-5, 2011 6567 p1
[20] Weyers S, Huebner U, Schroeder R, Tamm C, Bauch A 2001 Metrologia 38 343
[21] Gerginov V, Nemitz N, Weyers S, Schröder R, Griebsch D, Wynands R 2010 Metrologia 47 65
[22] Szymaniec K, Chalupczak W, Whibberley P B, Lea S N, Henderson D 2005 Metrologia 42 49
[23] Szymaniec K, Park S E, Marra G, Chałupczak W 2010 Metrologia 47 363
[24] Ovchinnikov Y, Marra G 2011 Metrologia 48 87
[25] Levi F, Calonico D, Lorini L, Godone A 2006 Metrologia 43 545
[26] Kumagai M, Ito H, Kajita M, Hosokawa M 2008 Metrologia 45 139
[27] Li T C 2006 Acta Metrol. Sin. 27 1 (in Chinese) [李天初 2006 计量学报 27 1]
[28] Fang F, Li M S, Lin P W, Chen W L, Liu N F, Lin Y G, Wang P, Liu K, Suo R, Li T C 2015 Metrologia 52 454
[29] Bureau International des Poids et Mesures, ftp://ftp2.bipm.org/pub/tai//Circular-T/cirthtm/cirt.358.html [2017-11-14]
[30] Audoin C, Santarelli G, Makdissi A, Clairon C 1998 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45 877
[31] Santarelli G, Audoin C, Makdissi A, Laurent P, Dick G J, Clairon A 1998 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45 887
[32] Santarelli G, Laurent P, Lemonde P, Clairon A, Mann A G, Chang S, Luiten A N, Salomon C 1999 Phys. Rev. Lett. 82 4619
[33] Zhou Z, Wei R, Shi C, L D, Li T, Wang Y 2009 Chin. Phys. Lett. 26 123
[34] Legere R, Gibble K 1998 Phys. Rev. Lett. 81 5780
[35] Dudle G, Joyet A, Berthoud P, Mileti G, Thomann P 2001 IEEE Trans. Instrum. Meas. 50 510
[36] Jefferts S R, Heavner T P, Donley E A, Shirley J H, Parker T E 2004 Proceedings of the 2003 IEEE International Frequency Control Symposium and PDA Exhibition jointly with the 17th European Frequency and Time Forum Tampa, USA, May 4-8, 2003 p1084
[37] Rovera G D, Abgrall M, Laurent P 2011 Proceedings of 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum San Francisco, USA, May 2-5, 2011 p45
[38] Petit G, Panfilo G 2013 IEEE Trans. Instrum. Meas. 62 1550
[39] Guéna J, Weyers S, Abgrall M, Grebing C, Gerginov V 2017 Metrologia 54 348
[40] Blinov I Y, Boiko A I, Domnin Y S, Kostromin V P, Kupalova O V 2017 Meas. Tech. 60 30
[41] Lorini L, Pavlenkoz K, Bize S, Desruelley B, Sterny G, Doroninz I, Pavlenkoz Y, Donchenko S 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon, France, July 9-13, 2017 p317
[42] Lee S, Heo M S, Kwon T Y, Hong H G, Lee S B, Park S E 2017 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon, France, July 9-13, 2017 p622
[43] Acharya A, Bharath V, Arora P, Yadav S, Agarwal A 2017 Mapan 32 67
[44] Ortiz C A, López J M, de Carlos López E 2017 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon, France, July 9-13, 2017 p326
[45] Dunst P, Nagórny B, Lemański D, Nogaś P, Nawrocki J, Hendricks R J, Ozimek F, Szymaniec K 2017 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon France, July 9-13, 2017 p628
[46] Beattie S, Jian B, Alcock A J, Bernard J, Gertsvolf M, Hendricks R, Ozimek F, Szymaniec K, Gibble K 2017 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon, France, July 9-13, 2017 p640
[47] Bureau International des Poids et Mesures, https:// www.bipm.org/utils/en/pdf/time_ann_rep/Time_annual_report_2014.pdf[2014]
[48] Shi C Y, Wei R, Zhou Z C, Li T, Li L,Wang Y Z 2011 Proceedings of 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum San Francisco, USA, May 2-5, 2011 p1
[49] Du Y B, Wei R, Dong R C, Zou F, Wang Y Z 2015 Chin. Phys. B 24 070601
[50] Liu L, L D S, Chen W B, Li T, Qu Q Z, Wang B, Li L, Ren W, Dong Z R, Zhao J B, Xia W B, Zhao X, Ji J W, Ye M F, Sun Y G, Yao Y Y, Song D, Liang Z G, Hu S J, Yu D H, Hou X, Shi W, Zang H G, Xiang J F, Peng X K, Wang Y Z 2017 axiv:1709.03256 [Atomic Physics]
[51] Ruan J, Wang Y B, Chang H, Jiang H F, Liu T, Dong R F, Zhang S G 2015 Acta Phys. Sin. 64 160308 (in Chinese) [阮军, 王叶兵, 常宏, 姜海峰, 刘涛, 董瑞芳, 张首刚 2015 物理学报 64 160308]
[52] Lin R, Wang X L, Liu D D, Guan Y, Zhang H, Chen J, Yu F X, Shi J R, Ruan J, Zhang S G \href https://doi.org/10.13875/j.issn.1674-0637.2016-03-0138-12 2017 Journal of Time and Frequency 41 p138 (in Chinese) [阮军, 王心亮, 刘丹丹, 管勇, 张辉, 陈江, 林睿, 余凤翔, 施俊如, 张首刚 2016 时间频率学报 41 p138]
[53] Wynands R, Weyers S 2005 Metrologia 42 64
[54] Wang Y Q 2012 Atomic Clock and Time Frequency System (Beijing: National Defense industry Press) pp77-96 (in Chinese) [王义遒 2012 原子钟与时间频率系统 (北京: 国防工业出版社) 第77-96页]
[55] Riehle F 2004 Frequency Standards Basics and Applications (Germany: Wiley-VCH) pp217-225
[56] Metcalf J H 1989 J. Opt. Soc. Am. B 6 2206
[57] Wang Y Q 2007 Laser Cooling and Trapping of Atoms (Beijing: Peking University Press) pp291-308 (in Chinese) [王义遒 2007 原子的激光冷却与陷俘 (北京: 北京大学出版社) 第291-308 页]
[58] Metcalf J H, van der Straten P 1999 Laser Cooling and Trapping (Berlin, Heidelberg: Springer Berlin Heidelberg) pp156-164
[59] Donley E A, Heavner T P, Jefferts S R 2005 IEEE Trans. Instrum. Meas. 54 1905
[60] Dobrev G, Gerginov V, Weyers S 2016 Phys. Rev. A 93 043423
[61] Szymaniec K, Park S E 2011 IEEE Trans. Instrum. Meas. 60 2475
[62] Szymaniec K, Noh H R, Park S E, Takamizawa A 2013 Appl. Phys. B 111 527
[63] Takamizawa A, Yanagimachi S, Tanabe T, Hagimoto K, Hirano I 2015 IEEE Trans. Instrum. Meas. 64 2504
[64] Riehle F 2004 Frequency Standards Basics and Applications (Germany: Wiley-VCH) p76
[65] Vanier J, Tomescu C 2016 The Quantum Physics of Atomic Frequency Standards, Recsent Development (Boca Raton: CRC Press) p34
[66] Biedermann G W, Takase K, Wu X, Deslauriers L, Roy S, Kasevich M A 2013 Phys. Rev. Lett. 111 170802
[67] Schioppo M, Brown R C, McGrew W F, Hinkley N, Fasano R J, Beloy K, Yoon T H, Milani G, Nicolodi D, Sherman J A \href https://doi.org/10.1038/nphoton.2016.231 2016 Nat. Photon. 11 48
[68] Meunier M, Dutta I, Geiger R, Guerlin C, Garrido Alzar C L, Landragin A 2014 Phys. Rev. A 90 063633
[69] Heavner T P, Jefferts S R, Donley E A, Parker T E, Levi F 2005 Proceedings of the 36th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting Washington D.C., USA, December 7-9, 2004 p308
[70] Rovera G D, Santarelli G, Clairon A 1996 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43 354
[71] Gupta A S, Popovic D, Walls F L 2000 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47 475
[72] Lipphardt B, Gerginov V, Weyers S 2017 IEEE Trans. on IEEE Trans. Ultrason. Ferroelectr. Freq. Control 64 761
[73] Haboucha A, Zhang W, Li T, Lours M, Luiten A N, Le Coq Y, Santarelli G 2011 Opt. Lett. 36 3654
[74] Dai S, Fang F, Cao S, Liu N, Suo R, Li T 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon, France, July 9-13, 2017 p302
[75] Guena J, Abgrall M, Clairon A, Bize S 2014 Metrologia 51 108
[76] Peil S, Swanson T B, Hanssen J, Taylor J S 2014 Metrologia 51 263
[77] Zhou Z C, Wei R, Shi C Y, Wang Y Z 2011 Chin. Phys. B 20 034206
[78] Lee T, Das T P, Sternheimer R M 1975 Phys. Rev. A 11 1784
[79] Itano W M, Lewis L L, Wineland D J 1982 Phys. Rev. A 25 1233
[80] Simon E, Laurent P, Clairon A 1998 Phys. Rev. A 57 436
[81] Levi F, Calosso C, Calonico D, Lorini L, Bertacco E K, Godone A, Costanzo G A, Mongino B, Jefferts S R, Heavner T P 2010 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57 600
[82] Sortais Y, Bize S, Nicolas C, Clairon A, Salomon C, Williams C 2000 Phys. Rev. Lett. 85 3117
[83] Ghezali S, Laurent P H, Lea S N, Clairon A 1996 Europhys. Lett. 36 25
[84] Sortais Y 2001 Ph. D. Dissertation (Paris: Bureau national de métrologie)
[85] Zhang S 2004 Ph. D. Dissertation (Paris: Université de Paris VI)
[86] Li R, Gibble K 2004 Metrologia 41 376
[87] Li R, Gibble K 2010 Metrologia 47 534
[88] Guéna J, Li R, Gibble K, Bize S, Clairon A 2011 Phys. Rev. Lett. 106 130801
[89] Li R, Gibble K, Szymaniec K 2011 Metrologia 48 283
[90] Weyers S, Gerginov V, Nemitz N, Li R, Gibble K 2012 Metrologia 49 82
[91] Gibble K, Lea S N, Szymaniec K 2012 Conference on Precision Electromagnetic Measurements Washington D.C., USA, July 1-6, 2012 p700
[92] Vanier J, Audoin C 1989 The Quantum Physics of Atomic Frequency Standards (Bristol: Hilger)
[93] Rabi I I, Ramsey N F, Schwinger J 1954 Rev. Mod. Phys. 26 167
[94] Bize S, Sortais Y, Mandache C, Clairon A, Salomon C 2001 IEEE Trans. Instrum. Meas. 50 503
[95] Bauch A, Schröder R 1993 Ann. Phys. 2 421
[96] Cutler L S, Flory C A, Giffardand R P, de Marchi A 1991 J. Appl. Phys. 69 2780
[97] Santarelli G, Governatori G, Chambon D, Lours M, Rosenbusch P, Guena J, Chapelet F, Bize S, Tobar M E, Laurent P, Potier T, Clairon A 2009 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56 1319
[98] Fang F, Liu K, Chen W, Liu N, Suo R, Li T 2014 Chin. Phys. Lett. 31 100601
[99] Audoin C, Jardino M, Cutler L S, Lacey R F 1978 IEEE Trans. Instrum. Meas. 27 325
[100] Levi F, Shirley J H, Heavner T P, Yu D H, Jefferts S R 2006 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53 1584
[101] Gibble K 2006 Phys. Rev. Lett. 97 073002
[102] Guéna J, Abgrall M, Rovera D, Laurent P, Chupin B, Lours M, Santarelli G, Rosenbusch P, Tobar M E, Li R X 2012 IEEE Trans. Ultrason Ferroelectr Freq. Control 59 391
[103] Angel J R P, Sandars P H G 1968 I. Theory, Proc. R. Soc. Lond. A 305 125
[104] Sakurai J J 1994 Modern Quantum Mechanics (New Jersey: Addison-Wesley) p500
[105] Szymaniec K, Lea S N, Gibble K, Park S E, Liu K, Głowacki P 2016 8th Symposium on Frequency Standards and Metrology 2015 Potsdam, Germany, October 12-16, 2016 p723
[106] Levi F, Calonico D, Calosso C E, Godone A, Micalizio S, Costanzo G A 2014 Metrologia 51 270
[107] Heavner T P, Donley E A, Levi F, Costanzo G, Parker T E, Shirley J H, Ashby N, Barlow S, Jefferts S R 2014 Metrologia 51 174
[108] Wei R 2003 Ph. D. Dissertation (Shanghai: Shanghai Institute of Optics and Fine Mechanics, the Chinese Academy of Sciences) (in Chinese) [魏荣 2003 博士学位论文 (上海: 中国科学院上海光学与精密机械研究所)]
[109] Shi C Y 2012 Ph. D. Dissertation (Shanghai: Shanghai Institute of Optics and Fine Mechanics, the Chinese Academy of Sciences) (in Chinese) [史春艳 2012 博士学位论文 (上海: 中国科学院上海光学与精密机械研究所)]
[110] Fertig C, Gibble K 2000 Phys. Rev. Lett. 85 1622
[111] Hart R A, Xu X, Legere R, Gibble K 2007 Nature 446 892
[112] Guéna J, Rosenbusch P, Laurent P, Abgrall M, Rovera D, Santarelli G, Tobar M, Bize S, Clairon A 2010 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57 647
[113] Bize S, Sortais Y, Santos M, Mandache C, Clairon A, Salomon C 1999 Europhys. Lett. 45 558
[114] Guéna J, Abgrall M, Rovera D, Rosenbusch P, Tobar M E, Laurent P, Clairon A, Bize S 2012 Phys. Rev. Lett. 109 080801
[115] Rovera D, Bize S, Chupin B, Guéna J, Laurent P, Rosenbusch P, Uhrich P 2016 Metrologia 53 81
[116] Berengut J C, Flambaum V V, Kava E M 2011 Phys. Rev. A 84 042510
[117] Lämmerzahl C, Ciufolini I, Dittus H, Iorio L, Mller H, Peters A, Samain E, Scheithauer S, Schiller S 2004 Gen. Relativ. Gravitation 36 615
[118] Lemonde P 1997 Ph. D. Dissertation (Paris: Bureau national de métrologie)
[119] Laurent P, Lemonde P, Simon E, Santarelli G, Clairon A, Dimarcq N, Petit P, Audoin C, Salomon C 1998 Eur. Phys. J. D 3 201
[120] Niering M, Holzwarth R, Reichert J, Pokasov P, Udem T, Weitz M, Hänsch T W, Lemonde P, Santarelli G, Abgrall M, Laurent P, Salomon C, Clairon A 2000 Phys. Rev. Lett. 84 5496
[121] Laurent P, Abgrall M, Jentsch C, Lemonde P, Santarelli G, Clairon A, Maksimovic I, Bize S, Salomon C, Blonde D 2006 Appl. Phys. B 84 683
[122] Laurent P, Massonnet D, Cacciapuoti L, Salomon C 2015 C. R. Phys. 16 540
[123] Wang X Q, Wang Y Z 1999 Chin. Phys. Lett. 17 478
[124] Bian F G, Wei R, Jiang H F, Wang Y Z 2005 Chin. Phys. Lett. 22 1645
[125] Li T, Gao Y C， Zhang F X, Liu L, Wang Y Z 2011 CN Patent 101807043 B (in Chinese) [李唐, 高源慈，张富鑫, 刘亮, 王育竹 2011 中国专利: CN 101807043 B]
[126] Devenoges L, Bernier L G, Morel J, Di Domenico G, Jallageas A, Petersen M, Thomann P 2013 2013 Joint European Frequency and Time Forum & International Frequency Control Symposium Prague, Czech Republic, July 21-25, 2013 p235
[127] Devenoges L, Stefanov A, Joyet A, Thomann P, Domenico G D 2012 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59 211
[128] Bauch A, Weyers S, Piester D, Staliuniene E, Yang W 2012 Metrologia 49 180
[129] Consultative Committee for Time and Frequency, https://www.bipm.org/utils/common/pdf/CC/CCTF/CCTF19.pdf [2012-09-14]
-
[1] Bureau International des Poids et Mesures https://www.bipm.org/metrology/time-frequency/units.html [2014]
[2] Lemonde P, Laurent P, Santarelli G, Abgrall M, Sortais Y, Bize S, Nicolas C, Zhang S, Clairon A, Dimarcq N, Petit P, Mann A G, Luiten A N, Chang S, Salomon C 2001 (Luiten A N ed) Frequency Measurement and Control: Advanced Techniques and Future Trends (Berlin, Heidelberg: Springer Berlin Heidelberg) pp131-153
[3] Metcalf J H, van der Straten P 1999 Laser Cooling and Trapping (Berlin, Heidelberg: Springer Berlin Heidelberg) pp71-175
[4] Chu S 1998 Rev. Mod. Phys. 70 685
[5] Cohen-Tannoudji C 1998 Rev. Mod. Phys. 70 707
[6] Phillips D W 1998 Rev. Mod. Phys. 70 721
[7] Kasevich A M, Riis E, Chu S, Devoe G R 1989 Phys. Rev. Lett. 63 612
[8] Gibble K, Chu S 1993 Phys. Rev. Lett. 70 1771
[9] Clairon A, Salomon C, Guellati S, Phillips D W 1991 Europhys. Lett. 16 165
[10] Lett D P, Watts N R, Westbrook I C, Phillips D W, Gould L P, Metcalf J H 1988 Phys. Rev. Lett. 61 169
[11] Dalibard J, Cohen-Tannoudji C 1989 J. Opt. Soc. Am. B 6 2023
[12] Clarion A, Laurent P, Stantarelli G, Ghezali S, Lea S, Bahoura M 1995 IEEE Trans. Instrum. Meas. 44 128
[13] Clarion A, Stantarelli G, Laurent P, Ghezali S, Lea S, Bahoura M, Simon E, Weyers S, Szymaniec K 1996 Proceedings of Fifth Symposium on Frequency Standards and Metrology Woods Hole, USA, October 15-19, 1995 p49
[14] Bize S 2001 Ph. D. Dissertation (Paris: Bureau National de Métrologie)
[15] Vian C, Rosenbusch P, Marion H, Bize S, Cacciapuoti L, Zhang S, Abgrall M 2005 IEEE Trans. Instrum. Meas. 54 833
[16] Jefferts S R, Shirley J, Parker T E, Heavner T P, Meekhof D M, Nelson C, Levi F, Costanzo G, de Marchi A, Drullinger R, Hollberg L, Lee W D, Walls F L 2002 Metrologia 39 321
[17] Heavner T P, Jefferts S R, Donley E A, Shirley J H, Parker T E 2005 Metrologia 42 411
[18] Ekstrom C, Peil S, Swanson T, Crane S 2009 Frequency Standards and Metrology: Proceedings of the 7th Symposium Pacific Grove, USA, October 5-11, 2008 p308
[19] Peil S, Crane S, Hanssen J, Swanson T B 2011 Proceedings of Frequency Control and the European Frequency and Time Forum San Francisco, USA, May 2-5, 2011 6567 p1
[20] Weyers S, Huebner U, Schroeder R, Tamm C, Bauch A 2001 Metrologia 38 343
[21] Gerginov V, Nemitz N, Weyers S, Schröder R, Griebsch D, Wynands R 2010 Metrologia 47 65
[22] Szymaniec K, Chalupczak W, Whibberley P B, Lea S N, Henderson D 2005 Metrologia 42 49
[23] Szymaniec K, Park S E, Marra G, Chałupczak W 2010 Metrologia 47 363
[24] Ovchinnikov Y, Marra G 2011 Metrologia 48 87
[25] Levi F, Calonico D, Lorini L, Godone A 2006 Metrologia 43 545
[26] Kumagai M, Ito H, Kajita M, Hosokawa M 2008 Metrologia 45 139
[27] Li T C 2006 Acta Metrol. Sin. 27 1 (in Chinese) [李天初 2006 计量学报 27 1]
[28] Fang F, Li M S, Lin P W, Chen W L, Liu N F, Lin Y G, Wang P, Liu K, Suo R, Li T C 2015 Metrologia 52 454
[29] Bureau International des Poids et Mesures, ftp://ftp2.bipm.org/pub/tai//Circular-T/cirthtm/cirt.358.html [2017-11-14]
[30] Audoin C, Santarelli G, Makdissi A, Clairon C 1998 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45 877
[31] Santarelli G, Audoin C, Makdissi A, Laurent P, Dick G J, Clairon A 1998 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45 887
[32] Santarelli G, Laurent P, Lemonde P, Clairon A, Mann A G, Chang S, Luiten A N, Salomon C 1999 Phys. Rev. Lett. 82 4619
[33] Zhou Z, Wei R, Shi C, L D, Li T, Wang Y 2009 Chin. Phys. Lett. 26 123
[34] Legere R, Gibble K 1998 Phys. Rev. Lett. 81 5780
[35] Dudle G, Joyet A, Berthoud P, Mileti G, Thomann P 2001 IEEE Trans. Instrum. Meas. 50 510
[36] Jefferts S R, Heavner T P, Donley E A, Shirley J H, Parker T E 2004 Proceedings of the 2003 IEEE International Frequency Control Symposium and PDA Exhibition jointly with the 17th European Frequency and Time Forum Tampa, USA, May 4-8, 2003 p1084
[37] Rovera G D, Abgrall M, Laurent P 2011 Proceedings of 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum San Francisco, USA, May 2-5, 2011 p45
[38] Petit G, Panfilo G 2013 IEEE Trans. Instrum. Meas. 62 1550
[39] Guéna J, Weyers S, Abgrall M, Grebing C, Gerginov V 2017 Metrologia 54 348
[40] Blinov I Y, Boiko A I, Domnin Y S, Kostromin V P, Kupalova O V 2017 Meas. Tech. 60 30
[41] Lorini L, Pavlenkoz K, Bize S, Desruelley B, Sterny G, Doroninz I, Pavlenkoz Y, Donchenko S 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon, France, July 9-13, 2017 p317
[42] Lee S, Heo M S, Kwon T Y, Hong H G, Lee S B, Park S E 2017 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon, France, July 9-13, 2017 p622
[43] Acharya A, Bharath V, Arora P, Yadav S, Agarwal A 2017 Mapan 32 67
[44] Ortiz C A, López J M, de Carlos López E 2017 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon, France, July 9-13, 2017 p326
[45] Dunst P, Nagórny B, Lemański D, Nogaś P, Nawrocki J, Hendricks R J, Ozimek F, Szymaniec K 2017 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon France, July 9-13, 2017 p628
[46] Beattie S, Jian B, Alcock A J, Bernard J, Gertsvolf M, Hendricks R, Ozimek F, Szymaniec K, Gibble K 2017 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon, France, July 9-13, 2017 p640
[47] Bureau International des Poids et Mesures, https:// www.bipm.org/utils/en/pdf/time_ann_rep/Time_annual_report_2014.pdf[2014]
[48] Shi C Y, Wei R, Zhou Z C, Li T, Li L,Wang Y Z 2011 Proceedings of 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum San Francisco, USA, May 2-5, 2011 p1
[49] Du Y B, Wei R, Dong R C, Zou F, Wang Y Z 2015 Chin. Phys. B 24 070601
[50] Liu L, L D S, Chen W B, Li T, Qu Q Z, Wang B, Li L, Ren W, Dong Z R, Zhao J B, Xia W B, Zhao X, Ji J W, Ye M F, Sun Y G, Yao Y Y, Song D, Liang Z G, Hu S J, Yu D H, Hou X, Shi W, Zang H G, Xiang J F, Peng X K, Wang Y Z 2017 axiv:1709.03256 [Atomic Physics]
[51] Ruan J, Wang Y B, Chang H, Jiang H F, Liu T, Dong R F, Zhang S G 2015 Acta Phys. Sin. 64 160308 (in Chinese) [阮军, 王叶兵, 常宏, 姜海峰, 刘涛, 董瑞芳, 张首刚 2015 物理学报 64 160308]
[52] Lin R, Wang X L, Liu D D, Guan Y, Zhang H, Chen J, Yu F X, Shi J R, Ruan J, Zhang S G \href https://doi.org/10.13875/j.issn.1674-0637.2016-03-0138-12 2017 Journal of Time and Frequency 41 p138 (in Chinese) [阮军, 王心亮, 刘丹丹, 管勇, 张辉, 陈江, 林睿, 余凤翔, 施俊如, 张首刚 2016 时间频率学报 41 p138]
[53] Wynands R, Weyers S 2005 Metrologia 42 64
[54] Wang Y Q 2012 Atomic Clock and Time Frequency System (Beijing: National Defense industry Press) pp77-96 (in Chinese) [王义遒 2012 原子钟与时间频率系统 (北京: 国防工业出版社) 第77-96页]
[55] Riehle F 2004 Frequency Standards Basics and Applications (Germany: Wiley-VCH) pp217-225
[56] Metcalf J H 1989 J. Opt. Soc. Am. B 6 2206
[57] Wang Y Q 2007 Laser Cooling and Trapping of Atoms (Beijing: Peking University Press) pp291-308 (in Chinese) [王义遒 2007 原子的激光冷却与陷俘 (北京: 北京大学出版社) 第291-308 页]
[58] Metcalf J H, van der Straten P 1999 Laser Cooling and Trapping (Berlin, Heidelberg: Springer Berlin Heidelberg) pp156-164
[59] Donley E A, Heavner T P, Jefferts S R 2005 IEEE Trans. Instrum. Meas. 54 1905
[60] Dobrev G, Gerginov V, Weyers S 2016 Phys. Rev. A 93 043423
[61] Szymaniec K, Park S E 2011 IEEE Trans. Instrum. Meas. 60 2475
[62] Szymaniec K, Noh H R, Park S E, Takamizawa A 2013 Appl. Phys. B 111 527
[63] Takamizawa A, Yanagimachi S, Tanabe T, Hagimoto K, Hirano I 2015 IEEE Trans. Instrum. Meas. 64 2504
[64] Riehle F 2004 Frequency Standards Basics and Applications (Germany: Wiley-VCH) p76
[65] Vanier J, Tomescu C 2016 The Quantum Physics of Atomic Frequency Standards, Recsent Development (Boca Raton: CRC Press) p34
[66] Biedermann G W, Takase K, Wu X, Deslauriers L, Roy S, Kasevich M A 2013 Phys. Rev. Lett. 111 170802
[67] Schioppo M, Brown R C, McGrew W F, Hinkley N, Fasano R J, Beloy K, Yoon T H, Milani G, Nicolodi D, Sherman J A \href https://doi.org/10.1038/nphoton.2016.231 2016 Nat. Photon. 11 48
[68] Meunier M, Dutta I, Geiger R, Guerlin C, Garrido Alzar C L, Landragin A 2014 Phys. Rev. A 90 063633
[69] Heavner T P, Jefferts S R, Donley E A, Parker T E, Levi F 2005 Proceedings of the 36th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting Washington D.C., USA, December 7-9, 2004 p308
[70] Rovera G D, Santarelli G, Clairon A 1996 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43 354
[71] Gupta A S, Popovic D, Walls F L 2000 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47 475
[72] Lipphardt B, Gerginov V, Weyers S 2017 IEEE Trans. on IEEE Trans. Ultrason. Ferroelectr. Freq. Control 64 761
[73] Haboucha A, Zhang W, Li T, Lours M, Luiten A N, Le Coq Y, Santarelli G 2011 Opt. Lett. 36 3654
[74] Dai S, Fang F, Cao S, Liu N, Suo R, Li T 2017 Joint Conference of the European Frequency and Time Forum, and the IEEE International Frequency Control Symposium Besancon, France, July 9-13, 2017 p302
[75] Guena J, Abgrall M, Clairon A, Bize S 2014 Metrologia 51 108
[76] Peil S, Swanson T B, Hanssen J, Taylor J S 2014 Metrologia 51 263
[77] Zhou Z C, Wei R, Shi C Y, Wang Y Z 2011 Chin. Phys. B 20 034206
[78] Lee T, Das T P, Sternheimer R M 1975 Phys. Rev. A 11 1784
[79] Itano W M, Lewis L L, Wineland D J 1982 Phys. Rev. A 25 1233
[80] Simon E, Laurent P, Clairon A 1998 Phys. Rev. A 57 436
[81] Levi F, Calosso C, Calonico D, Lorini L, Bertacco E K, Godone A, Costanzo G A, Mongino B, Jefferts S R, Heavner T P 2010 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57 600
[82] Sortais Y, Bize S, Nicolas C, Clairon A, Salomon C, Williams C 2000 Phys. Rev. Lett. 85 3117
[83] Ghezali S, Laurent P H, Lea S N, Clairon A 1996 Europhys. Lett. 36 25
[84] Sortais Y 2001 Ph. D. Dissertation (Paris: Bureau national de métrologie)
[85] Zhang S 2004 Ph. D. Dissertation (Paris: Université de Paris VI)
[86] Li R, Gibble K 2004 Metrologia 41 376
[87] Li R, Gibble K 2010 Metrologia 47 534
[88] Guéna J, Li R, Gibble K, Bize S, Clairon A 2011 Phys. Rev. Lett. 106 130801
[89] Li R, Gibble K, Szymaniec K 2011 Metrologia 48 283
[90] Weyers S, Gerginov V, Nemitz N, Li R, Gibble K 2012 Metrologia 49 82
[91] Gibble K, Lea S N, Szymaniec K 2012 Conference on Precision Electromagnetic Measurements Washington D.C., USA, July 1-6, 2012 p700
[92] Vanier J, Audoin C 1989 The Quantum Physics of Atomic Frequency Standards (Bristol: Hilger)
[93] Rabi I I, Ramsey N F, Schwinger J 1954 Rev. Mod. Phys. 26 167
[94] Bize S, Sortais Y, Mandache C, Clairon A, Salomon C 2001 IEEE Trans. Instrum. Meas. 50 503
[95] Bauch A, Schröder R 1993 Ann. Phys. 2 421
[96] Cutler L S, Flory C A, Giffardand R P, de Marchi A 1991 J. Appl. Phys. 69 2780
[97] Santarelli G, Governatori G, Chambon D, Lours M, Rosenbusch P, Guena J, Chapelet F, Bize S, Tobar M E, Laurent P, Potier T, Clairon A 2009 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56 1319
[98] Fang F, Liu K, Chen W, Liu N, Suo R, Li T 2014 Chin. Phys. Lett. 31 100601
[99] Audoin C, Jardino M, Cutler L S, Lacey R F 1978 IEEE Trans. Instrum. Meas. 27 325
[100] Levi F, Shirley J H, Heavner T P, Yu D H, Jefferts S R 2006 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53 1584
[101] Gibble K 2006 Phys. Rev. Lett. 97 073002
[102] Guéna J, Abgrall M, Rovera D, Laurent P, Chupin B, Lours M, Santarelli G, Rosenbusch P, Tobar M E, Li R X 2012 IEEE Trans. Ultrason Ferroelectr Freq. Control 59 391
[103] Angel J R P, Sandars P H G 1968 I. Theory, Proc. R. Soc. Lond. A 305 125
[104] Sakurai J J 1994 Modern Quantum Mechanics (New Jersey: Addison-Wesley) p500
[105] Szymaniec K, Lea S N, Gibble K, Park S E, Liu K, Głowacki P 2016 8th Symposium on Frequency Standards and Metrology 2015 Potsdam, Germany, October 12-16, 2016 p723
[106] Levi F, Calonico D, Calosso C E, Godone A, Micalizio S, Costanzo G A 2014 Metrologia 51 270
[107] Heavner T P, Donley E A, Levi F, Costanzo G, Parker T E, Shirley J H, Ashby N, Barlow S, Jefferts S R 2014 Metrologia 51 174
[108] Wei R 2003 Ph. D. Dissertation (Shanghai: Shanghai Institute of Optics and Fine Mechanics, the Chinese Academy of Sciences) (in Chinese) [魏荣 2003 博士学位论文 (上海: 中国科学院上海光学与精密机械研究所)]
[109] Shi C Y 2012 Ph. D. Dissertation (Shanghai: Shanghai Institute of Optics and Fine Mechanics, the Chinese Academy of Sciences) (in Chinese) [史春艳 2012 博士学位论文 (上海: 中国科学院上海光学与精密机械研究所)]
[110] Fertig C, Gibble K 2000 Phys. Rev. Lett. 85 1622
[111] Hart R A, Xu X, Legere R, Gibble K 2007 Nature 446 892
[112] Guéna J, Rosenbusch P, Laurent P, Abgrall M, Rovera D, Santarelli G, Tobar M, Bize S, Clairon A 2010 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57 647
[113] Bize S, Sortais Y, Santos M, Mandache C, Clairon A, Salomon C 1999 Europhys. Lett. 45 558
[114] Guéna J, Abgrall M, Rovera D, Rosenbusch P, Tobar M E, Laurent P, Clairon A, Bize S 2012 Phys. Rev. Lett. 109 080801
[115] Rovera D, Bize S, Chupin B, Guéna J, Laurent P, Rosenbusch P, Uhrich P 2016 Metrologia 53 81
[116] Berengut J C, Flambaum V V, Kava E M 2011 Phys. Rev. A 84 042510
[117] Lämmerzahl C, Ciufolini I, Dittus H, Iorio L, Mller H, Peters A, Samain E, Scheithauer S, Schiller S 2004 Gen. Relativ. Gravitation 36 615
[118] Lemonde P 1997 Ph. D. Dissertation (Paris: Bureau national de métrologie)
[119] Laurent P, Lemonde P, Simon E, Santarelli G, Clairon A, Dimarcq N, Petit P, Audoin C, Salomon C 1998 Eur. Phys. J. D 3 201
[120] Niering M, Holzwarth R, Reichert J, Pokasov P, Udem T, Weitz M, Hänsch T W, Lemonde P, Santarelli G, Abgrall M, Laurent P, Salomon C, Clairon A 2000 Phys. Rev. Lett. 84 5496
[121] Laurent P, Abgrall M, Jentsch C, Lemonde P, Santarelli G, Clairon A, Maksimovic I, Bize S, Salomon C, Blonde D 2006 Appl. Phys. B 84 683
[122] Laurent P, Massonnet D, Cacciapuoti L, Salomon C 2015 C. R. Phys. 16 540
[123] Wang X Q, Wang Y Z 1999 Chin. Phys. Lett. 17 478
[124] Bian F G, Wei R, Jiang H F, Wang Y Z 2005 Chin. Phys. Lett. 22 1645
[125] Li T, Gao Y C， Zhang F X, Liu L, Wang Y Z 2011 CN Patent 101807043 B (in Chinese) [李唐, 高源慈，张富鑫, 刘亮, 王育竹 2011 中国专利: CN 101807043 B]
[126] Devenoges L, Bernier L G, Morel J, Di Domenico G, Jallageas A, Petersen M, Thomann P 2013 2013 Joint European Frequency and Time Forum & International Frequency Control Symposium Prague, Czech Republic, July 21-25, 2013 p235
[127] Devenoges L, Stefanov A, Joyet A, Thomann P, Domenico G D 2012 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59 211
[128] Bauch A, Weyers S, Piester D, Staliuniene E, Yang W 2012 Metrologia 49 180
[129] Consultative Committee for Time and Frequency, https://www.bipm.org/utils/common/pdf/CC/CCTF/CCTF19.pdf [2012-09-14]
计量
- 文章访问数: 9725
- PDF下载量: 414
- 被引次数: 0
下载:
