锶原子光晶格钟
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摘要
进入21世纪以来,锶原子光晶格钟经历了快速的发展,系统频移的不确定度指标已经超越现有的秒定义基准铯原子喷泉钟,进入到10~(-18)量级,体现了人类精密测量能力的最高水平,是精密测量物理的热点研究内容.本综述简要介绍了锶原子光晶格钟的发展水平;详细介绍了锶原子光晶格钟的各个组成部分和关键技术、如何进行精密光谱探测和闭环锁定以及各项系统频移的不确定度评估方法和锶原子跃迁绝对频率测量的方法等;最后简要介绍了锶光钟的应用和未来发展趋势.
The strontium optical lattice clock has experienced a rapid development since the beginning of the 21 st century.Its relative frequency uncertainty, on the order of 10~(-18), has surpassed that of the cesium fountain clock, the current primary standard for time and frequency. This supreme level of precision reflects one of the most advanced measurement capabilities of mankind. This article reviews the current progress of the strontium optical lattice clock, and describes its key components and techniques, including high-resolution spectroscopy, close-loop operation, evaluation of systematic shifts, and absolute frequency measurement. The applications and future outlook of the strontium clock are also summarized.
The strontium optical lattice clock has experienced a rapid development since the beginning of the 21 st century.Its relative frequency uncertainty, on the order of 10~(-18), has surpassed that of the cesium fountain clock, the current primary standard for time and frequency. This supreme level of precision reflects one of the most advanced measurement capabilities of mankind. This article reviews the current progress of the strontium optical lattice clock, and describes its key components and techniques, including high-resolution spectroscopy, close-loop operation, evaluation of systematic shifts, and absolute frequency measurement. The applications and future outlook of the strontium clock are also summarized.
引文
[1]Lombardi M A 2017 J.Res.NIST JRES 122 1
[2]Essen L,Parry J V L 1957 Phil.Trans.R.Soc.Lond.A 250 45
[3]Ye J,Ma L S,Hall J L 2001 Phys.Rev.Lett.87 270801
[4]Clairon A,Laurent P,Santarelli G,Ghezali S,Lea S N,Bahoura M 1995 IEEE Trans.Instrum.Meas.44 128
[5]Vian C,Rosenbusch P,Marion H,Bize S,Cacciapuoti L,Zhang S,Abgrall M,Chambon D,Maksimovic I,Laurent P,Santarelli G,Clairon A,Luiten A,Tobar M,Salomon C 2005 IEEE Trans.Instrum.Meas.54 833
[6]Dehmelt H 1982 Thirty Fifth Annual Frequency Control Symposium Philadelphia,Pennsylvania,USA,May27–29,1981 p596
[7]Hall J L,Zhu M,Buch P 1989 J.Opt.Soc.Am.B 62194
[8]Walls F L,Wineland D J,Drullinger R E 1978 Proc.32nd Ann.Symp.Freq.Control Atlantic City,USA,May31–June 2,1978 453
[9]Drever R W P,Hall J L,Kowalski F V,Hough J,Ford G M,Munley A J,Ward H 1983 Appl.Phys.B:Lasers Opt.31 97
[10]Evenson K M,Wells J S,Petersen F R,Danielson B L,Day G W 1973 Appl.Phys.Lett.22 192
[11]Jennings D A,Evenson K M,Knight D J E 1986 Proc.IEEE 74 168
[12]Hall J L 2000 IEEE J.Sel.Top.Quantum Electron.61136
[13]H?nsch T W 1990 Opt.Commun.80 71
[14]Diddams S A,Udem T,Bergquist J C,Curtis E A,Drullinger R E,Hollberg L,Itano W M,Lee W D,Oates C W,Vogel K R,Wineland D J 2001 Science 293 825
[15]Chou C W,Hume D B,Koelemeij J C J,Wineland D J,Rosenband T 2010 Phys.Rev.Lett.104 070802
[16]Riehle F,Schnatz H,Lipphardt B,Zinner G,Trebst T,Helmcke J 1999 IEEE Trans.Instrum.Meas.48 613
[17]Oates C W,Curtis E A,Hollberg L 2000 Opt.Lett.251603
[18]Katori H,Takamoto M,Pal’chikov V G,Ovsiannikov V D 2003 Phys.Rev.Lett.91 173005
[19]Itano W M,Bergquist J C,Bollinger J J,Gilligan J M,Heinzen D J,Moore F L,Raizen M G,Wineland D J1993 Phys.Rev.A 47 3554
[20]Jiang Y Y,Ludlow A D,Lemke N D,Fox R W,Sherman J A,Ma L S,Oates C W 2011 Nat.Photon.5 158
[21]Hinkley N,Sherman J A,Phillips N B,Schioppo M,Lemke N D,Beloy K,Pizzocaro M,Oates C W,Ludlow A D 2013 Science 341 1215
[22]Bloom B J,Nicholson T L,Williams J R,Campbell S L,Bishof M,Zhang X,Zhang W,Bromley S L,Ye J 2014Nature 506 71
[23]Nicholson T L,Campbell S L,Hutson R B,Marti G E,Bloom B J,Mc Nally R L,Zhang W,Barrett M D,Safronova M S,Strouse G F,Tew W L,Ye J 2015 Nat.Commun.6 6896
[24]Campbell S L,Hutson R B,Marti G E,Goban A,Oppong N D,Mc Nally R L,Sonderhouse L,Robinson J M,Zhang W,Bloom B J,Ye J 2017 Science 358 90
[25]Lin Y G,Wang Q,Li Y,Meng F,Lin B K,Zang E J,Sun Z,Fang F,Li T C,Fang Z J 2015 Chin.Phys.Lett.32 090601
[26]Gao Q,Zhou M,Han C,Li S,Zhang S,Yao Y,Li B,Qiao H,Ai D,Lou G,Zhang M,Jiang Y,Bi Z,Ma L,Xu X 2018 Sci.Rep.8 8022
[27]Liu H,Zhang X,Jiang K L,Wang J Q,Zhu Q,Xiong Z X,He L X,LüB L 2017 Chin.Phys.Lett.34 20601
[28]Wang Y B,Yin M J,Ren J,Xu Q F,Lu B Q,Han J X,Guo Y,Chang H 2018 Chin.Phys.B 27 023701
[29]Fu X F,Fang S,Zhao R C,Zhang Y,Huang J C,Sun J F,Xu Z,Wang Y Z 2018 Chin.Opt.Lett.16 060202
[30]Jaseja T S,Javan A,Townes C H 1963 Phys.Rev.Lett.10 165
[31]Hall J 1969 IEEE J.Quantum Electron.5 324
[32]Black E D 2001 Am.J.Phys.69 79
[33]Wong N C,Hall J L 1985 J.Opt.Soc.Am.B 2 1527
[34]Whittaker E A,Grebel H,Lotem H,Shum C M 1988 J.Opt.Soc.Am.B 5 1253
[35]Salomon C,Hils D,Hall J L 1988 J.Opt.Soc.Am.B 51576
[36]Zhu M,Hall J L 1992 Proceedings of the 1992 IEEE Frequency Control Symposium Hershey,Pennsylvania,USA,May 27–29,1992 p44
[37]Young B C,Cruz F C,Itano W M,Bergquist J C 1999Phys.Rev.Lett.82 3799
[38]Fox R W 2008 Proc.SPIE 7099 70991R
[39]Fox R W 2009 Opt.Express 17 15023
[40]Zhao Y N,Zhang J,Stuhler J,Schuricht G,Lison F,Lu Z H,Wang L J 2010 Opt.Commun.283 4696
[41]Millo J,Abgrall M,Lours M,English E M L,Jiang H,Guéna J,Clairon A,Tobar M E,Bize S,Le Coq Y,Santarelli G 2009 Appl.Phys.Lett.94 141105
[42]Swallows M D,Martin M J,Bishof M,Benko C,Lin Y,Blatt S,Rey A M,Ye J 2012 IEEE Trans.Ultrason.Ferroelectr.Freq.Control 59 416
[43]Notcutt M,Ma L S,Ye J,Hall J L 2005 Opt.Lett.301815
[44]Chen L,Hall J,Ye J,Yang T,Zang E,Li T 2006 Phys.Rev.A 74 5
[45]Nazarova T,Riehle F,Sterr U 2006 Appl.Phys.B 83531
[46]Ludlow A D,Huang X,Notcutt M,Zanon-Willette T,Foreman S M,Boyd M M,Blatt S,Ye J 2007 Opt.Lett.32 641
[47]Webster S A,Oxborrow M,Pugla S,Millo J,Gill P 2008Phys.Rev.A 77 033847
[48]Leibrandt D R,Thorpe M J,Bergquist J C,Rosenband T 2011 Opt.Express 19 10278
[49]Leibrandt D R,Thorpe M J,Notcutt M,Drullinger R E,Rosenband T,Bergquist J C 2011 Opt.Express 193471
[50]Yang T,Li W B,Zang E J,Chen L S 2007 Chin.Phys.16 1374
[51]Jiang Y,Fang S,Bi Z,Xu X,Ma L 2010 Appl.Phys.B98 61
[52]Harry G M,Gretarsson A M,Saulson P R,Kittelberger S E,Penn S D,Startin W J,Rowan S,Fejer M M,Crooks D R M,Cagnoli G,Hough J,Nakagawa N 2002 Class.Quantum Gravity 19 897
[53]Numata K,Kemery A,Camp J 2004 Phys.Rev.Lett.93 250602
[54]Notcutt M,Ma L S,Ludlow A D,Foreman S M,Ye J,Hall J L 2006 Phys.Rev.A 73 031804
[55]Kessler T,Legero T,Sterr U 2012 JOSA B 29 178
[56]Hagemann C,Grebing C,Kessler T,Falke S,Lemke N,Lisdat C,Schnatz H,Riehle F,Sterr U 2013 IEEE Trans.Instrum.Meas.62 1556
[57]Takamoto M,Ushijima I,Das M,Nemitz N,Ohkubo T,Yamanaka K,Ohmae N,Takano T,Akatsuka T,Yamaguchi A,Katori H 2015 Comptes Rendus Phys.16489
[58]Nicholson T L,Martin M J,Williams J R,Bloom B J,Bishof M,Swallows M D,Campbell S L,Ye J 2012 Phys.Rev.Lett.109 230801
[59]Li Y,Lin Y G,Wang Q,Yang T,Sun Z,Zang E J,Fang Z J 2018 Chin.Opt.Lett.16 051402
[60]Bishof M,Zhang X,Martin M J,Ye J 2013 Phys.Rev.Lett.111 093604
[61]H?fner S,Falke S,Grebing C,Vogt S,Legero T,Merimaa M,Lisdat C,Sterr U 2015 Opt.Lett.40 2112
[62]Ma L S,Jungner P,Ye J,Hall J L 1994 Opt.Lett.191777
[63]Foreman S M,Holman K W,Hudson D D,Jones D J,Ye J 2007 Rev.Sci.Instrum.78 021101
[64]Santarelli G,Laurent P,Lemonde P,Clairon A,Mann A G,Chang S,Luiten A N,Salomon C 1999 Phys.Rev.Lett.82 4619
[65]Reichert J,Holzwarth R,Udem T,H?nsch T W 1999Opt.Commun.172 59
[66]Diddams S A,Jones D J,Ye J,Cundiff S T,Hall J L,Ranka J K,Windeler R S,Holzwarth R,Udem T,H?nsch T W 2000 Phys.Rev.Lett.84 5102
[67]Peters E,Diddams S A,Fendel P,Reinhardt S,H?nsch T W,Udem T 2009 Opt.Express 17 9183
[68]Cing?z A,Yost D C,Allison T K,Ruehl A,Fermann M E,Hartl I,Ye J 2012 Nature 482 68
[69]Takamoto M,Katori H 2003 Phys.Rev.Lett.91 223001
[70]Ido T,Katori H 2003 Phys.Rev.Lett.91 053001
[71]Ye J,Kimble H J,Katori H 2008 Science 320 1734
[72]Brusch A,Le Targat R,Baillard X,FouchéM,Lemonde P 2006 Phys.Rev.Lett.96 103003
[73]Katori H 2002 Frequency Standards and Metrology—Proceedings of the 6th Symposium Fife,Scotland,September 9–14 2001 p323
[74]Safronova M S,Kozlov M G,Clark C W 2012 IEEE Trans.Ultrason.Ferroelectr.Freq.Control 59 439
[75]Hachisu H,Miyagishi K,Porsev S G,Derevianko A,Ovsiannikov V D,Pal’chikov V G,Takamoto M,Katori H 2008 Phys.Rev.Lett.100 053001
[76]Petersen M,Chicireanu R,Dawkins S T,Magalh?es D V,Mandache C,Le Coq Y,Clairon A,Bize S 2008 Phys.Rev.Lett.101 183004
[77]Santra R,Arimondo E,Ido T,Greene C H,Ye J 2005Phys.Rev.Lett.94 173002
[78]Taichenachev A V,Yudin V I,Oates C W,Hoyt C W,Barber Z W,Hollberg L 2006 Phys.Rev.Lett.96 083001
[79]Poli N,Barber Z W,Lemke N D,Oates C W,Ma L S,Stalnaker J E,Fortier T M,Diddams S A,Hollberg L,Bergquist J C,Brusch A,Jefferts S,Heavner T,Parker T 2008 Phys.Rev.A 77 050501
[80]Lin Y G,Wang Q,Li Y,Lin B K,Wang S K,Meng F,Zhao Y,Cao J P,Zang E J,Li T C,Fang Z J 2013 Chin.Phys.Lett.30 014206
[81]Ovsiannikov V D,Pal’chikov V G,Taichenachev A V,Yudin V I,Katori H,Takamoto M 2007 Phys.Rev.A75 020501
[82]Baillard X,FouchéM,Le Targat R,Westergaard P G,Lecallier A,Le Coq Y,Rovera G D,Bize S,Lemonde P2007 Opt.Lett.32 1812
[83]Akatsuka T,Takamoto M,Katori H 2008 Nat.Phys.4954
[84]Bober M,Morzyński P,Cygan A,Lisak D,Mas?owski P,Prymaczek M,Piotr Wcis?o,Ablewski P,Piwiński M,Wójtewicz S,Bielska K,Dobros?awa Bartoszek-Bober,Trawiński R S,Zawada M,Ciury?o R,Zachorowski J,Marcin Piotrowski,Gawlik W,Ozimek F,Radzewicz C2015 Meas.Sci.Technol.26 075201
[85]Ludlow A D,Boyd M M,Ye J,Peik E,Schmidt P O2015 Rev.Mod.Phys.87 637
[86]Origlia S,Pramod M S,Schiller S,Singh Y,Bongs K,Schwarz R,Al-Masoudi A,D?rscher S,Herbers S,H?fner S,Sterr U,Lisdat C 2018 ar Xiv:1803.03157[physics,physics:quant-ph][2018-3-8]
[87]Phillips W D,Metcalf H 1982 Phys.Rev.Lett.48 596
[88]Xu X Y,Wang W L,Zhou Q H,Li G H,Jiang H L,Chen L F,Ye J,Zhou Z H,Cai Y,Tang H Y,Zhou M2009 Front.Phys.China 4 160
[89]Wang S K,Wang Q,Lin Y G,Wang M M,Lin B K,Zang E J,Li T C,Fang Z J 2009 Chin.Phys.Lett.26093202
[90]Zhao P Y,Xiong Z X,Long Y,He L X,LüB L 2009Chin.Phys.Lett.26 083702
[91]Hill I R,Ovchinnikov Y B,Bridge E M,Curtis E A,Gill P 2014 J.Phys.B:At.Mol.Opt.Phys.47 075006
[92]Wang Q,Lin Y G,Gao F L,Li Y,Lin B K,Meng F,Zang E J,Li T C,Fang Z J 2015 Chin.Phys.Lett.32100701
[93]Koller S B,Grotti J,Vogt S,Al-Masoudi A,D?rscher S,H?fner S,Sterr U,Lisdat C 2017 Phys.Rev.Lett.118073601
[94]Li Y,Ido T,Eichler T,Katori H 2004 Appl.Phys.B:Lasers Opt.78 315
[95]Ferrari G,Cancio P,Drullinger R,Giusfredi G,Poli N,Prevedelli M,Toninelli C,Tino G M 2003 Phys.Rev.Lett.91 243002
[96]Loftus T H,Ido T,Boyd M M,Ludlow A D,Ye J 2004Phys.Rev.A 70 063413
[97]Mukaiyama T,Katori H,Ido T,Li Y,Kuwata-Gonokami M 2003 Phys.Rev.Lett.90 113002
[98]Chanelière T,He L,Kaiser R,Wilkowski D 2008 Eur.Phys.J.:At.Mol.Opt.Plasma Phys.46 507
[99]Sterr U,Degenhardt C,Stoehr H,Lisdat C,Schnatz H,Helmcke J,Riehle F,Wilpers G,Oates C,Hollberg L2004 Comptes Rendus Phys.5 845
[100]Boyd M M,Zelevinsky T,Ludlow A D,Foreman S M,Blatt S,Ido T,Ye J 2006 Science 314 1430
[101]Blatt S,Thomsen J W,Campbell G K,Ludlow A D,Swallows M D,Martin M J,Boyd M M,Ye J 2009 Phys.Rev.A 80 052703
[102]Martin M,Bishof M,Swallows M D,Zhang X,Benko C,von Stecher J,Gorshkov A V,Rey A M,Ye J 2013Science 341 632
[103]Matei D G,Legero T,H?fner S,Grebing C,Weyrich R,Zhang W,Sonderhouse L,Robinson J M,Ye J,Riehle F,Sterr U 2017 Phys.Rev.Lett.118 263202
[104]Derevianko A,Katori H 2011 Rev.Mod.Phys.83 331
[105]Boyd M,Zelevinsky T,Ludlow A,Blatt S,ZanonWillette T,Foreman S,Ye J 2007 Phys.Rev.A 76022510
[106]Falke S,Schnatz H,Winfred J S R V,Middelmann T,Vogt S,Weyers S,Lipphardt B,Grosche G,Riehle F,Sterr U,Lisdat C 2011 Metrologia 48 399
[107]Westergaard P G,Lodewyck J,Lorini L,Lecallier A,Burt E A,Zawada M,Millo J,Lemonde P 2011 Phys.Rev.Lett.106 210801
[108]Wang Q,Lin Y G,Li Y,Lin B K,Meng F,Zang E J,Li T C,Fang Z J 2014 Chin.Phys.Lett.31 123201
[109]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,Naidon P,Julienne P,Ye J,Ludlow A D 2009 Science 324 360
[110]Ramsey N F 1950 Phys.Rev.78 695
[111]Campbell G K,Ludlow A D,Blatt S,Thomsen J W,Martin M J,de Miranda M H G,Zelevinsky T,Boyd M M,Ye J,Diddams S A,Heavner T P,Parker T E,Jefferts S R 2008 Metrologia 45 539
[112]Ludlow A D,Zelevinsky T,Campbell G K,Blatt S,Boyd M M,de Miranda M H G,Martin M J,Thomsen J W,Foreman S M,Ye J,Fortier T M,Stalnaker J E,Diddams S A,Le Coq Y,Barber Z W,Poli N,Lemke N D,Beck K M,Oates C W 2008 Science 319 1805
[113]Peik E,Schneider T,Tamm C 2006 J.Phys.B:At.Mol.Opt.Phys.39 145
[114]Dick G J 1987[http://www.dtic.mil/docs/citations/ADA502386][2018-7-10]
[115]Dick G J,Greenhall C A 1998 Proceedings of the1998 IEEE International Frequency Control Symposium Pasadena,CA,USA,May 29,1998 p99
[116]Westergaard P,Lodewyck J,Lemonde P 2010 IEEE Trans.Ultrason.Ferroelectr.Freq.Control 57 623
[117]Stefani F,Lopez O,Bercy A,Lee W K,Chardonnet C,Santarelli G,Pottie P E,Amy-Klein A 2015 J.Opt.Soc.Am.B 32 787
[118]Lopez O,Amy-Klein A,Lours M,Chardonnet C,Santarelli G 2010 Appl.Phys.B 98 723
[119]Terra O,Grosche G,Predehl K,Holzwarth R,Legero T,Sterr U,Lipphardt B,Schnatz H 2009 Appl.Phys.B 97541
[120]Droste S,Ozimek F,Udem T,Predehl K,H?nsch T W,Schnatz H,Grosche G,Holzwarth R 2013 Phys.Rev.Lett.111 110801
[121]Ma C Q,Wu L F,Jiang Y Y,Yu H F,Bi Z Y,Ma L S2015 Chin.Phys.B 24 084209
[122]Lisdat C,Grosche G,Quintin N,Shi C,Raupach S M F,Grebing C,Nicolodi D,Stefani F,Al-Masoudi A,D?rscher S,H?fner S,Robyr J L,Chiodo N,Bilicki S,Bookjans E,Koczwara A,Koke S,Kuhl A,Wiotte F,Meynadier F,Camisard E,Abgrall M,Lours M,Legero T,Schnatz H,Sterr U,Denker H,Chardonnet C,Coq Y L,Santarelli G,Amy-Klein A,Targat R L,Lodewyck J,Lopez O,Pottie P E 2016 Nat.Commun.7 12443
[123]Falke S,Misera M,Sterr U,Lisdat C 2012 Appl.Phys.B 107 301
[124]Ye J,Peng J L,Jones R J,Holman K W,Hall J L,Jones D J,Diddams S A,Kitching J,Bize S,Bergquist J C,Hollberg L W,Robertsson L,Ma L S 2003 J.Opt.Soc.Am.B 20 1459
[125]Wang B,Gao C,Chen W L,Miao J,Zhu X,Bai Y,Zhang J W,Feng Y Y,Li T C,Wang L J 2012 Sci.Rep.2 556
[126]Ye J,Cundiff S T 2005 Femtosecond Optical Frequency Comb:Principle,Operation,and Applications(Norwell,MA:Springer Verlag)p18
[127]Ma L S,Bi Z Y,Bartels A,Robertsson L,Zucco M,Windeler R S,Wilpers G,Oates C,Hollberg L,Diddams S A 2004 Science 303 1843
[128]Fang S,Jiang Y Y,Chen H Q,Yao Y,Bi Z Y,Ma L S2015 Chin.Phys.B 24 084209
[129]Benko C,Ruehl A,Martin M J,Eikema K S E,Fermann M E,Hartl I,Ye J 2012 Opt.Lett.37 2196
[130]Legero T,Lisdat C,Vellore Winfred J S R,Schnatz H,Grosche G,Riehle F,Sterr U 2009 IEEE Trans.Instrum.Meas.58 1252
[131]Nicolodi D,Argence B,Zhang W,Targat R L,Santarelli G,Coq Y L 2014 Nat.Photon.8 219
[132]Leopardi H,Davila-Rodriguez J,Quinlan F,Olson J,Sherman J A,Diddams S A,Fortier T M 2017 Optica 4879
[133]Ohmae N,Kuse N,Fermann M E,Katori H 2017 Appl.Phys.Express 10 062503
[134]Falke S,Lemke N,Grebing C,Lipphardt B,Weyers S,Gerginov V,Huntemann N,Hagemann C,Al-Masoudi A,H?fner S,Vogt S,Sterr U,Lisdat C 2014 New J.Phys.16 073023
[135]Lin Y G,Wang Q,Li Y,Meng F,Lin B K,Zang E J,Sun Z,Fang F,Li T C,Fang Z J 2016 J.Phys.:Conf.Ser.723 012021
[136]Hazlett E L,Zhang Y,Stites R W,Gibble K,O’Hara K M 2013 Phys.Rev.Lett.110 160801
[137]Lemke N D,von Stecher J,Sherman J A,Rey A M,Oates C W,Ludlow A D 2011 Phys.Rev.Lett.107103902
[138]Swallows M D,Bishof M,Lin Y,Blatt S,Martin M J,Rey A M,Ye J 2011 Science 331 1043
[139]Barber Z,Stalnaker J,Lemke N,Poli N,Oates C,Fortier T,Diddams S,Hollberg L,Hoyt C,Taichenachev A,Yudin V 2008 Phys.Rev.Lett.100 103002
[140]Brown R C,Phillips N B,Beloy K,Mc Grew W F,Schioppo M,Fasano R J,Milani G,Zhang X,Hinkley N,Leopardi H,Yoon T H,Nicolodi D,Fortier T M,Ludlow A D 2017 Phys.Rev.Lett.119 253001
[141]Itano W M,Lewis L L,Wineland D J 1982 Phys.Rev.A 25 1233
[142]Hollberg L,Hall J L 1984 Phys.Rev.Lett.53 230
[143]Porsev S G,Derevianko A 2006 Phys.Rev.A 74 020502
[144]Safronova M S,Porsev S G,Safronova U I,Kozlov M G,Clark C W 2013 Phys.Rev.A 87 012509
[145]Yudin V I,Taichenachev A V,Okhapkin M V,Bagayev S N,Tamm C,Peik E,Huntemann N,Mehlst?ubler T E,Riehle F 2011 Phys.Rev.Lett.107 030801
[146]Middelmann T,Lisdat C,Falke S,Winfred J S R V,Riehle F,Sterr U 2011 IEEE Trans.Instrum.Meas.602550
[147]Middelmann T,Falke S,Lisdat C,Sterr U 2012 Phys.Rev.Lett.109 263004
[148]Beloy K,Hinkley N,Phillips N B,Sherman J A,Schioppo M,Lehman J,Feldman A,Hanssen L M,Oates C W,Ludlow A D 2014 Phys.Rev.Lett.113 260801
[149]Lodewyck J,Zawada M,Lorini L,Gurov M,Lemonde P2012 IEEE Trans.Ultrason.Ferroelectr.Freq.Control59 411
[150]Beloy K,Zhang X,Mc Grew W F,Hinkley N,Yoon T H,Nicolodi D,Fasano R J,Sch?ffer S A,Brown R C,Ludlow A D 2018 Phys.Rev.Lett.120 183201
[151]Ushijima I,Takamoto M,Das M,Ohkubo T,Katori H2015 Nat.Photon.9 185
[152]Bowden W,Hobson R,Huillery P,Gill P,Jones M P A,Hill I R 2017 Phys.Rev.A 96 023419
[153]Baillard X,FouchéM,Le Targat R,Westergaard P G,Lecallier A,Chapelet F,Abgrall M,Rovera G D,Laurent P,Rosenbusch P,Bize S,Santarelli G,Clairon A,Lemonde P,Grosche G,Lipphardt B,Schnatz H 2008Eur.Phys.J.:At.Mol.Opt.Plasma Phys.48 11
[154]Le Targat R,Lorini L,Le Coq Y,Zawada M,Guéna J,Abgrall M,Gurov M,Rosenbusch P,Rovera D G,Nagórny B,Gartman R,Westergaard P G,Tobar M E,Lours M,Santarelli G,Clairon A,Bize S,Laurent P,Lemonde P,Lodewyck J 2013 Nat.Commun.4 2109
[155]Lodewyck J,Bilicki S,Bookjans E,Robyr J L,Shi C,Vallet G,Targat R L,Nicolodi D,Coq Y L,Guéna J,Abgrall M,Rosenbusch P,Bize S 2016 Metrologia 531123
[156]Levine J 2008 Metrologia 45 S162
[157]Fujieda M,Piester D,Gotoh T,Becker J,Aida M,Bauch A 2014 Metrologia 51 253
[158]Hong F L,Musha M,Takamoto M,Inaba H,Yanagimachi S,Takamizawa A,Watabe K,Ikegami T,Imae M,Fujii Y,Amemiya M,Nakagawa K,Ueda K,Katori H 2009 Opt.Lett.34 692
[159]Hachisu H,Petit G,Nakagawa F,Hanado Y,Ido T 2017Opt.Express 25 8511
[160]Baynham C F A,Godun R M,Jones J M,King S A,Nisbet-Jones P B R,Baynes F,Rolland A,Baird P E G,Bongs K,Gill P,Margolis H S 2018 J.Mod.Opt.65585
[161]Boyd M M,Ludlow A D,Blatt S,Foreman S M,Ido T,Zelevinsky T,Ye J 2007 Phys.Rev.Lett.98 083002
[162]Yamaguchi A,Shiga N,Nagano S,Li Y,Ishijima H,Hachisu H,Kumagai M,Ido T 2012 Appl.Phys.Express5 022701
[163]Akamatsu D,Inaba H,Hosaka K,Yasuda M,Onae A,Suzuyama T,Amemiya M,Hong F L 2014 Appl.Phys.Express 7 012401
[164]Tanabe T,Akamatsu D,Kobayashi T,Takamizawa A,Yanagimachi S,Ikegami T,Suzuyama T,Inaba H,Okubo S,Yasuda M 2015 J.Phys.Soc.Jpn.84 115002
[165]Grebing C,Al-Masoudi A,D?rscher S,H?fner S,Gerginov V,Weyers S,Lipphardt B,Riehle F,Sterr U,Lisdat C 2016 Optica 3 563
[166]Hachisu H,Petit G,Ido T 2017 Appl.Phys.B 123 34
[167]Szymaniec K,Park S E,Marra G,Cha?upczak W 2010Metrologia 47 363
[168]Gerginov V,Nemitz N,Weyers S,Schr?der R,Griebsch D,Wynands R 2010 Metrologia 47 65
[169]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 52454
[170]Ido T,Hachisu H,Nakagawa F,Hanado Y 2016 J.Phys.:Conf.Ser.723 012041
[171]Yao J,Parker T E,Ashby N,Levine J 2018 IEEE Trans.Ultrason.Ferroelectr.Freq.Control 65 127
[172]Gill P 2011 Phil.Trans.R.Soc.A 369 4109
[173]Riehle F 2015 Comptes Rendus Physique 16 506
[174]Chou C W,Hume D B,Rosenband T,Wineland D J2010 Science 329 1630
[175]Takano T,Takamoto M,Ushijima I,Ohmae N,Akatsuka T,Yamaguchi A,Kuroishi Y,Munekane H,Miyahara B,Katori H 2016 Nat.Photonics 10 662
[176]Grotti J,Koller S,Vogt S,H?fner S,Sterr U,Lisdat C,Denker H,Voigt C,Timmen L,Rolland A,Baynes F N,Margolis H S,Zampaolo M,Thoumany P,Pizzocaro M,Rauf B,Bregolin F,Tampellini A,Barbieri P,Zucco M,Costanzo G A,Clivati C,Levi F,Calonico D 2018 Nat.Phys.14 437
[177]Shang H,Zhang X,Zhang S,Pan D,Chen H,Chen J2017 Opt.Express 25 30459
[178]Zhang S,Zhang X,Cui J,Jiang Z,Shang H,Zhu C,Chang P,Zhang L,Tu J,Chen J 2017 Rev.Sci.Instrum.88 103106
[179]Bize S,Diddams S A,Tanaka U,Tanner C E,Oskay W H,Drullinger R E,Parker T E,Heavner T P,Jefferts S R,Hollberg L,Itano W M,Bergquist J C 2003 Phys.Rev.Lett.90 150802
[180]Blatt S,Ludlow A D,Campbell G K,Thomsen J W,Zelevinsky T,Boyd M M,Ye J,Baillard X,FouchéM,Le Targat R,Brusch A,Lemonde P,Takamoto M,Hong F L,Katori H,Flambaum V V 2008 Phys.Rev.Lett.100140801
[181]Ludlow A D,Blatt S,Zelevinsky T,Campbell G K,Martin M J,Thomsen J W,Boyd M M,Ye J 2008 Eur.Phys.J.Spec.Top.163 9
[182]Rosenband T,Hume D B,Schmidt P O,Chou C W,Brusch A,Lorini L,Oskay W H,Drullinger R E,Fortier T M,Stalnaker J E,Diddams S A,Swann W C,Newbury N R,Itano W M,Wineland D J,Bergquist J C 2008Science 319 1808
[183]Derevianko A,Pospelov M 2014 Nat.Phys.10 933
[184]Arvanitaki A,Huang J,van Tilburg K 2015 Phys.Rev.D 91 015015
[185]Katori H,Ido T,Kuwatagonokami M 1999 J.Phys.Soc.Jpn.68 2479
[186]Cole G D,Zhang W,Martin M J,Ye J,Aspelmeyer M2013 Nat.Photonics 7 644
[187]Cole G D,Zhang W,Bjork B J,Follman D,Heu P,Deutsch C,Sonderhouse L,Robinson J,Franz C,Alexandrovski A,Notcutt M,Heckl O H,Ye J,Aspelmeyer M 2016 Optica 3 647
[188]Kessler T,Hagemann C,Grebing C,Legero T,Sterr U,Riehle F,Martin M J,Chen L,Ye J 2012 Nat.Photon.6 687
[189]Zhang W,Robinson J M,Sonderhouse L,Oelker E,Benko C,Hall J L,Legero T,Matei D G,Riehle F,Sterr U,Ye J 2017 Phys.Rev.Lett.119 243601
[190]Schioppo M,Brown R C,Mc Grew W F,Hinkley N,Fasano R J,Beloy K,Yoon T H,Milani G,Nicolodi D,Sherman J A,Phillips N B,Oates C W,Ludlow A D2017 Nat.Photonics 11 48
[191]Chen J,Chen X 2005 Proceedings of the 2005 IEEE International Frequency Control Symposium Vancouver,Canada,August 29–31,2005 p608
[192]Bohnet J G,Chen Z,Weiner J M,Meiser D,Holland M J,Thompson J K 2012 Nature 484 78
[193]Norcia M A,Cline J R K,Muniz J A,Robinson J M,Hutson R B,Goban A,Marti G E,Ye J,Thompson J K 2018 Phys.Rev.X 8 021036
[2]Essen L,Parry J V L 1957 Phil.Trans.R.Soc.Lond.A 250 45
[3]Ye J,Ma L S,Hall J L 2001 Phys.Rev.Lett.87 270801
[4]Clairon A,Laurent P,Santarelli G,Ghezali S,Lea S N,Bahoura M 1995 IEEE Trans.Instrum.Meas.44 128
[5]Vian C,Rosenbusch P,Marion H,Bize S,Cacciapuoti L,Zhang S,Abgrall M,Chambon D,Maksimovic I,Laurent P,Santarelli G,Clairon A,Luiten A,Tobar M,Salomon C 2005 IEEE Trans.Instrum.Meas.54 833
[6]Dehmelt H 1982 Thirty Fifth Annual Frequency Control Symposium Philadelphia,Pennsylvania,USA,May27–29,1981 p596
[7]Hall J L,Zhu M,Buch P 1989 J.Opt.Soc.Am.B 62194
[8]Walls F L,Wineland D J,Drullinger R E 1978 Proc.32nd Ann.Symp.Freq.Control Atlantic City,USA,May31–June 2,1978 453
[9]Drever R W P,Hall J L,Kowalski F V,Hough J,Ford G M,Munley A J,Ward H 1983 Appl.Phys.B:Lasers Opt.31 97
[10]Evenson K M,Wells J S,Petersen F R,Danielson B L,Day G W 1973 Appl.Phys.Lett.22 192
[11]Jennings D A,Evenson K M,Knight D J E 1986 Proc.IEEE 74 168
[12]Hall J L 2000 IEEE J.Sel.Top.Quantum Electron.61136
[13]H?nsch T W 1990 Opt.Commun.80 71
[14]Diddams S A,Udem T,Bergquist J C,Curtis E A,Drullinger R E,Hollberg L,Itano W M,Lee W D,Oates C W,Vogel K R,Wineland D J 2001 Science 293 825
[15]Chou C W,Hume D B,Koelemeij J C J,Wineland D J,Rosenband T 2010 Phys.Rev.Lett.104 070802
[16]Riehle F,Schnatz H,Lipphardt B,Zinner G,Trebst T,Helmcke J 1999 IEEE Trans.Instrum.Meas.48 613
[17]Oates C W,Curtis E A,Hollberg L 2000 Opt.Lett.251603
[18]Katori H,Takamoto M,Pal’chikov V G,Ovsiannikov V D 2003 Phys.Rev.Lett.91 173005
[19]Itano W M,Bergquist J C,Bollinger J J,Gilligan J M,Heinzen D J,Moore F L,Raizen M G,Wineland D J1993 Phys.Rev.A 47 3554
[20]Jiang Y Y,Ludlow A D,Lemke N D,Fox R W,Sherman J A,Ma L S,Oates C W 2011 Nat.Photon.5 158
[21]Hinkley N,Sherman J A,Phillips N B,Schioppo M,Lemke N D,Beloy K,Pizzocaro M,Oates C W,Ludlow A D 2013 Science 341 1215
[22]Bloom B J,Nicholson T L,Williams J R,Campbell S L,Bishof M,Zhang X,Zhang W,Bromley S L,Ye J 2014Nature 506 71
[23]Nicholson T L,Campbell S L,Hutson R B,Marti G E,Bloom B J,Mc Nally R L,Zhang W,Barrett M D,Safronova M S,Strouse G F,Tew W L,Ye J 2015 Nat.Commun.6 6896
[24]Campbell S L,Hutson R B,Marti G E,Goban A,Oppong N D,Mc Nally R L,Sonderhouse L,Robinson J M,Zhang W,Bloom B J,Ye J 2017 Science 358 90
[25]Lin Y G,Wang Q,Li Y,Meng F,Lin B K,Zang E J,Sun Z,Fang F,Li T C,Fang Z J 2015 Chin.Phys.Lett.32 090601
[26]Gao Q,Zhou M,Han C,Li S,Zhang S,Yao Y,Li B,Qiao H,Ai D,Lou G,Zhang M,Jiang Y,Bi Z,Ma L,Xu X 2018 Sci.Rep.8 8022
[27]Liu H,Zhang X,Jiang K L,Wang J Q,Zhu Q,Xiong Z X,He L X,LüB L 2017 Chin.Phys.Lett.34 20601
[28]Wang Y B,Yin M J,Ren J,Xu Q F,Lu B Q,Han J X,Guo Y,Chang H 2018 Chin.Phys.B 27 023701
[29]Fu X F,Fang S,Zhao R C,Zhang Y,Huang J C,Sun J F,Xu Z,Wang Y Z 2018 Chin.Opt.Lett.16 060202
[30]Jaseja T S,Javan A,Townes C H 1963 Phys.Rev.Lett.10 165
[31]Hall J 1969 IEEE J.Quantum Electron.5 324
[32]Black E D 2001 Am.J.Phys.69 79
[33]Wong N C,Hall J L 1985 J.Opt.Soc.Am.B 2 1527
[34]Whittaker E A,Grebel H,Lotem H,Shum C M 1988 J.Opt.Soc.Am.B 5 1253
[35]Salomon C,Hils D,Hall J L 1988 J.Opt.Soc.Am.B 51576
[36]Zhu M,Hall J L 1992 Proceedings of the 1992 IEEE Frequency Control Symposium Hershey,Pennsylvania,USA,May 27–29,1992 p44
[37]Young B C,Cruz F C,Itano W M,Bergquist J C 1999Phys.Rev.Lett.82 3799
[38]Fox R W 2008 Proc.SPIE 7099 70991R
[39]Fox R W 2009 Opt.Express 17 15023
[40]Zhao Y N,Zhang J,Stuhler J,Schuricht G,Lison F,Lu Z H,Wang L J 2010 Opt.Commun.283 4696
[41]Millo J,Abgrall M,Lours M,English E M L,Jiang H,Guéna J,Clairon A,Tobar M E,Bize S,Le Coq Y,Santarelli G 2009 Appl.Phys.Lett.94 141105
[42]Swallows M D,Martin M J,Bishof M,Benko C,Lin Y,Blatt S,Rey A M,Ye J 2012 IEEE Trans.Ultrason.Ferroelectr.Freq.Control 59 416
[43]Notcutt M,Ma L S,Ye J,Hall J L 2005 Opt.Lett.301815
[44]Chen L,Hall J,Ye J,Yang T,Zang E,Li T 2006 Phys.Rev.A 74 5
[45]Nazarova T,Riehle F,Sterr U 2006 Appl.Phys.B 83531
[46]Ludlow A D,Huang X,Notcutt M,Zanon-Willette T,Foreman S M,Boyd M M,Blatt S,Ye J 2007 Opt.Lett.32 641
[47]Webster S A,Oxborrow M,Pugla S,Millo J,Gill P 2008Phys.Rev.A 77 033847
[48]Leibrandt D R,Thorpe M J,Bergquist J C,Rosenband T 2011 Opt.Express 19 10278
[49]Leibrandt D R,Thorpe M J,Notcutt M,Drullinger R E,Rosenband T,Bergquist J C 2011 Opt.Express 193471
[50]Yang T,Li W B,Zang E J,Chen L S 2007 Chin.Phys.16 1374
[51]Jiang Y,Fang S,Bi Z,Xu X,Ma L 2010 Appl.Phys.B98 61
[52]Harry G M,Gretarsson A M,Saulson P R,Kittelberger S E,Penn S D,Startin W J,Rowan S,Fejer M M,Crooks D R M,Cagnoli G,Hough J,Nakagawa N 2002 Class.Quantum Gravity 19 897
[53]Numata K,Kemery A,Camp J 2004 Phys.Rev.Lett.93 250602
[54]Notcutt M,Ma L S,Ludlow A D,Foreman S M,Ye J,Hall J L 2006 Phys.Rev.A 73 031804
[55]Kessler T,Legero T,Sterr U 2012 JOSA B 29 178
[56]Hagemann C,Grebing C,Kessler T,Falke S,Lemke N,Lisdat C,Schnatz H,Riehle F,Sterr U 2013 IEEE Trans.Instrum.Meas.62 1556
[57]Takamoto M,Ushijima I,Das M,Nemitz N,Ohkubo T,Yamanaka K,Ohmae N,Takano T,Akatsuka T,Yamaguchi A,Katori H 2015 Comptes Rendus Phys.16489
[58]Nicholson T L,Martin M J,Williams J R,Bloom B J,Bishof M,Swallows M D,Campbell S L,Ye J 2012 Phys.Rev.Lett.109 230801
[59]Li Y,Lin Y G,Wang Q,Yang T,Sun Z,Zang E J,Fang Z J 2018 Chin.Opt.Lett.16 051402
[60]Bishof M,Zhang X,Martin M J,Ye J 2013 Phys.Rev.Lett.111 093604
[61]H?fner S,Falke S,Grebing C,Vogt S,Legero T,Merimaa M,Lisdat C,Sterr U 2015 Opt.Lett.40 2112
[62]Ma L S,Jungner P,Ye J,Hall J L 1994 Opt.Lett.191777
[63]Foreman S M,Holman K W,Hudson D D,Jones D J,Ye J 2007 Rev.Sci.Instrum.78 021101
[64]Santarelli G,Laurent P,Lemonde P,Clairon A,Mann A G,Chang S,Luiten A N,Salomon C 1999 Phys.Rev.Lett.82 4619
[65]Reichert J,Holzwarth R,Udem T,H?nsch T W 1999Opt.Commun.172 59
[66]Diddams S A,Jones D J,Ye J,Cundiff S T,Hall J L,Ranka J K,Windeler R S,Holzwarth R,Udem T,H?nsch T W 2000 Phys.Rev.Lett.84 5102
[67]Peters E,Diddams S A,Fendel P,Reinhardt S,H?nsch T W,Udem T 2009 Opt.Express 17 9183
[68]Cing?z A,Yost D C,Allison T K,Ruehl A,Fermann M E,Hartl I,Ye J 2012 Nature 482 68
[69]Takamoto M,Katori H 2003 Phys.Rev.Lett.91 223001
[70]Ido T,Katori H 2003 Phys.Rev.Lett.91 053001
[71]Ye J,Kimble H J,Katori H 2008 Science 320 1734
[72]Brusch A,Le Targat R,Baillard X,FouchéM,Lemonde P 2006 Phys.Rev.Lett.96 103003
[73]Katori H 2002 Frequency Standards and Metrology—Proceedings of the 6th Symposium Fife,Scotland,September 9–14 2001 p323
[74]Safronova M S,Kozlov M G,Clark C W 2012 IEEE Trans.Ultrason.Ferroelectr.Freq.Control 59 439
[75]Hachisu H,Miyagishi K,Porsev S G,Derevianko A,Ovsiannikov V D,Pal’chikov V G,Takamoto M,Katori H 2008 Phys.Rev.Lett.100 053001
[76]Petersen M,Chicireanu R,Dawkins S T,Magalh?es D V,Mandache C,Le Coq Y,Clairon A,Bize S 2008 Phys.Rev.Lett.101 183004
[77]Santra R,Arimondo E,Ido T,Greene C H,Ye J 2005Phys.Rev.Lett.94 173002
[78]Taichenachev A V,Yudin V I,Oates C W,Hoyt C W,Barber Z W,Hollberg L 2006 Phys.Rev.Lett.96 083001
[79]Poli N,Barber Z W,Lemke N D,Oates C W,Ma L S,Stalnaker J E,Fortier T M,Diddams S A,Hollberg L,Bergquist J C,Brusch A,Jefferts S,Heavner T,Parker T 2008 Phys.Rev.A 77 050501
[80]Lin Y G,Wang Q,Li Y,Lin B K,Wang S K,Meng F,Zhao Y,Cao J P,Zang E J,Li T C,Fang Z J 2013 Chin.Phys.Lett.30 014206
[81]Ovsiannikov V D,Pal’chikov V G,Taichenachev A V,Yudin V I,Katori H,Takamoto M 2007 Phys.Rev.A75 020501
[82]Baillard X,FouchéM,Le Targat R,Westergaard P G,Lecallier A,Le Coq Y,Rovera G D,Bize S,Lemonde P2007 Opt.Lett.32 1812
[83]Akatsuka T,Takamoto M,Katori H 2008 Nat.Phys.4954
[84]Bober M,Morzyński P,Cygan A,Lisak D,Mas?owski P,Prymaczek M,Piotr Wcis?o,Ablewski P,Piwiński M,Wójtewicz S,Bielska K,Dobros?awa Bartoszek-Bober,Trawiński R S,Zawada M,Ciury?o R,Zachorowski J,Marcin Piotrowski,Gawlik W,Ozimek F,Radzewicz C2015 Meas.Sci.Technol.26 075201
[85]Ludlow A D,Boyd M M,Ye J,Peik E,Schmidt P O2015 Rev.Mod.Phys.87 637
[86]Origlia S,Pramod M S,Schiller S,Singh Y,Bongs K,Schwarz R,Al-Masoudi A,D?rscher S,Herbers S,H?fner S,Sterr U,Lisdat C 2018 ar Xiv:1803.03157[physics,physics:quant-ph][2018-3-8]
[87]Phillips W D,Metcalf H 1982 Phys.Rev.Lett.48 596
[88]Xu X Y,Wang W L,Zhou Q H,Li G H,Jiang H L,Chen L F,Ye J,Zhou Z H,Cai Y,Tang H Y,Zhou M2009 Front.Phys.China 4 160
[89]Wang S K,Wang Q,Lin Y G,Wang M M,Lin B K,Zang E J,Li T C,Fang Z J 2009 Chin.Phys.Lett.26093202
[90]Zhao P Y,Xiong Z X,Long Y,He L X,LüB L 2009Chin.Phys.Lett.26 083702
[91]Hill I R,Ovchinnikov Y B,Bridge E M,Curtis E A,Gill P 2014 J.Phys.B:At.Mol.Opt.Phys.47 075006
[92]Wang Q,Lin Y G,Gao F L,Li Y,Lin B K,Meng F,Zang E J,Li T C,Fang Z J 2015 Chin.Phys.Lett.32100701
[93]Koller S B,Grotti J,Vogt S,Al-Masoudi A,D?rscher S,H?fner S,Sterr U,Lisdat C 2017 Phys.Rev.Lett.118073601
[94]Li Y,Ido T,Eichler T,Katori H 2004 Appl.Phys.B:Lasers Opt.78 315
[95]Ferrari G,Cancio P,Drullinger R,Giusfredi G,Poli N,Prevedelli M,Toninelli C,Tino G M 2003 Phys.Rev.Lett.91 243002
[96]Loftus T H,Ido T,Boyd M M,Ludlow A D,Ye J 2004Phys.Rev.A 70 063413
[97]Mukaiyama T,Katori H,Ido T,Li Y,Kuwata-Gonokami M 2003 Phys.Rev.Lett.90 113002
[98]Chanelière T,He L,Kaiser R,Wilkowski D 2008 Eur.Phys.J.:At.Mol.Opt.Plasma Phys.46 507
[99]Sterr U,Degenhardt C,Stoehr H,Lisdat C,Schnatz H,Helmcke J,Riehle F,Wilpers G,Oates C,Hollberg L2004 Comptes Rendus Phys.5 845
[100]Boyd M M,Zelevinsky T,Ludlow A D,Foreman S M,Blatt S,Ido T,Ye J 2006 Science 314 1430
[101]Blatt S,Thomsen J W,Campbell G K,Ludlow A D,Swallows M D,Martin M J,Boyd M M,Ye J 2009 Phys.Rev.A 80 052703
[102]Martin M,Bishof M,Swallows M D,Zhang X,Benko C,von Stecher J,Gorshkov A V,Rey A M,Ye J 2013Science 341 632
[103]Matei D G,Legero T,H?fner S,Grebing C,Weyrich R,Zhang W,Sonderhouse L,Robinson J M,Ye J,Riehle F,Sterr U 2017 Phys.Rev.Lett.118 263202
[104]Derevianko A,Katori H 2011 Rev.Mod.Phys.83 331
[105]Boyd M,Zelevinsky T,Ludlow A,Blatt S,ZanonWillette T,Foreman S,Ye J 2007 Phys.Rev.A 76022510
[106]Falke S,Schnatz H,Winfred J S R V,Middelmann T,Vogt S,Weyers S,Lipphardt B,Grosche G,Riehle F,Sterr U,Lisdat C 2011 Metrologia 48 399
[107]Westergaard P G,Lodewyck J,Lorini L,Lecallier A,Burt E A,Zawada M,Millo J,Lemonde P 2011 Phys.Rev.Lett.106 210801
[108]Wang Q,Lin Y G,Li Y,Lin B K,Meng F,Zang E J,Li T C,Fang Z J 2014 Chin.Phys.Lett.31 123201
[109]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,Naidon P,Julienne P,Ye J,Ludlow A D 2009 Science 324 360
[110]Ramsey N F 1950 Phys.Rev.78 695
[111]Campbell G K,Ludlow A D,Blatt S,Thomsen J W,Martin M J,de Miranda M H G,Zelevinsky T,Boyd M M,Ye J,Diddams S A,Heavner T P,Parker T E,Jefferts S R 2008 Metrologia 45 539
[112]Ludlow A D,Zelevinsky T,Campbell G K,Blatt S,Boyd M M,de Miranda M H G,Martin M J,Thomsen J W,Foreman S M,Ye J,Fortier T M,Stalnaker J E,Diddams S A,Le Coq Y,Barber Z W,Poli N,Lemke N D,Beck K M,Oates C W 2008 Science 319 1805
[113]Peik E,Schneider T,Tamm C 2006 J.Phys.B:At.Mol.Opt.Phys.39 145
[114]Dick G J 1987[http://www.dtic.mil/docs/citations/ADA502386][2018-7-10]
[115]Dick G J,Greenhall C A 1998 Proceedings of the1998 IEEE International Frequency Control Symposium Pasadena,CA,USA,May 29,1998 p99
[116]Westergaard P,Lodewyck J,Lemonde P 2010 IEEE Trans.Ultrason.Ferroelectr.Freq.Control 57 623
[117]Stefani F,Lopez O,Bercy A,Lee W K,Chardonnet C,Santarelli G,Pottie P E,Amy-Klein A 2015 J.Opt.Soc.Am.B 32 787
[118]Lopez O,Amy-Klein A,Lours M,Chardonnet C,Santarelli G 2010 Appl.Phys.B 98 723
[119]Terra O,Grosche G,Predehl K,Holzwarth R,Legero T,Sterr U,Lipphardt B,Schnatz H 2009 Appl.Phys.B 97541
[120]Droste S,Ozimek F,Udem T,Predehl K,H?nsch T W,Schnatz H,Grosche G,Holzwarth R 2013 Phys.Rev.Lett.111 110801
[121]Ma C Q,Wu L F,Jiang Y Y,Yu H F,Bi Z Y,Ma L S2015 Chin.Phys.B 24 084209
[122]Lisdat C,Grosche G,Quintin N,Shi C,Raupach S M F,Grebing C,Nicolodi D,Stefani F,Al-Masoudi A,D?rscher S,H?fner S,Robyr J L,Chiodo N,Bilicki S,Bookjans E,Koczwara A,Koke S,Kuhl A,Wiotte F,Meynadier F,Camisard E,Abgrall M,Lours M,Legero T,Schnatz H,Sterr U,Denker H,Chardonnet C,Coq Y L,Santarelli G,Amy-Klein A,Targat R L,Lodewyck J,Lopez O,Pottie P E 2016 Nat.Commun.7 12443
[123]Falke S,Misera M,Sterr U,Lisdat C 2012 Appl.Phys.B 107 301
[124]Ye J,Peng J L,Jones R J,Holman K W,Hall J L,Jones D J,Diddams S A,Kitching J,Bize S,Bergquist J C,Hollberg L W,Robertsson L,Ma L S 2003 J.Opt.Soc.Am.B 20 1459
[125]Wang B,Gao C,Chen W L,Miao J,Zhu X,Bai Y,Zhang J W,Feng Y Y,Li T C,Wang L J 2012 Sci.Rep.2 556
[126]Ye J,Cundiff S T 2005 Femtosecond Optical Frequency Comb:Principle,Operation,and Applications(Norwell,MA:Springer Verlag)p18
[127]Ma L S,Bi Z Y,Bartels A,Robertsson L,Zucco M,Windeler R S,Wilpers G,Oates C,Hollberg L,Diddams S A 2004 Science 303 1843
[128]Fang S,Jiang Y Y,Chen H Q,Yao Y,Bi Z Y,Ma L S2015 Chin.Phys.B 24 084209
[129]Benko C,Ruehl A,Martin M J,Eikema K S E,Fermann M E,Hartl I,Ye J 2012 Opt.Lett.37 2196
[130]Legero T,Lisdat C,Vellore Winfred J S R,Schnatz H,Grosche G,Riehle F,Sterr U 2009 IEEE Trans.Instrum.Meas.58 1252
[131]Nicolodi D,Argence B,Zhang W,Targat R L,Santarelli G,Coq Y L 2014 Nat.Photon.8 219
[132]Leopardi H,Davila-Rodriguez J,Quinlan F,Olson J,Sherman J A,Diddams S A,Fortier T M 2017 Optica 4879
[133]Ohmae N,Kuse N,Fermann M E,Katori H 2017 Appl.Phys.Express 10 062503
[134]Falke S,Lemke N,Grebing C,Lipphardt B,Weyers S,Gerginov V,Huntemann N,Hagemann C,Al-Masoudi A,H?fner S,Vogt S,Sterr U,Lisdat C 2014 New J.Phys.16 073023
[135]Lin Y G,Wang Q,Li Y,Meng F,Lin B K,Zang E J,Sun Z,Fang F,Li T C,Fang Z J 2016 J.Phys.:Conf.Ser.723 012021
[136]Hazlett E L,Zhang Y,Stites R W,Gibble K,O’Hara K M 2013 Phys.Rev.Lett.110 160801
[137]Lemke N D,von Stecher J,Sherman J A,Rey A M,Oates C W,Ludlow A D 2011 Phys.Rev.Lett.107103902
[138]Swallows M D,Bishof M,Lin Y,Blatt S,Martin M J,Rey A M,Ye J 2011 Science 331 1043
[139]Barber Z,Stalnaker J,Lemke N,Poli N,Oates C,Fortier T,Diddams S,Hollberg L,Hoyt C,Taichenachev A,Yudin V 2008 Phys.Rev.Lett.100 103002
[140]Brown R C,Phillips N B,Beloy K,Mc Grew W F,Schioppo M,Fasano R J,Milani G,Zhang X,Hinkley N,Leopardi H,Yoon T H,Nicolodi D,Fortier T M,Ludlow A D 2017 Phys.Rev.Lett.119 253001
[141]Itano W M,Lewis L L,Wineland D J 1982 Phys.Rev.A 25 1233
[142]Hollberg L,Hall J L 1984 Phys.Rev.Lett.53 230
[143]Porsev S G,Derevianko A 2006 Phys.Rev.A 74 020502
[144]Safronova M S,Porsev S G,Safronova U I,Kozlov M G,Clark C W 2013 Phys.Rev.A 87 012509
[145]Yudin V I,Taichenachev A V,Okhapkin M V,Bagayev S N,Tamm C,Peik E,Huntemann N,Mehlst?ubler T E,Riehle F 2011 Phys.Rev.Lett.107 030801
[146]Middelmann T,Lisdat C,Falke S,Winfred J S R V,Riehle F,Sterr U 2011 IEEE Trans.Instrum.Meas.602550
[147]Middelmann T,Falke S,Lisdat C,Sterr U 2012 Phys.Rev.Lett.109 263004
[148]Beloy K,Hinkley N,Phillips N B,Sherman J A,Schioppo M,Lehman J,Feldman A,Hanssen L M,Oates C W,Ludlow A D 2014 Phys.Rev.Lett.113 260801
[149]Lodewyck J,Zawada M,Lorini L,Gurov M,Lemonde P2012 IEEE Trans.Ultrason.Ferroelectr.Freq.Control59 411
[150]Beloy K,Zhang X,Mc Grew W F,Hinkley N,Yoon T H,Nicolodi D,Fasano R J,Sch?ffer S A,Brown R C,Ludlow A D 2018 Phys.Rev.Lett.120 183201
[151]Ushijima I,Takamoto M,Das M,Ohkubo T,Katori H2015 Nat.Photon.9 185
[152]Bowden W,Hobson R,Huillery P,Gill P,Jones M P A,Hill I R 2017 Phys.Rev.A 96 023419
[153]Baillard X,FouchéM,Le Targat R,Westergaard P G,Lecallier A,Chapelet F,Abgrall M,Rovera G D,Laurent P,Rosenbusch P,Bize S,Santarelli G,Clairon A,Lemonde P,Grosche G,Lipphardt B,Schnatz H 2008Eur.Phys.J.:At.Mol.Opt.Plasma Phys.48 11
[154]Le Targat R,Lorini L,Le Coq Y,Zawada M,Guéna J,Abgrall M,Gurov M,Rosenbusch P,Rovera D G,Nagórny B,Gartman R,Westergaard P G,Tobar M E,Lours M,Santarelli G,Clairon A,Bize S,Laurent P,Lemonde P,Lodewyck J 2013 Nat.Commun.4 2109
[155]Lodewyck J,Bilicki S,Bookjans E,Robyr J L,Shi C,Vallet G,Targat R L,Nicolodi D,Coq Y L,Guéna J,Abgrall M,Rosenbusch P,Bize S 2016 Metrologia 531123
[156]Levine J 2008 Metrologia 45 S162
[157]Fujieda M,Piester D,Gotoh T,Becker J,Aida M,Bauch A 2014 Metrologia 51 253
[158]Hong F L,Musha M,Takamoto M,Inaba H,Yanagimachi S,Takamizawa A,Watabe K,Ikegami T,Imae M,Fujii Y,Amemiya M,Nakagawa K,Ueda K,Katori H 2009 Opt.Lett.34 692
[159]Hachisu H,Petit G,Nakagawa F,Hanado Y,Ido T 2017Opt.Express 25 8511
[160]Baynham C F A,Godun R M,Jones J M,King S A,Nisbet-Jones P B R,Baynes F,Rolland A,Baird P E G,Bongs K,Gill P,Margolis H S 2018 J.Mod.Opt.65585
[161]Boyd M M,Ludlow A D,Blatt S,Foreman S M,Ido T,Zelevinsky T,Ye J 2007 Phys.Rev.Lett.98 083002
[162]Yamaguchi A,Shiga N,Nagano S,Li Y,Ishijima H,Hachisu H,Kumagai M,Ido T 2012 Appl.Phys.Express5 022701
[163]Akamatsu D,Inaba H,Hosaka K,Yasuda M,Onae A,Suzuyama T,Amemiya M,Hong F L 2014 Appl.Phys.Express 7 012401
[164]Tanabe T,Akamatsu D,Kobayashi T,Takamizawa A,Yanagimachi S,Ikegami T,Suzuyama T,Inaba H,Okubo S,Yasuda M 2015 J.Phys.Soc.Jpn.84 115002
[165]Grebing C,Al-Masoudi A,D?rscher S,H?fner S,Gerginov V,Weyers S,Lipphardt B,Riehle F,Sterr U,Lisdat C 2016 Optica 3 563
[166]Hachisu H,Petit G,Ido T 2017 Appl.Phys.B 123 34
[167]Szymaniec K,Park S E,Marra G,Cha?upczak W 2010Metrologia 47 363
[168]Gerginov V,Nemitz N,Weyers S,Schr?der R,Griebsch D,Wynands R 2010 Metrologia 47 65
[169]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 52454
[170]Ido T,Hachisu H,Nakagawa F,Hanado Y 2016 J.Phys.:Conf.Ser.723 012041
[171]Yao J,Parker T E,Ashby N,Levine J 2018 IEEE Trans.Ultrason.Ferroelectr.Freq.Control 65 127
[172]Gill P 2011 Phil.Trans.R.Soc.A 369 4109
[173]Riehle F 2015 Comptes Rendus Physique 16 506
[174]Chou C W,Hume D B,Rosenband T,Wineland D J2010 Science 329 1630
[175]Takano T,Takamoto M,Ushijima I,Ohmae N,Akatsuka T,Yamaguchi A,Kuroishi Y,Munekane H,Miyahara B,Katori H 2016 Nat.Photonics 10 662
[176]Grotti J,Koller S,Vogt S,H?fner S,Sterr U,Lisdat C,Denker H,Voigt C,Timmen L,Rolland A,Baynes F N,Margolis H S,Zampaolo M,Thoumany P,Pizzocaro M,Rauf B,Bregolin F,Tampellini A,Barbieri P,Zucco M,Costanzo G A,Clivati C,Levi F,Calonico D 2018 Nat.Phys.14 437
[177]Shang H,Zhang X,Zhang S,Pan D,Chen H,Chen J2017 Opt.Express 25 30459
[178]Zhang S,Zhang X,Cui J,Jiang Z,Shang H,Zhu C,Chang P,Zhang L,Tu J,Chen J 2017 Rev.Sci.Instrum.88 103106
[179]Bize S,Diddams S A,Tanaka U,Tanner C E,Oskay W H,Drullinger R E,Parker T E,Heavner T P,Jefferts S R,Hollberg L,Itano W M,Bergquist J C 2003 Phys.Rev.Lett.90 150802
[180]Blatt S,Ludlow A D,Campbell G K,Thomsen J W,Zelevinsky T,Boyd M M,Ye J,Baillard X,FouchéM,Le Targat R,Brusch A,Lemonde P,Takamoto M,Hong F L,Katori H,Flambaum V V 2008 Phys.Rev.Lett.100140801
[181]Ludlow A D,Blatt S,Zelevinsky T,Campbell G K,Martin M J,Thomsen J W,Boyd M M,Ye J 2008 Eur.Phys.J.Spec.Top.163 9
[182]Rosenband T,Hume D B,Schmidt P O,Chou C W,Brusch A,Lorini L,Oskay W H,Drullinger R E,Fortier T M,Stalnaker J E,Diddams S A,Swann W C,Newbury N R,Itano W M,Wineland D J,Bergquist J C 2008Science 319 1808
[183]Derevianko A,Pospelov M 2014 Nat.Phys.10 933
[184]Arvanitaki A,Huang J,van Tilburg K 2015 Phys.Rev.D 91 015015
[185]Katori H,Ido T,Kuwatagonokami M 1999 J.Phys.Soc.Jpn.68 2479
[186]Cole G D,Zhang W,Martin M J,Ye J,Aspelmeyer M2013 Nat.Photonics 7 644
[187]Cole G D,Zhang W,Bjork B J,Follman D,Heu P,Deutsch C,Sonderhouse L,Robinson J,Franz C,Alexandrovski A,Notcutt M,Heckl O H,Ye J,Aspelmeyer M 2016 Optica 3 647
[188]Kessler T,Hagemann C,Grebing C,Legero T,Sterr U,Riehle F,Martin M J,Chen L,Ye J 2012 Nat.Photon.6 687
[189]Zhang W,Robinson J M,Sonderhouse L,Oelker E,Benko C,Hall J L,Legero T,Matei D G,Riehle F,Sterr U,Ye J 2017 Phys.Rev.Lett.119 243601
[190]Schioppo M,Brown R C,Mc Grew W F,Hinkley N,Fasano R J,Beloy K,Yoon T H,Milani G,Nicolodi D,Sherman J A,Phillips N B,Oates C W,Ludlow A D2017 Nat.Photonics 11 48
[191]Chen J,Chen X 2005 Proceedings of the 2005 IEEE International Frequency Control Symposium Vancouver,Canada,August 29–31,2005 p608
[192]Bohnet J G,Chen Z,Weiner J M,Meiser D,Holland M J,Thompson J K 2012 Nature 484 78
[193]Norcia M A,Cline J R K,Muniz J A,Robinson J M,Hutson R B,Goban A,Marti G E,Ye J,Thompson J K 2018 Phys.Rev.X 8 021036