[1] Leschiutta S. The definition of the ‘atomic’ second[J]. Metrologia, 42, S10-S19(2005).

[2] General Conference on Weights and Measures. Report of the president of the CIPM on the work accomplished since the 25th meeting of the CGPM[R], 14(2018).

[3] Lin Y G, Liang K, Fang Z J. Time unit-evolution of seconds[J]. China Metrology, 16-17, 49(2018).

[4] Riehle F[M]. Frequency standards: fundamentals and applications, 384-438(2021).

[5] Wang Q, Wei R, Wang Y Z. Atomic fountain frequency standard: principle and development[J]. Acta Physica Sinica, 67, 163202(2018).

[6] Santarelli G, Laurent P, Lemonde P et al. Quantum projection noise in an atomic fountain: a high stability cesium frequency standard[J]. Physical Review Letters, 82, 4619-4622(1999).

[7] Santarelli G, Audoin C, Makdissi A et al. Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 45, 887-894(1998).

[8] Lemonde P, Laurent P, Santarelli G et al[M]. Frequency measurement and control: advanced techniques and future trends, 397, 131-153(2001).

[9] Metcalf H J, van der Straten P[M]. Laser cooling and trapping, 324, 71-76(1999).

[10] Kasevich M A, Riis E, Chu S et al. Rf spectroscopy in an atomic fountain[J]. Physical Review Letters, 63, 612-615(1989).

[11] Clairon A, Salomon C, Guellati S et al. Ramsey resonance in a Zacharias fountain[J]. Europhysics Letters, 16, 165(1991).

[12] Clairon A, Stantarelli G, Laurent P. Frequency standards and metrology[C]. World Scientific, 1-574(1996).

[13] Gerginov V, Nemitz N, Weyers S et al. Uncertainty evaluation of the caesium fountain clock PTB-CSF2[J]. Metrologia, 47, 65-79(2010).

[14] Weyers S, Hübner U, Schröder R et al. Uncertainty evaluation of the atomic caesium fountain CSF1 of the PTB[J]. Metrologia, 38, 343-352(2001).

[15] Heavner T P, Jefferts S R, Donley E A et al. NIST-F1: recent improvements and accuracy evaluations[J]. Metrologia, 42, 411-422(2005).

[16] Bize S, Laurent P, Abgrall M et al. Cold atom clocks and applications[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 38, S449-S468(2005).

[17] Ekstrom C, Peil S, Swanson T et al. Atomic fountains for the USNO master clock[C], 308-313(2008).

[18] Jefferts S R, Shirley J, Parker T E et al. Accuracy evaluation of NIST-F1[J]. Metrologia, 39, 321-336(2002).

[19] Bize S. Tests fondamentaux à l’aide d’horloges à atomes froids de rubidium et de césium[D], 61-87(2001).

[20] Szymaniec K, Chalupczak W, Whibberley P B et al. Evaluation of the primary frequency standard NPL-CsF1[J]. Metrologia, 42, 49-57(2005).

[21] Li R X, Gibble K. Phase variations in microwave cavities for atomic clocks[J]. Metrologia, 41, 376-386(2004).

[22] Li R X, Gibble K. Evaluating and minimizing distributed cavity phase errors in atomic clocks[J]. Metrologia, 47, 534-551(2010).

[23] Chen J, Feng Y X, Li X Z et al. A fully quantum description of the free-energy in high pressure hydrogen[J]. Acta Physica Sinica, 64, 183101(2015).

[24] Kokkelmans S J J M F, Verhaar B J, Gibble K et al. Predictions for laser-cooled Rb clocks[J]. Physical Review A, 56, R4389-R4392(1997).

[25] The Consultative Committee for Time and Frequency. Consultative committee for time and frequency report of the 16th meeting to the International Committee for Weights and Measures[R], 9(2004).

[26] The International Committee for Weights and Measures. Comité international des poids et mesures 95th meeting[R], 153(2006).

[27] International Committee for Weights and Measures. Recommended values of standard frequencies[EB/OL]. https:∥www.bipm.org/en/publications/mises-en-pratique/standard-frequencies-second

[28] Peil S, Hanssen J L, Swanson T B et al. Evaluation of long term performance of continuously running atomic fountains[J]. Metrologia, 51, 263(2014).

[29] Ovchinnikov Y B, Szymaniec K, Edris S. Measurement of rubidium ground-state hyperfine transition frequency using atomic fountains[J]. Metrologia, 52, 595-599(2015).

[30] Lorini L, Pavlenko K, Bize S et al. Preliminary stability analysis of Rb fountains for timescale generation[C], 317-321(2017).

[31] Weyers S, Gerginov V, Kazda M et al. Advances in the accuracy, stability, and reliability of the PTB primary fountain clocks[J]. Metrologia, 55, 789-805(2018).

[32] Peil S, Swanson T B, Hanssen J et al. Microwave-clock timescale with instability on order of 10-17[J]. Metrologia, 54, 247(2017).

[33] Acharya A, Bharath V, Arora P et al. Systematic uncertainty evaluation of the cesium fountain primary frequency standard at NPL India[J]. MAPAN, 32, 67-76(2017).

[34] Beattie S, Jian B, Alcock A J et al. The NRC-FCs2 primary frequency standard at the National Research Council Canada[C], 640-641(2017).

[35] Dunst P, Nagórny B, Lemański D et al. Preliminary evaluation of the AOS-CsF1 primary frequency standard[C], 628-13(2017).

[36] Lee S M, Heo M S, Kwon T Y et al. Increasement of effective number of detected atoms in KRISS-F1(Cs) fountain clock by optical pumping[C], 622(2017).

[37] Ortiz C A, López J M, de Carlos López E et al. Progress in Mexican cesium atomic fountain-CsF1 using an ultra-stable laser[C], 326-327(2017).

[38] Beattie S, Jian B, Alcock J et al. First accuracy evaluation of the NRC-FCs2 primary frequency standard[J]. Metrologia, 57, 035010(2020).

[39] Jian B, Beattie S, Alcock A J et al. Evaluation of the distributed cavity phase shifts of the NRC-FCs2 fountain primary frequency standard[C], 14-18(2019).

[40] Fang F, Li M S, Lin P W et al. NIM5 Cs fountain clock and its evaluation[J]. Metrologia, 52, 454-468(2015).

[41] Wang X B, Shi F F, Gong D L et al. Realization of a free-running timescale based on a CsF1 cesium fountain clock and multiple active hydrogen masers[J]. Metrologia, 57, 065009(2020).

[42] Ruan J, Wang Y B, Chang H et al. Progress towards primary frequency standard[J]. Acta Physica Sinica, 64, 160308(2015).

[43] Shi J R. Research on second-order Zeeman frequency shift and Majorana transition frequency shift in fountain clock NTSC-F2[D], 41-80(2022).

[44] Zhang H, Ruan J, Liu D D et al. Development and preliminary operation of 87Rb continuously running atomic fountain clock at NTSC[J]. IEEE Transactions on Instrumentation and Measurement, 71, 1008312(2022).

[45] Wei R. Design and prior work of a compact rubidium atomic fountain[D], 108-174(2003).

[46] Shi C Y. Operation and performance evaluation of rubidium 87 atomic fountain clock[D], 87-162(2012).

[47] Liu L, Lü D S, Chen W B et al. In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms[J]. Nature Communications, 9, 2760(2018).

[48] Zhao W J, Qian W, Lü D S et al. Improvement of average magnetic field measurement based on magnetic-field-sensitive Ramsey fringes[J]. Optics Letters, 47, 2073-2076(2022).

[49] Lee T, Das T P, Sternheimer R M. Perturbation theory for the Stark effect in the hyperfine structure of alkali-metal atoms[J]. Physical Review A, 11, 1784-1786(1975).

[50] Itano W M, Lewis L L, Wineland D J. Shift of 2S1/2 hyperfine splittings due to blackbody radiation[J]. Physical Review A, 25, 1233-1235(1982).

[51] Simon E, Laurent P, Clairon A. Measurement of the Stark shift of the Cs hyperfine splitting in an atomic fountain[J]. Physical Review A, 57, 436-439(1998).

[52] Levi F, Calonico D, Calosso C E et al. Accuracy evaluation of ITCsF2: a nitrogen cooled caesium fountain[J]. Metrologia, 51, 270-284(2014).

[53] Ghezali S, Laurent P, Lea S N et al. An experimental study of the spin-exchange frequency shift in a laser-cooled cesium fountain frequency standard[J]. Europhysics Letters, 36, 25-30(1996).

[54] Sortais Y, Bize S, Nicolas C et al. Cold collision frequency shifts in a 87Rb atomic fountain[J]. Physical Review Letters, 85, 3117-3120(2000).

[55] Pereira Dos Santos F, Marion H, Bize S et al. Controlling the cold collision shift in high precision atomic interferometry[J]. Physical Review Letters, 89, 233004(2002).

[56] Fertig C, Gibble K. Measurement and cancellation of the cold collision frequency shift in an 87Rb fountain clock[J]. Physical Review Letters, 85, 1622-1625(2000).

[57] Weyers S, Gerginov V, Nemitz N et al. Distributed cavity phase frequency shifts of the caesium fountain PTB-CSF2[J]. Metrologia, 49, 82-87(2012).

[58] Guéna J, Li R X, Gibble K et al. Evaluation of Doppler shifts to improve the accuracy of primary atomic fountain clocks[J]. Physical Review Letters, 106, 130801(2011).

[59] Wynands R, Weyers S. Atomic fountain clocks[J]. Metrologia, 42, S64-S79(2005).

[60] Guéna J, Dudle G, Thomann P. An experimental study of intermodulation effects in an atomic fountain frequency standard[J]. European Physical Journal Applied Physics, 38, 183-189(2007).

[61] Devenoges L, di Domenico G, Stefanov A et al. Measurement of the magnetic field profile in the atomic fountain clock FoCS-2 using Zeeman spectroscopy[J]. Metrologia, 54, 239-246(2017).

[62] Wang Q, Zhang N, Guang W et al. Precision measurements of the ground-state hyperfine splitting of 85Rb using an atomic fountain clock[J]. Physical Review A, 100, 022510(2019).

[63] Guena J, Abgrall M, Rovera D et al. Progress in atomic fountains at LNE-SYRTE[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 59, 391-410(2012).

[64] Guéna J, Abgrall M, Rovera D et al. Progress in atomic fountains at LNE-SYRTE[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 59, 391-410(2012).

[65] Li R X, Gibble K, Szymaniec K. Improved accuracy of the NPL-CsF2 primary frequency standard: evaluation of distributed cavity phase and microwave lensing frequency shifts[J]. Metrologia, 48, 283-289(2011).

[66] Fang F, Chen W L, Liu K et al. Advances in the NIM Cs fountain clocks[C], 14-18(2019).

[67] Domnin Y S, Baryshev V N, Boyko A I et al. The MTsR-F2 fountain-type cesium frequency standard[J]. Measurement Techniques, 55, 1155-1162(2013).

[68] Lin R, Wang X L, Liu D D et al. Research on differential measurement method of the cold atomic collision shift in the Cesium fountain clock[J]. Journal of Time and Frequency, 40, 207-212(2017).

[69] Ruan J, Wang X L, Liu D D et al. Progress of cesium fountain clock NTSC-F1[J]. Journal of Time and Frequency, 39, 138-149(2016).

[70] Blinov I, Boiko A, Kosheliaevskii N et al. First experiments on application of Rb fountain frequency standards for TA(SU) time scale maintenance[C], 257-262(2018).

[71] Zhang N, Wang Q, Zhao W J et al. Design of low phase noise microwave frequency synthesizer for 85Rb fountain clock[J]. Acta Optica Sinica, 40, 1002001(2020).

[72] Besson B, Moutrey M, Galliou S et al. 10 MHz hyperstable quartz oscillators performances[C]. 16, 326-330(99).

[73] Hartnett J G, Nand N R. Ultra-low vibration pulse-tube cryocooler stabilized cryogenic sapphire oscillator with 10-16 fractional frequency stability[J]. IEEE Transactions on Microwave Theory and Techniques, 58, 3580-3586(2010).

[74] Hartnett J G, Parker S R, Ivanov E N et al. Radio frequency signals synthesised from independent cryogenic sapphire oscillators[J]. Electronics Letters, 50, 294-295(2014).

[75] Bartels A, Diddams S A, Oates C W et al. Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references[J]. Optics Letters, 30, 667-669(2005).

[76] Fortier T M, Kirchner M S, Quinlan F et al. Generation of ultrastable microwaves via optical frequency division[J]. Nature Photonics, 5, 425-429(2011).

[77] Fortier T M, Rolland A, Quinlan F et al. Optically referenced broadband electronic synthesizer with 15 digits of resolution[J]. Laser & Photonics Reviews, 10, 780-790(2016).

[78] Millo J, Abgrall M, Lours M et al. Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock[J]. Applied Physics Letters, 94, 141105(2009).

[79] Xie X P, Bouchand R, Nicolodi D et al. Photonic microwave signals with zeptosecond-level absolute timing noise[J]. Nature Photonics, 11, 44-47(2017).

[80] Lipphardt B, Grosche G, Sterr U et al. The stability of an optical clock laser transferred to the interrogation oscillator for a Cs fountain[J]. IEEE Transactions on Instrumentation and Measurement, 58, 1258-1262(2009).

[81] Lipphardt B, Gerginov V, Weyers S. Optical stabilization of a microwave oscillator for fountain clock interrogation[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 64, 761-766(2017).

[82] Portuondo-Campa E, Buchs G, Kundermann S et al. Ultra-low phase-noise microwave generation using a diode-pumped solid-state laser based frequency comb and a polarization-maintaining pulse interleaver[J]. Optics Express, 23, 32441-32451(2015).

[83] Yan L L, Zhao W Y, Zhang Y Y et al. Photonic generation of RF and microwave signal with relative frequency instability of 10-15[J]. Chinese Physics B, 27, 030601(2018).

[84] Dai S Y, Fang F, Cao S Y et al. The ultra-stable microwave based on ultra-stable laser[J]. Proceedings of SPIE, 10457, 1045722(2017).

[85] Wang L K, Huang J C, Liu L et al. Low insertion loss optical pulse interleaving for ultra-low phase noise photonic microwave generation[J]. Optics Express, 25, 12161-12170(2017).

[86] Duan Y F, Huang Y F, Li Y L et al. All-fiber-based photonic microwave generation with 10-15 frequency instability[J]. Chinese Optics Letters, 20, 021406(2022).

[87] Huang Y F, Hu D, Ye M F et al. All-fiber-based ultrastable laser with long-term frequency stability of 1.1×10-14[J]. Chinese Optics Letters, 21, 031404(2023).

[88] Li M, Huang Y F, Ye M F et al. Low-noise frequency stabilized laser for space-based gravitational wave detection[J]. Acta Optica Sinica, 43, 1914001(2023).

[89] Heavner T P, Hollberg L, Jefferts S R et al. Characterization of a cold cesium source for PARCS: primary atomic reference clock in space[C]. CPEM, 313-314(19).

[90] Laurent P, Lemonde P, Simon E et al. A cold atom clock in absence of gravity[J]. The European Physical Journal D: Atomic, Molecular, Optical and Plasma Physics, 3, 201-204(1998).

[91] Bian F G, Wei R, Jiang H F et al. A movable-cavity cold atom space clock[J]. Chinese Physics Letters, 22, 1645-1648(2005).

[92] Lü D S, Liu L, Wang Y Z. Space cold atomic clock and its scientific applications[J]. Manned Spaceflight, 17, 47-51(2011).

[93] Wang X Q, Wang Y Z. Frequency shifts of a new prototype space atomic clock[J]. Chinese Journal of Lasers, 27, 401-406(2000).

[94] Lü D S, Peng X K, Ren W et al. Design of a space atomic clock with intracavity cooling[C], 623-624(2017).

[95] Altschul B, Bailey Q G, Blanchet L et al. Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission[J]. Advances in Space Research, 55, 501-524(2015).

[96] Ren W, Gao Y C, Li T et al. Microwave interrogation cavity for the rubidium space cold atom clock[J]. Chinese Physics B, 25, 060601(2016).

[97] Bauch A, Achkar J, Bize S et al. Comparison between frequency standards in Europe and the USA at the 10-15 uncertainty level[J]. Metrologia, 43, 109-120(2006).

[98] Riedel F, Al-Masoudi A, Benkler E et al. Direct comparisons of European primary and secondary frequency standards via satellite techniques[J]. Metrologia, 57, 045005(2020).

[99] Bureau International des Poids et Mesures. Primary and secondary frequency standards participating to TAI[EB/OL]. https:∥webtai.bipm.org/database/show_psfs.html

[100] Mehlstäubler T E, Grosche G, Lisdat C et al. Atomic clocks for geodesy[J]. Reports on Progress in Physics, 81, 064401(2018).