1. The Development of Optical Frequency Standards and its Application to Space Missions Naicheng Shen Joint Laboratory of Advanced Technology in Measurements ( 中科院计量测试高技术联合实验室 ), Institute of Physics Chinese Academy of Sciences, Beijing 100080 ASTROD Symposium 2006, July 14-16, Beijing

2. Outline  Motivation and Background  Optical Frequency Standards  532 nm Iodine Stabilized Nd:YAG Laser  Optical Frequency Comb  A Method of Synchronization of Clocks Using  Signals From Orbiting Satellite such as GPS ASTROD Symposium 2006, July 14-16, Beijing

3. Motivation  To develop optical frequency standads  To improve on reproducibility of 532 nm iodine stabilized Nd:YAG laser  To pursue phase control femtosecond laser  To develop optical frequency comb  To develop a new technology for synchronization of clocks ASTROD Symposium 2006, July 14-16, Beijing

5. AuthorsLabAtoms and transitions R  /m  1 Andreae et al.(1992) MPQ H ： 1S-2S 10 973 731.568 41(42) Nez et al. (1992) LKB H ： 2S-8S/8D 10 973 731.568 30(31) Weitz et al. (1995) MPQ H ： 1S-2S 10 973 731.568 44(31) Bourzeix et al. (1996) LKB H ： 2S-8S/8D 10 973 731.568 36(18) de Beauvoir et al. (1997) LKB LPTF H,D ： 2S-8S/8D 10 973 731.568 59(10) Udem et al. (1997) MPQ H ： 1S-2S 10 973 731.568 639(91) ASTROD Symposium 2006, July 14-16, Beijing

7. F  1 Control the carrier envelope phase offset (CEO) is a very important topics in ultrafast science and frequency metrology. E(w,t) =E 0 (t)exp(iw t+f) CEO lead to the comb shift Df =2pd /F Repetition rate f= c /2nl Longtitudinal mode frequency f n =d+nF Optical frequency comb  D.J.Jones et al., Science 288, 635(2000) ASTROD Symposium 2006, July 14-16, Beijing

8. fs laser spetrum Broaden the femtosecond laser spectrum to cover an octave by photonic crystal fiber (PCF). f 1 =d+nF f 2 =d+2nF Heterodyne measure the beat of 2f 1 and f 2 will reveal the signal d 2 f 1 - f 2 = 2(nF+d) -(2nF+d ) = d ASTROD Symposium 2006, July 14-16, Beijing

9. 3.2 Generation of Continuum with PCF

10. Frequency Measurement Experimental Layout antenna Pump Laser PCF Reference 10MHz Phase loop for repetition rate Phase loop for CEO Grating

11. 532 nm iodine stabilized Nd:YAG frequency standard Dr R. L. Byer Groups, Stanford University, 1992 Unprecedented frequency stability: 5  10 -14 (1 s), 5  10 -15 (after 400 s), Dr J. L. Hall Groups, JILA,1999 Frequency stability: 5  10 -14 (relative short term), 6  10 -15 (longer durations), BIPM, 2001 New hyperfine structure transitions and frequency stability and reproducibility had obtained exciting results at AIST Absolute frequency measurements have been developed in several countries The accuracy and long term stability are similar to the small Cs clock of CCTV The short term stability depend on itself Specifications Refer to the small Cs clock (HP-5071

12. Optical Parts of 532nm I 2 -stabilized Nd:YAG Laser 532nm 1064nm Reflection Prism Reflection Prism Aperture AOM EOM PD & pre-amplifier Nd:YAG Laser PBS1 /4 /2 PBS2 PBS3 Temperature control of I 2 cell Side view Aperture 35 cm × 70 cm ASTROD Symposium 2006, July 14-16, Beijing

13. Molecular Iodine Absorption Cell 3-stage cooling quartz glass Temperature control Cold finger Sealed box 1.Windows are optically contacted to the tube 2.Baked and vacuumized 3 days continuously 3.Filled with highly pure iodine at AIST of Japan or JLAST,CAS, China 4.Applied 3-stage cooling 5. Using a sealed box for 6. The temperature is set ensured lower temperature isolating the cooling at - 18  C, a vapor components pressure of 0.54 Pa ASTROD Symposium 2006, July 14-16, Beijing 4.Applied 3-stage cooling 5. Using a sealed box for 6. The temperature is set ensured lower temperature isolating the cooling at - 18  C, a vapor components pressure of 0.54 Pa

14. Optical Extending in Lengthways and Transverse Orientation Bigger beam diameter benefit for increasing transverse transit time Low vapor pressure Narrow linewidth Good SNR ASTROD Symposium 2006, July 14-16, Beijing

15. Electrics Parts of I 2 -stabilized Nd:YAG Laser Modulated probe beam Monolithic ring laser and SHG PD & pre-amplifierFilter and amplifier Servo control SlowFast PI control DBMOscillatorPhase shift EOM Driver EOM AOM AOM Drive Frequency synthesizer Rubidium clock RF LO IF 10MHz 80MHz Frequency stabilized electrics ASTROD Symposium 2006, July 14-16, Beijing

16. Beat Frequency measurements ASTROD Symposium 2006, July 14-16, Beijing

17. Allan Standard Deviation of Each Laser (  10 -15 ) Averaging time Continuous measurement time （ s ） 15  10 4 5  10 4 2  10 4 1  10 4 6  10 3 1s24.1123.4422.0121.5720.57 10s8.3317.7057.2377.3286.906 100s4.5094.8623.9874.4143.950 1000s3.8603.4543.3743.6252.541 2000s3.8863.1413.5961.240 5000s4.0251.967 10000s3.864 ASTROD Symposium 2006, July 14-16, Beijing

19. Frequency Shift Measurements Pressure frequency shift Power frequency shift ASTROD Symposium 2006, July 14-16, Beijing

20. Theoretical and Current Observed Linewidths of Trapped Ion Clock Transitions Ion Clock (nm) Theoretical Current Lowestune.(1  ) (Hz) transitiuon linewidth(Hz) linewidth(Hz) of fre. meas.(Hz) 199 Hg + 2 S 1/2 - 2 D 5/2 282 1.7 6.7 10 171 Yb + 2 S 1/2 - 2 D 3/2 435 3.1 30 6 88 Sr + 2 S 1/2 - 2 D 3/2 674 0.4 70 100 115 In + 1 S 0 - 3 P 0 236 0.8 170 230 171 Yb + 2 S 1/2 - 2 F 7/2 467 ~10 -9 180 230 40 Ca + 2 S 1/2 - 2 D 5/2 729 0.2 1000 Frequency value of 40 Ca + was not recommended by CIPM as reference for the Realization of the meter

22. Contributions to the standard uncertainty of the 40 Ca optical frequency standard determined at T=3 mK and envisaged for T=6  K Effect T=3mK(Hz) T=6  K (mHz) Residdual fist-order Doppler effect 2.6 150 Second-order Doppler effect 0.005 0.025 Asymmetry of line shape 0.05 50 Other phase Contributions 4 100 Magnetic field(60Hz mT -2 ) 0.1 80 Quadratic Stark effect 0.06 20 (|E|<2V cm -1 ) Blackbody radiation 4.3 50 Servo electronics 3.2 100 Influence of cold atom coll 1.8 260 Statistical uncertainty of 3 <5 frequency comparison Total uncertainty  8 350 Total relative uncertainty  / 2  10 –14 8  10 -16

27. ASTROD Symposium 2006, July 14-16, Beijing The optical part of Sr atom apparatus ， six Brewster’s windows are input sides of lasers ， cool trapped Sr atoms are in the center part

29. Developing Definition of Second and Frequency Standards Cold atom microwave frequency standards: Cs,Rb Optical cold atom frequency standards : Ca, Mg, Sr Ion frequency standards : ： 199 Hg +, 115 In +, 88 Sr +, 87 Sr +, 171 Yb +,Ca + CIPM – CCTF adopted a 2001resolution to seek secondary ‘representations’ of the second. Such representations can be based on the different cold ion and atom standards,both optical and microwave, and would be able to take full advantage of improved stability and reproducibility, but remain limited to the caesium accuracy. This position represents a useful intermediate stage for evaluating the systematics of different systems prior to making any rational choice for a new time definition.

30. Method of synchronization between satellite clock B and earth reference clock A: 1. Define the characteristic parameter of relative motion  : assume that A sends two signals to B which are spaced  t A seconds apart according to clock A. Due to the relative motion of A and B, the two signals will arrive at B with a different time spacing as measured by B. The parameter  is simply the ratio of the latter time spacing to the former, i.e., the two signals arrive with time spacing  t A according to clock B. Because the relative motion is uniform,  does not depend on  t A. If there is no relative motion between A and B,  = 1. 2. If B sends two signals to A which are spaced  t B seconds apart according to clock B. According relativity principle, the two signals will arrive at A with time spacing   t B as measured by A. From the definition of  given above, we see that  = (t 2B – t 1B )/(t 2A – t 1A ) = (t 3A – t 2A )/(t 2B – t 1B )  =[(t 3A – t 2A )/(t 2A – t 1A )] 1/2 ASTROD Symposium 2006, July 14-16, Beijing

31. Without Locking Locking

32. Method of Synchronization If B were synchronized to A, the time reading t 1B and t 2B would become s 1B and s 2B. This is accomplished by determining s 1B, which determines the correction s 1B - t 1B that needs to be applied, defined as  B. One determines s 1B by assuming the clocks were synchronized, so that each would indicate the same time t 0 at the fictional moment of spatial coincidence. Imaging that A sends a radio signal at that very moment. The signal is simultaneously received at time t 0 according to synchronized clock B. We have  = (s 1B – t 0 )/(t 1A – t 0 ) = (t 2A – t 0 )/(s 1B – t 0 ),  2 = (t 2A – t 0 )/(t 1A – t 0 ) Then, t 0 = (  2 t 1A – t 2A )/(  2 –1), s 1B = (t 2A +  t 1A )/(  +1). Define the starred distance d 1AB from A to B at the instant s 1B of reception of the signal sent by A at time t 1A, as follow: d 1AB = c (s 1B – t 1A ), where c is the speed of light as it travels from A to B. Then d 1AB = c (t 2A – t 1A )/(  +1). Now define the starred radial velocity v rAB between A and B as follow: v rAB =d 1AB /s 1B = [c (t 2A –t 1A )/(  +1)]/[(t 2A +  t 1A )/(  +1)] =c (t 2A –t 1A )/(t 2A +  t 1A ) = c (  -1)/ . ASTROD Symposium 2006, July 14-16, Beijing

33. 1. Define the characteristic parameter of relative motion  : assume that A sends two signals to B which are spaced  t A seconds apart according to clock A. Due to the relative motion of A and B, the two signals will arrive at B with a different time spacing as measured by B. The parameter  is simply the ratio of the latter time spacing to the former, i.e., the two signals arrive with time spacing  t A according to clock B. Because the relative motion is uniform,  does not depend on  t A. If there is no relative motion between A and B,  = 1. 2If B sends two signals to A which are spaced  t B seconds apart according to clock B. According relativity principle, the two signals will arrive at A with time spacing   t B as measured by A. From the definition of  given above, we see that  = (t 2B – t 1B )/(t 2A – t 1A ) = (t 3A – t 2A )/(t 2A – t 1A )  =[(t 3A – t 2A )/(t 2A – t 1A )] 1/2 ASTROD Symposium 2006, July 14-16, Beijing Method of synchronization between satellite clock B and earth reference clock A:

34. ASTROD Symposium 2006, July 14-16, Beijing

35. Method of Synchronization If B were synchronized to A, the time reading t 1B and t 1B would become s 1B and s 2B. This is accomplished by determining s 1B, which determines the correction s 1B - t 1B that needs to be applied, defined as  B. One determines s 1B by assuming the clocks were synchronized, so that each would indicate the same timet 0 at the fictional moment of spatial coincidence. Imaging that A sends a radio signal at that very moment. The signal is simultaneously received at time t 0 according to synchronized clock B. We have  = (s 1B – t 0 )/(t 1A – t 0 ) = (t 2A – t 0 )/(s 1B – t 0 ),  2 = (t 2A – t 0 )/(t 1A – t 0 ) Then, t 0 = (  2 t 1A – t 2A )/(  2 –1), s 1B = (t 2A +  t 1A )/(  +1). Define the starred distance d 1AB from A to B at the instant s 1B of reception of the signal sent by A at time t 1A, as follow: d 1AB = c (s 1B – t 1A ), where c is the speed of light as it travels from A to B. Then d 1AB = c (t 2A – t 1A )/(  +1). Now define the starred radial velocity v rAB between A and B as follow: v rAB =d 1AB /s 1B = [c (t 2A –t 1A )/(  +1)]/[(t 2A +  t 1A )/(  +1)] = c (t 2A –t 1A )/(t 2A +  t 1A ) = c (  -1)/ .

36. The End Thank you for your attention! ASTROD Symposium 2006, July 14-16, Beijing