The Development of Optical Frequency Standards and its Application to Space Missions

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

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

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

5. Authors Lab Atoms and transitionsR /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. ASTROD Symposium 2006, July 14-16, Beijing Df1 F Optical frequency comb Control the carrier envelope phase offset (CEO) is a very important topics in ultrafast science and frequency metrology. E(w,t) =E0(t)exp(iw t+f) CEO lead to the comb shift Df =2pd /F Repetition rate f= c /2nl Longtitudinal mode frequency fn=d+nF D.J.Jones et al., Science 288, 635(2000)

8. ASTROD Symposium 2006, July 14-16, Beijing fs laser spetrum Broaden the femtosecond laser spectrum to cover an octave by photonic crystal fiber (PCF). f1=d+nF f2=d+2nF Heterodyne measure the beat of 2f1and f2 will reveal the signal d 2 f1 - f2 = 2(nF+d) -(2nF+d ) = d

9. 3.2 Generation of Continuum with PCF

10. Frequency Measurement Experimental Layout antenna Reference 10MHz Phase loop for repetition rate Phase loop for CEO Pump Laser PCF 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. ASTROD Symposium 2006, July 14-16, Beijing Aperture Aperture Side view Reflection Prism Temperature control of I2 cell Reflection Prism PBS3 EOM PD & pre-amplifier 532nm Aperture AOM Nd:YAG Laser 1064nm /4 PBS2 PBS1 /2 /2 35 cm × 70 cm Optical Parts of 532nm I2-stabilizedNd:YAG Laser

13. 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 Molecular Iodine Absorption Cell quartz glass 3-stage cooling Sealed box 3.Filled with highly pure iodine at AIST of Japan or JLAST,CAS, China Cold finger 2.Baked and vacuumized 3 days continuously Temperature control components pressure of 0.54 Pa 1.Windows are optically contacted to the tube 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

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

15. ASTROD Symposium 2006, July 14-16, Beijing Modulated probe beam Frequency stabilized electrics PD & pre-amplifier Filter and amplifier AOM 10MHz 80MHz Frequency synthesizer Rubidium clock Monolithic ring laser and SHG AOM Drive EOM Slow Fast IF EOM Driver Servo control PI control RF LO Phase shift Oscillator DBM Electrics Parts of I2-stabilized Nd:YAG Laser

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

17. ASTROD Symposium 2006, July 14-16, Beijing Allan Standard Deviation of Each Laser (10-15 )

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

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

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) 199Hg + 2S 1/2-2D 5/2 282 1.7 6.7 10 171Yb + 2S 1/2-2D 3/2 435 3.1 30 6 88Sr + 2S 1/2-2D 3/2 674 0.4 70 100 115In + 1S 0-3P0 236 0.8 170 230 171Yb + 2S 1/2-2F 7/2 467 ~10-9 180 230 40Ca + 2S 1/2- 2D5/2 729 0.2 1000 • Frequency value of 40Ca + was not recommended by CIPM as reference for the • Realization of the meter

22. Contributions to the standard uncertainty of the 40Ca 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 Contributions4 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  8350 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 : ： 199Hg +,115In + ,88Sr + , 87Sr + , 171Yb + ,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. ASTROD Symposium 2006, July 14-16, Beijing 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 tA 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 tA according to clock B. Because the relative motion is uniform,  does not depend on tA . If there is no relative motion between A and B,  = 1. 2. If B sends two signals to Awhich are spaced tB seconds apart according to clock B. According relativity principle, the two signals will arrive at A with time spacing  tB as measured by A. From the definition of  given above, we see that  = (t2B– t1B)/(t2A– t1A) = (t3A– t2A )/(t2B– t1B)  =[(t3A– t2A )/(t2A– t1A )]1/2

31. Locking Without Locking

32. ASTROD Symposium 2006, July 14-16, Beijing Method of Synchronization If B were synchronized to A, the time reading t1Band t2B would become s1Band s2B . This is accomplished by determining s1B , which determines the correction s1B - t1B that needs to be applied, defined as  B . One determines s1B by assuming the clocks were synchronized , so that each would indicate the same time t0 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 t0 according to synchronized clock B. We have  = (s1B– t0)/(t1A– t0) = (t2A– t0)/(s1B– t0) , 2 = (t2A– t0)/(t1A– t0) Then, t0= (2t1A– t2A)/(2 –1) , s1B= (t2A +t1A)/(+1). Define the starred distance d1ABfrom A to B at the instant s1B of reception of the signal sent by A at time t1A , as follow: d1AB= c (s1B– t1A), where c is the speed of light as it travels from A to B. Then d1AB= c (t2A– t1A)/(+1). Now define the starred radial velocity vrAB between A and B as follow: vrAB=d1AB/s1B= [c (t2A–t1A)/(+1)]/[(t2A+t1A)/(+1)] =c (t2A–t1A)/(t2A+t1A) = c (-1)/.

33. ASTROD Symposium 2006, July 14-16, Beijing • 1. Define the characteristic parameter of relative motion : • assume that A sends two signals to B which are spaced tA 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 tA according to clock B. Because the relative motion is uniform,  does not depend on tA.If there is no relative motion between A and B,  = 1. • If B sends two signals to A which are spaced tB seconds apart according to clock B. According relativity principle, the two signals will arrive at A with time spacing tB as measured by A. From the definition of  given above, we see that •  = (t2B – t1B )/(t2A – t1A ) • = (t3A – t2A )/(t2A – t1A ) •  =[(t3A – t2A )/(t2A – t1A )]1/2 Method of synchronization between satellite clock B and earth reference clock A:

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

35. One determines s1B by assuming the clocks were synchronized, so that each would indicate the same timet0 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 t0 according to synchronized clock B. We have  = (s1B– t0)/(t1A– t0) = (t2A– t0)/(s1B– t0 ) , 2 = (t2A– t0)/(t1A– t0) Then, t 0= (2t1A– t2A)/(2 –1) , s1B= (t2A+t1A)/(+1). Define the starred distance d 1ABfrom A to B at the instant s1B of reception of the signal sent by A at time t1A , as follow: d 1AB= c (s1B– t1A), where c is the speed of light as it travels from A to B. Then d1AB = c (t2A– t1A)/(+1). Now define the starred radial velocity v rAB between A and B as follow: v rAB=d 1AB/s 1B= [c (t2A–t1A)/(+1)]/[(t2A+ t1A)/(+1)] = c (t2A–t1A)/(t2A+t1A)= c (-1)/. ASTROD Symposium 2006, July 14-16, Beijing Method of Synchronization If B were synchronized to A, the time reading t1Band t1B would become s1Band s2B . This is accomplished by determining s1B , which determines the correction s1B - t1B that needs to be applied, defined as B .

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