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 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 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 ASTROD Symposium 2006, July 14-16, Beijing

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

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

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

3.2 Generation of Continuum with PCF

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

532 nm iodine stabilized Nd:YAG frequency standard Dr R. L. Byer Groups, Stanford University, 1992 Unprecedented frequency stability: 5  (1 s), 5  (after 400 s), Dr J. L. Hall Groups, JILA,1999 Frequency stability: 5  (relative short term), 6  (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

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

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

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

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

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

Allan Standard Deviation of Each Laser (  ) Averaging time Continuous measurement time （ s ） 15      s s s s s s s3.864 ASTROD Symposium 2006, July 14-16, Beijing

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

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/ Yb + 2 S 1/2 - 2 D 3/ Sr + 2 S 1/2 - 2 D 3/ In + 1 S P Yb + 2 S 1/2 - 2 F 7/2 467 ~ Ca + 2 S 1/2 - 2 D 5/ Frequency value of 40 Ca + was not recommended by CIPM as reference for the Realization of the meter

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 Second-order Doppler effect Asymmetry of line shape Other phase Contributions Magnetic field(60Hz mT -2 ) Quadratic Stark effect (|E|<2V cm -1 ) Blackbody radiation Servo electronics Influence of cold atom coll Statistical uncertainty of 3 <5 frequency comparison Total uncertainty  Total relative uncertainty  / 2  10 –14 8 

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

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.

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,  = 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

Without Locking Locking

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

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:

ASTROD Symposium 2006, July 14-16, Beijing

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)/ .

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