Center for Time and Frequency Korea Research Institute of Standards and Science (KRISS)

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1 Recent Improvements of Yb Optical Lattice Clock at Won-Kyu Lee Chang Yong Park, Dai-Hyuk Yu, Sangkyung Lee, Sang Eon Park, Jongchul Mun, Sang-Bum Lee, Myoung-Sun Heo, and Taeg Yong Kwon Center for Time and Frequency Korea Research Institute of Standards and Science (KRISS)

2 Better Standards, Better Life 2/ 32 Outline of This Talk 1. Introduction evaluation of KRISS Yb Clock 3. System Improvements 4. Summary

3 Better Standards, Better Life 3/ 32 Yb Optical Lattice Clock Optical clocks are surpassing Cs microwave clocks approaching the uncertainty level below Single ion in a Paul trap; Al +, Hg +, Yb +, Sr +, - Neutral atoms in optical lattice; Sr, Yb, Hg, Mg much better short-term stability Brief history of KRISS Yb optical lattice clock ; Start of Yb project, Blue MOT ~8; Green MOT ~9; Trapping in an optical lattice ; Absolute frequency measurement & first uncertainty evaluation (published in Metrologia (2013)) ~1212 ; Further system improvement for better frequency uncertainty

4 Better Standards, Better Life 4/ Yb energy levels 3 D 1 (329.3 ns) 1 P 1 (5.68 ns) 1 st stage cooling & probing (399 nm) 2 nd stage cooling (556 nm) 1398 nm repumping 3 P 2 (15 s) 3 P 1 (866.1 ns) 3 P 0 (20 s) clock 1 transition lattice laser S 0 (578 nm) 759 nm Magic Wavelength 3 P 0 Light shift Clock transition 1 Light shift S 0 Frequency unchanged. H. Katori et al, Phys.Rev. Lett. (2003)

nm) 1398 nm 3 P 2 2 nd stage 3 P 1 cooling 3 P 0 probing

5 Better Standards, Better Life 5/ 32 Timing Sequence of Experiment 3 D 1 1 P 1 repumping 1 st stage cooling (399 nm) 1398 nm 3 P 2 2 nd stage 3 P 1 cooling 3 P 0 probing (556 nm) clock (399 nm) transition (578 nm) 1 S 0 lattice laser 759 nm

6 Better Standards, Better Life 6/ 32 Experimental Setup

7 Better Standards, Better Life 7/ 32 Outline of This Talk 1. Introduction evaluation of KRISS Yb Clock 3. System Improvements 4. Summary

Better Standards, Better Life 8/ 32 Spectrum of

F=1/2 m F =-1/2 m F =1/2 w 0 σ - σ + π π 1 S 0

double peak Lorentzian Curve fitting by double peak

transition frequency Clock laser frequency

8 Better Standards, Better Life 8/ 32 Spectrum of Clock Transition in Yb (I = 1/2) 3 P 0 F=1/2 m F =-1/2 m F =1/2 w 0 σ - σ + π π 1 S 0 F=1/2 m F =-1/2 m F =1/2 B = 0 B 0 Curve fitting by double peak Lorentzian Curve fitting by double peak Lorentzian Average of the two peak; Clock transition frequency Clock laser frequency simultaneously was measured by a optical frequency comb referenced to a H-maser.

9 Better Standards, Better Life 9/ 32 Magic Wavelength in 2011 Magic Wavelength; (79) GHz ; agrees with previous results. Lattice laser frequency was not stabilized but was monitored with a calibrated wavelength meter.

10 Better Standards, Better Life 10 / 32 Collision (Density) Shift in 2011 Density was varied by controlling the blue-mot time Density was varied by controlling the blue-mot time. Collision shift was estimated to be 0.6 (2.7) Hz.

11 Better Standards, Better Life 11 / 32 Absolute Frequency Measurement in 2011 Clock laser frequency simultaneously was measured by a optical frequency comb referenced to a H-maser. Frequency off set of the H-maser; compensated by using TT reported in circular-t. With 592 measurements in three days; (8.1) Hz (1.5x10-14 )

12 Better Standards, Better Life 12 / 32 Absolute Frequency Measurement in 2011 The 3 rd independent measurement of this transition. 4 measurement results have been reported up to now. 40 f (Hz) NMIJ (2009) 10 NIST (2009) KRISS(2011) NMIJ(2012) Kohno et. al., Appl. Phys. Express 2, (2009) Lemke et. al., Phys. Rev. Lett. 103, (2009) Park et. al., Metrologia 50, 119 (2013) Yasuda et. al., Appl. Phys. Express 5, (2012)

13 Better Standards, Better Life 13 / 32 Uncertainty Budget in 2011 Effect U(10-15 ) Mainly limited by clock laser performance Linear lattice ac Stark shift 14 - Large short-term linewidth Hyper polarizability 0.4 (~80 Hz@80 ms) - Large mid-term jitter Second order Zeeman 0.4 (> 500 Hz@10 s) - Supporting points, temperature Gravitational shift 0.2 not optimized Blackbody radiation shift Large residual vibration (2 nd Collisional shift 5.2 floor) - Small control loop bandwidth Total Yb 15 (30 khz)

14 Better Standards, Better Life 14 / Introduction evaluation of KRISS Yb Clock 3. System Improvements 4. Summary

15 Better Standards, Better Life 15 / 32 Strategy for Improvement Effect U(10-15 ) Clock laser improvement: linewidth ~Hz Linear lattice ac Stark shift 14 Build-up cavity for the lattice laser Hyperpolarizability 0.4 Second order Zeeman 0.4 Atomic beam shutter Gravitational shift 0.2 Trap laser system improvement e Blackbody radiation shift nm (master-slave, freq. lock) Collisional shift nm (freq. lock) Total Yb nm (freq. lock) Statistical nm (simple, stable repumping) H-maser link to UTC 9.1 Total 18 Clock laser locking servo

16 Better Standards, Better Life 16 / 32 Clock Laser Improvement 1 Short-term Linewidth 1. Clock was moved to base floor (residual vibration 1/10 ) 2. Feedback bandwidth was increased (35 khz 500 khz) ~ 80 Hz in 2011 < 5 Hz in 2012 ) Beatno ote Signal (a.u ~ 80 Hz e Signal (a.u.) Beatnot Hz RBW=1 Hz Frequency (Hz) Relative Frequency (Hz)

17 Better Standards, Better Life 17 / 32 Clock Laser Improvement 2 Mid-term Jitter ~ 450 Hz in 2011 < 25 Hz in jitter = 467 Hz (in 10 s) 1.2 Bea atnote Signal (a a.u.) Hz RFSA RBW=47 Hz ST=43.2 ms 10 s Max. Hold..u.) tnote Signal (a. Beat jitter = 25 Hz (in 10 s) Relative Frequency (Hz) Relative Frequency (Hz) Possible to obtain the clock transition spectrum at 10-Hz level And the clock laser can be locked to the clock transition.

18 Better Standards, Better Life 18 / 32 Clock Laser Improvement 3 Long-term Drift Super-cavity was temperature-stabilized for the zero-thermal expansion coefficient. Irregular Drift in 2011 Linear Drift (only Creep) in 2012 f(co omb)-f(171) (MHz) , f(171)=518,295,836,590,865 Hz DOY2011 (day) z) Hz requency (khz 5,836,590,865 Relative F from 518, , , , , ,158 Clock Laser Frequency (CAV1) Slope = Hz/s Time since 0:00 of Oct. 1, 2012 (h)

19 Better Standards, Better Life 19 / 32 Clock Transition Spectrum Nearly Fourier transform limited spectrum achieved

20 Better Standards, Better Life 20 / 32 Other Improvements 1 Lattice laser frequency was locked to an optical frequency comb. Build-up cavity for the lattice laser. ; better uncertainty due to lattice Stark shift ; accurate measurement of uncertainty due to hyperpolarizability

21 Better Standards, Better Life 21 / 32 Other Improvements 2 Laser output power and the frequency lock robustness were increased for both MOT. Rep mp laser impro ement Repump laser improvement ; 4 lasers 1 laser

22 Better Standards, Better Life 22 / 32 Lattice Depth and Temperature Vibrational state 3 P 0 Δn=1 Δ n=0 Δ n=-1 v z =73kHz (~400E R ) 3 S 0 Tz= 8.6 μk, Tr = 18.2 μk

23 Better Standards, Better Life 23 / 32 Lattice Beam Waist excited fraction excited fraction frequency offset(hz) frequency offset(hz) Radial sideband: ~220 Hz ω = U νπ r m Beam waist 65 μm Longitudinal sideband: ~82 khz U 0 = hν 4ν 2 z rec

24 Better Standards, Better Life 24 / 32 Spin-Polarization 2 nd MOT transition used as pumping transition with bias B-field 2 nd stage MOOT laser in the B- field direction used for pumping 556 nm laser freq. tuned -3/2 3 P 1 (F=3/2) -3/2 3 P 1 (F=3/2) 3/2 3/2-1/2 1/2 1 S 0 (F=1/2) -1/2 1/2 1 S 0 (F=1/2)

25 Better Standards, Better Life 25 / 32 Observation of Rabi Oscillation

26 Better Standards, Better Life 26 / 32 Laser Lock to Clock Transition Need 4 cycles to locate the center frequency Splitting gives the B-field magnitude s

27 Better Standards, Better Life 27 / 32 Zeeman Shift 2 nd Zeeman shift -1.64(34)x10-16

28 Better Standards, Better Life 28 / 32 Magic Frequency To make full use of the stability of the clock laser, we measure the magic frequency by interleaving deep and shallow depth of the lattice We need to consider density shift accompanying the d1 d2 = Δν/ΔU depth variation to get final magic frequency value and uncertainty. (d1+d2)/2 minimize - Evaluation drift effect of the density shift is underway

29 Better Standards, Better Life 29 / 32 Uncertainty Budget Expected Effect U(10-15 ) Linear lattice ac Stark shift 14 Hyper polarizability Second order Zeeman 0.4 Gravitational i shift Blackbody radiation shift 0.6 Collisional shift 5.2 Total Yb Uncertainty level of is expected to be possible.

Better Standards, Better Life 30 / 32 Second Clock ;

lattice and 2) cryogenic environment to reduce the blackbody

(swinging chamber) clockout trap read transition status

75 W @ 77 K Flange will be modified for UHV use Swing speed

1 Positioning 0 1 mm Uncertainty of BBR shift by PA <

30 Better Standards, Better Life 30 / 32 Second Clock ; Cryogenic y g Cooler We want to have 1) cavity enhanced lattice and 2) cryogenic environment to reduce the blackbody radiation shift uncertainty move the cryogenic chamber! (swinging chamber) clockout trap read transition status Cryogenic chamber T ~ 100 K Weight : 600 g Cooling rate : K Flange will be modified for UHV use Swing speed ~ 3 H z P iti i accuracy (PA) < 0.1 Positioning 0 1 mm Uncertainty of BBR shift by PA < 1*10-18 BBR shift ~ 70 mhz (~1.5x10-16) 18 uncertainty ~2 * Dominated by BBR from holes. Park et. al. EFTF 2013

31 Better Standards, Better Life 31 / 32 Summary Clock laser linewidth of 3.5 Hz achieved Nearly Fourier transform limited spectrum obtained Yb clock parameters characterized - lattice depth, temperature etc. Clock laser locked to the clock transition s) 2 nd Zeeman shift evaluated ( (34)x10-16 ) Magic frequency measured (density shift and other accuracy evaluation are underway) 2 nd clock with cryogenic chamber is under development

32 Better Standards, Better Life 32 / 32 Thank you for your attention ti!

33 Absolute frequency of cesium 6S 8S hyperfine transition by two photon interfered spectrum Chien Ming Wu 1, Tze Wei Liu 1, Shinn Yang Lin 2 and Wang Yau Cheng 1 1 Department of Physics, National Central University, Taoyuan, Taiwan 2 Telecommun. Labs., Taoyuan, Taiwan Published in Optics Letters, Vol. 38 Issue 16, pp (2013)

34 Outline Improving the uncertainty of the absolute frequency measurement to 10 khz. Using an EOM to achieve three tasks simultaneously: 1. narrow the laser linewidth 2. lock the laser frequency to the Cs TPT 3. point-by-point resolve out a narrow spectrum Two-photon interfered spectrum. The spectrum linewidth measurement could be a good guidance of choosing a suitable cesium cell for better frequency accuracy.

35 Cesium 6s 8s two photon transition Energy levels of the cesium atom

36 1. By frequency comparison with standards (1999) By comparing to some frequency standards they said they have adopted a conservative 100 khz uncertainty for the absolute frequencies on these transitions. 13 AOM

37 2. By direct frequency comb spectroscopy (2007) They quote 15 khz uncertainly which is a factor of 6 better than previous results.

38 Table 1: Absolute frequencies of 133 Cs 6S-8S hyperfine transitions * khz; ** khz; * F=3 ** F=4 hyperfine constant (khz) (khz) (khz) 2007 Germany 417 (15) 351 (15) (7) 97 khz 91 khz 1999 France 320 (100) 260 (100) (10) Their results agreed with each other within their claimed uncertainties. However, the 100 khz uncertainty is a conservative estimation. Therefore, it is worthwhile to measure these transitions again.

39 Using an EOM: 1. narrowing the laser linewidth 2. stabilizing the laser frequency 3. resolving the two photon spectrum of the Cs cell#2 simultaneously Stabilized, Unmodulated, and Frequency Variable compensation by changing Laser the intensity driving frequency stabilization of EOM Driving freq. is fixed Two-photon interfered spectrum

Fabry- Perot fixed signal J 12 (M) J 02 (M) J 12 (M) EOM Cs

J 1 1 J 1 f 0 0 1 1 + + + 7p signal PMT 6s J 0 J 1 J 1 106

40 Fabry- Perot fixed signal J 12 (M) J 02 (M) J 12 (M) EOM Cs cell system #2 Mod. Index=0.6 Index=0.76 Index=0.94 Index=1.34 S 1 C 10 C 10 S Lock in 1 MI=0.6 MI=0.76 MI=0.94 MI=1.34 Cs 6s 8s F=3 F =3: Phase: 0 π π 8s Cs cell system #1 J 0 J 1 1 J 1 f p signal PMT 6s J 0 J 1 J MHz Laser frequency scan at 822nm Two-photon interfered spectrum

41 The spectrum of the Cs 6s 8s two photon transition Cs cell system #2 peak fitting uncertainty 300 Hz The black fitting curve is the convolution of Lorentzian and (double-exponential) exponential) transittime lineshape. Step by step ( 100 khz/step ) 932 khz Lorentzian part linewidth idth The laser is stabilized to the Cs cell system#1 at each point residual peak to peak :1.5*10 2 fitting residual is symmetric

42 The Allan deviation of the beat signal between the stabilized ECDL and the frequency comb laser 4.7* s 170Hz uncertainty for absolute frequency measurement at 600 s averaging time

43 The Cs clock (HP 5071a) provided by the National Time and Frequency Standard Laboratory of Taiwan 13 Cesium clocks 1.8* H maser clocks 600s 4*10 13 frequency offset uncertainty for 600 s sampling time 145 Hz frequency shifts for absolute frequency measurement (@ 600 s)

44 Error budget for determining the absolute frequency 1. AC stark shift 2. Zeeman shift 3. Collision shift To sum over all error budget above: we quote 4 khz uncertainty for the absolute frequency measurement for a specific cell We can t assure the accuracy unless examining more Cs cells.

45 We examined ten cells from different sources 2007 Germany 1999 France 10 Pa buffer gas

46 Frequency and linewidth relation of 10 cells in our lab 10 Pascal Xenon buffer gas We chose two narrowest linewidth cells to determine the absolute frequency We chose two narrowest linewidth cells to determine the absolute frequency values and quote 10 khz uncertainty

47 Table 2: Absolute frequencies of 133 Cs 6S 8S hyperfine transitions * khz; ** khz; * F=3 ** F=4 hyperfine constant (khz) (khz) (khz) 2007 Germany 417 (15) 351 (15) (7) 54 khz 54 khz Our work 363 (10) 297 (10) (5) 43 khz 37 khz 1999 France 320 (100) 260 (100) (10) The hyperfine constant is deduced as (clock frequency-2δν m ) / F max e ype e co sta t s deduced as (c oc eque cy ν m )/ max Δν m is the difference of two frequencies and F max is the largest total angular momentum and is 4 in our case

48 Conclusions We measured ten cells to determine the absolute frequency and quoted a 10 khz uncertainty. The spectrum linewidth measurement could be a good guidance of choosing a suitable cesium cell for better frequency accuracy The discrepancies between our work and previous results might be caused by: 1. The purity of the gas cells 2. The collision from residual wall outgassing 3. Other reasons Next step: Using direct comb spectroscopy method to double check the value.

49 Thanks for attention!

50 The benefits of stabilizing laser frequency to the C 10 ability ) ion proba ormalized Transiti (no C 10 crossover S 1 sideband Modulation index (MI) 1. At small modulation region,the S/N of C 10 is better than S 1 2. C 10 is insensitive to the modulation index. 3.less modulation shift

51 E= E 0 cos(ω c t+ф) Ф = M cos(δt) E= E 0 cos(ω c t+ф) Ф = M cos(δt) Δ = Δ 0 + A cosω d t Δ 0 :106MHz A:1MHz ω d :27kHz M:0.4

52 Simulation

53 A project locking all comb laser parameters by cesium cells 8S 6 D 884 nm 822 nm 6 P F=3 F=4 884 nm 822 nm 6 S 170 mm Opt. lett. 36, 76 (2011) Opt. lett. 32, 563 (2007) I(f) 884 nm 822 nm f m = mδ + δ 0 Δ Accuracy, comb-based CPT submitted f Apply Physics B 92, (2008)

54 The Lock in demodulation signal of Cs Cell #1 J 12 (M) J 02 (M) J +12 (M) Δ=106 MHz Δ 6s F=3 > 8s F=3 f laser f EOM = f Cs cell#1 f laser = f Cs cell#1 + f EOM f laser f AOM f laser f AOM = f Cs cell#1 + f EOM f AOM = f Cs cell#2 To match Cs cell#2 Resonant frequency Δ Δ 3.5 MHz~ Δ+3.5 MHz Δ

56 Recent Progress of Optical Frequency Comb Research in NIM Fei Meng, Shiying Cao, Tianchu Li, Zhanjun Fang National Institute of Metrology(NIM),China ATF Taipei

57 Outline Introduction Ti:Sapphire Comb Er:doped Fiber Comb Future work

58 Organization of TFM Division of NIM In March, 2011, TFMD of NIM was founded. Time Keeping group Cs Fountain group Sr optical clock group Comb group 532nm frequency standard Time and Frequency Metrology Division

59 Ti:Sapphire Comb Ti:Sapphire, linear cavity; Pulse length:<30fs; repetition rate:>100mhz; PCF coupling efficiency> 40%

Ti:Sapphire Comb fceo S/N:~40dB @RBW: 300kHz; Continued woking time: >5 hours; Key

60 Ti:Sapphire Comb fceo 300kHz; Continued woking time: >5 hours; Key comparisons of APMP K11, Apr , 2010 in NMIJ, Japan: NMIJ: khz NIM: khz

61 Er: doped Frequency Comb A D A: fiber femtosecond oscillator B: power amplification B C C: spectra expansion D: f-2f spectrometer

62 Er: doped Frequency Comb NPE mode-locking; Repetition rate:~200mhz ; Pulse length:~100fs ; HNLF length:~40cm Pump :~ power:~700mw; Spectral coverage 100nm;

63 Er: doped Frequency Comb Amplifier + Spectrum expansion: Two-stage amplifier; Average output power:>350mw; Super continuum spectrum: 1100nm~2200nm;

64 Er: doped Frequency Comb f-2f interferometer: single beam type,mgo:ppln; f ceo S/N:~40dB; f ceo linewidth:<400khz;

65 Er: doped Frequency Comb Tracking

66 Er: doped Frequency Comb frep stabilized: Dual loop locking; Long term operation: >1week

67 Er: doped Frequency Comb fceo stabilized: Long term operation: >1 week

68 Er: doped Frequency Comb Oscillator 2. Amplifier & Spectrum expansion 3. f-2f interferometer 4. Pump diodes

69 Er: doped Frequency Comb

70 1064nm Nd:YAG Iodine Stabilized laser absolutely frequency measurement: f 1064 = ± 0.2(kHz)

71 Future workultra stable μw generator for Cs fountain clock local oscillator 9.19GHz Stable laser fiber comb

72 Future workstabilized the ECDL frequency for Sr clock

73 Future work Improve the reliability Narrow Comb.

74 Special thanks to Dr. Jinlong Peng (ITRI) Dr. Zhigang Zhang(Peking University)!

75 Thanks for your attention!

76 2013 Asia-Pacific Time and Frequency (ATF) Workshop Determination of Mode Number Using Two Laser Combs with Large Difference in Repetition Rate Jin-Long Peng, Tze-An Liu, and Ren-Huei Shu Center for Measurement Standards, Industrial Technology Research Institute, 321, Sec. 2, Kuang Fu Rd., Hsinchu 30011, Taiwan Abstract Two Er-fiber laser combs with repetition frequency of 500 MHz and 400 MHz are used to measure the frequency of a free-running external cavity diode laser (ECDL). The beat frequencies between the ECDL and the two combs are simultaneously measured at three different repetition rates of the 500 MHz comb while keeping the repetition rate of the 400 MHz comb unchanged. The mode number of the beating comb line can be determined from the measured beat frequencies with short average time of 1 s. Key words: optical frequency comb, frequency measurement, fber laser I. INTRODUCTION Mode-locked (ML) femtosecond laser functioning as an optical frequency comb has revolutionized optical frequency metrology over a decade [1]. To measure the frequency of a laser under measurement (LUM) using a mode-locked laser comb, the mode number of the beating comb line must be determined. Besides using a wavelength meter to offer a precise a priori knowledge of the frequency of the LUM, mode number can be determined by measuring the beat frequencies at various repetition rates [2, 3]. Using single comb operated at different repetition rate is limited to measure stable optical frequency with fluctuations of some tens of khz [3]. Peng et al. developed methods based on two combs with repetition rate difference of khz to measure the mode number, which can be independent of the frequency fluctuations of the LUM [4-6]. However, the two combs need to have almost the same length of laser cavity. This demands delicate control of the fiber length during the construction of the laser oscillator. Inaba et al. demonstrated the comb mode determination using two combs with large difference in repetition rate [7]. But, they need long measurement time of 1000 s to average down the uncertainty of the beat frequency. Newbury et al. demonstrated dual-comb spectrometer capable of rapid absolute measurement of a dynamic continuous-wave laser within submillisecond [8]. However, they need highly coherent dual-comb system phase-locked to optical frequency reference. In this paper, we demonstrate a method that can determine the mode number in short average time of 1 s using two fiber laser combs with large difference in repetition rate and phase-locked to a microwave frequency reference. II. THEORY This method relies on simultaneously measuring the beat frequencies of the LUM using two laser combs. The first comb (comb1) is successively operated at three different repetition rates f r11, f r12 and 1

77 2013 Asia-Pacific Time and Frequency (ATF) Workshop f r13, where two repetition rates f r11 and f r12 are close enough to have the same beating comb mode, while keeping the repetition rate of the second comb (comb2) unchanged. For simplicity, assume that the offset frequencies are zero and the signs of the beat frequencies are determined to be positive. Thus, the frequency of the LUM can be expressed as: f L =n f r11 +f b11 = k f r21 +f b21, (1) f L =n f r12 +f b12 = k f r21 +f b22, (2) f L =(n+m) f r13 +f b13 = k f r21 +f b23, (3) where f b1x and f b2x are the beat frequencies measured at repetition rate f r1x of comb1 with x=1, 2 and 3, and at single repetition rate f r21 of comb2; n and k are the mode number of the beating comb line of comb1 and comb2, respectively; m is the mode number shift of comb1 when the repetition rate is changed from f r11 to f r13. From (1), (2) and (3), the mode number shift m and the mode number n can be derived as m = n (f b21 fb11 ) (f f f r11 b22 r12 f b12 ) (f r11 f f r13 r13 ) + (f b11 f b21 ) (f b13 f b23 ), (4) m fr13 + (fb21 fb11 ) (fb23 fb13 ) =. (5) fr11 fr13 The mode number difference m is calculated with (4) first and then substituted into (5) to get n. Both n and m are independent of the frequency fluctuations of the LUM since the two beat frequencies in all parentheses of (4) and (5) are measured simultaneously. They depend only on the relative fluctuation between the two comb lines beating with the LUM. Equations (4) and (5) is similar to (6) and (5) in [5], which are derived for two combs with about khz difference in repetition rate. Since the two combs are phase-locked to a common highly stable microwave frequency standard, therefore, the mode number can be determined using average time of as short as 1 s similar to that demonstrated in [5]. Actually, the term [(f b21 f b11 ) (f b22 f b12 )]/(f r11 f r12 ) in (4) is equal to the mode number n, and (4) and (5) has the same form in such kind of substitution. But, this term is not used to calculate the real n in this proposal, because f r11 f r12 is small and it needs long measurement time to average down the uncertainty of the beat frequency difference to be much less than f r11 -f r12, which was as demonstrated in [7]. This term can be used only as an approximate mode number for the calculation of m in (4). The other way to get an approximate mode number from a monochromator to replace this term to calculate the mode number shift m was demonstrated in [9]. Since only the beat frequency between comb2 and the LUM appears in (4) and (5), the repetition frequency of comb2 can be any other values different from comb1 as long as the beat frequency can be effectively separated for measurement. III. EXPERIMENTAL SETUP AND RESULTS The experiment is demonstrated using two Er-fiber laser combs with repetition rates of 500 MHz and 400 MHz to measure the frequency of a free-running external cavity diode laser (ECDL) at wavelength of 1560 nm (NewFocus velocity 6328H). Figure 1 shows the block diagram of the experimental setup. The two Er-fiber laser combs have similar σ-type ring oscillator mode-locked by semiconductor saturable absorber mirror and deliver pulses centered at 1560 nm with bandwidth larger than 10 nm. The other part of the fiber laser comb construction is similar to that one published in [10]. Each comb has three output ports. One port is used to detect the repetition frequency and monitor the fiber laser 2

78 2013 Asia-Pacific Time and Frequency (ATF) Workshop Figure 1. Experimental setup for the optical frequency measurement. oscillator. The other two ports are two branches of supercontinua. One branch is used for the CEO frequency detection and the other is used for optical frequency measurement. Each fiber comb is located inside an aluminumm box of A3 paper size with 6.5 cm thick. To the best of our knowledge, this is the most compact fiber laser comb with an f-2f interferometer inside. The output of the ECDL is split into two parts by a 3-dB coupler and then combined with the monitor ports of the two combs with two 3-dB combiners. Two monochromators were used to filter the beating comb lines from the outputs of the two combiners. The maximum power passed throughh the monochromator is used to determine the location of the ECDL while the two combiners are disconnected from the two combs. Then, the two combiners are connected to the two combs again. The beat frequencies are detected by two InGaAs photodiodes. Two polarization controllers are used before the 3-dB combiners to control the polarization of the comb lines and optimize the beat signals. The beat signals are filtered by low pass filters and counted by two universal frequency counters (Agilent Technologies 53132A). To perform synchronous counting, the counters are triggered by an external signal generated from a pulse generator. The gate time of the counters is set to 1s. The frequency measurement processes are as following. The repetition frequency of comb1 is first controlled to be 500 MHz and that of comb2 is about 400 MHz. The CEO frequencies of the two combs are controlled to be the same value of 140 MHz. The signs of the CEO frequencies are determined by observing the variation of the beat frequency while changing the CEO frequencies, which are determined to be negative. The control of the repetition and the CEO frequency is similar to that published in [10]. The two beat frequencies of comb1 and comb2 mixed with the ECDL are simultaneously counted by the triggered counter and collected by a personal computer through Labview program. The measured beat frequencies are shown in Fig. 2 (a). They are correlated with the frequency drift of the free-running ECDL. The difference of the two beat frequencies is shown in Fig. 2 (b) and not dependent on the drift of the ECDL. The signs of the beat frequencies are determined by monitoring the beat frequency variations while changing the repetition rates of the two combs. Then, the repetition frequency of comb1 is changed to be 0.5 Hz less than 500 MHz and that of comb2 is not changed. Another two beat frequencies are measured as shown in Fig. 2 (c) and their differences is shown in Fig. 2 (d). The 0.5-Hz-shift in repetition rate changes the beat frequency by about 0.2 MHz; therefore, the mode number of the beating comb line is still the same. Then, the repetition rate of comb 1 is set to MHz and that of comb2 still remains the same value. Another two beat frequencies are measured as shown in Fig. 2 (e) and their differences is shown in Fig. 2 (f). The signss of the beat frequencies are determined by the same method used in previous step. All beat frequencies have positive sign. The mode number shift m of comb1 for repetition rate changing from 5000 MHz to MHz is calculated using Eq. [4] and shown in Fig. 2 (g). It is obviously m=1. The calculated n is shown in Fig. 2 (f). The uncertainty is only Clearly, n= The frequency of the free running ECDL can then be determined to be MHz-140 MHz+f b11. 3

79 2013 Asia-Pacific Time and Frequency (ATF) Workshop Figure 2. (a), (c), and (e) are the measured beat frequencies at f r11 =500 MHz, f r12 =500MHz- 0.5 Hz, and f r13 = MHz, respectively; comb2 at about 400 MHz; dashed line for comb1 and solid line for comb2; (b), (d), and (f) are the frequency difference of (a), (c), and (e), respectively; (g) is the calculated mode number shift m; (h) is the calculated n. For average time of 1 s, the maximum fluctuation of the calculated n is only about 0.2; therefore, this method can determine n in short average time of 1 s and is suitable for measuring the frequency of the free-running laser as demonstrated. IV. CONCLUSIONS We have demonstrated using two fiber laser combs with repetition frequency of 500 MHz and 400 MHz to measure the frequency of a free-running external cavity diode laser. The required average time for the determination of the mode number of the beating comb line is as short as 1s. This method is suitable for measuring the frequency of a free running laser as long as its frequency drift does not interfere with the beat frequency measurement. ACKNOWLEDGMENT The authors thank Yuh-Chuan Cheng for her contribution to the electronics used in the fiber laser comb. REFERENCES [1] Th. Udem, R. Holzwarth, and T. W. Hänsch, Optical frequency metrology, Nature, 416: ,

80 2013 Asia-Pacific Time and Frequency (ATF) Workshop [2] L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, A new method to determine the absolute mode number of a mode-locked femtosecond laser comb used for absolute optical frequency measurements, IEEE J. Sel. Top. Quantum Electron., 9: , [3] J. Zhang, Z. H. Lu, Y. H. Wang, T. Liu, A. Stejskal, Y. N. Zhao, R. Dumke, Q. H. Gong, and L. J. Wang, Exact frequency comb mode number determination in precision optical frequency measurements, Laser Phys., 17: , [4] J.-L. Peng and R.-H. Shu, Determination of absolute mode number using two mode-locked laser combs in optical frequency metrology, Opt. Express, 15: , [5] J.-L. Peng, T.-A. Liu, and R.-H. Shu, Optical frequency counter based on two mode-locked fiber laser combs, Appl. Phys. B, 92: , [6] T.-A. Liu, R.-H. Shu, and J.-L. Peng, Semi-automatic, octave-spanning optical frequency counter, Opt. Express, 16: , [7] H. Inaba, Y. Nakajima, F.-L. Hong, K. Minoshima, J. Ishikawa, A. Onae, H. Matsumoto, M. Wouters, B. Warrington, and N. Brown, Frequency measurement capability of a fiber-based frequency comb at 633 nm, IEEE. Tran. Instru. Meas., 58: , [8] F. R. Giorgetta, I. Coddington, E. Baumann, W. C. Swann, and N. R. Newbury, Fast highresolution spectroscopy of dynamic cintinuous-wave laser sources, Nature Photon., 4: , [9] J.-L. Peng, T.-A. Liu, and R.-H. Shu, Determination of mode number using two laser combs with large difference in repetition rate, Proceedings of the 2013 IEEE International Frequency Control Symposium jointly with the 26 th European Frequency and Time Forum (IFCS/EFTF), in press. IFCS Abstract book 2013, IFCS-EFTF6-PCD-14. [10] J.-L. Peng, T.-A. Liu, and R.-H. Shu, Self-referenced Er-fiber laser comb with 300 MHz comb spacing, Proceedings of the 2009 IEEE International Frequency Control Symposium jointly with the 22 nd European Frequency and Time Forum (IFCS/EFTF), pp ,

Optical phase-coherent link between an optical atomic clock. and 1550 nm mode-locked lasers

Optical phase-coherent link between an optical atomic clock and 1550 nm mode-locked lasers Kevin W. Holman, David J. Jones, Steven T. Cundiff, and Jun Ye* JILA, National Institute of Standards and Technology