Precision Control Optical Pulse Train Long-Sheng Ma2,1, Zhiyi Bi2, Albrecht Bartels3, Kyoungsik Kim3 Lennart Robertsson1, Massimo Zucco1, Robert S. Windeler4 Guido Wilpers3, Chris Oates3, Leo Hollberg3, Scott A. Diddams3 1Bureau International des Poids et Mesures, Pavillon de Breteuil, 92312 Sevres, FRANCE. 2Key Laboratory of Optical and Magnetic Resonance Spectroscopy, East China Normal University, Shanghai 200062, CHINA 3National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA. 4OFS Laboratories, 700 Mountain Avenue, Murray Hill, New Jersey 07974, USA

Femtosecond laser frequency comb Pump 532 nm Ti:Sapphire t E(t) f Time t frep frep Frequency f f0 f(N) = fo + N frep

RF-Referenced Femtosecond Laser Frequency Comb H maser f(N) = fo + N frep Phase Locks Δf(N) =Δf ceo + N ×Δf rep frep fo fo fr Femtosecond Laser Frequency Comb f 1/frep Time PD Spectrum of PD output Microwave Freq. frep

Link the Beating between Two Combs fR Femtosecond Laser Synthesizer 1 f1(k1) frep1 fceo1 fb1 fceo1 frep1 Phase Control frep1 = frep2 fceo1 = fceo2 H maser fb1+ fb2 Phase Control fceo2 frep2 fb2 frep2 fceo2 Femtosecond Laser Synthesizer 2 f2(k2)

The Agreement among Three Femtosecond Laser Combs Ma, et al. Opt. Lett.29, 641 (2004) Df [ECNU-C1 – BIPM-C1] = 0.15 Hz uc = 1.24 Hz Df [BIPM-C2 – BIPM-C1] = 0.09 Hz uc = 0.83 Hz Df [ECNU-C1 – BIPM-C2] = 0.06 Hz uc = 1.49 Hz The measured frequency is 563 THz. Including all the 21 data points the average difference is 0.11 Hz with uc = 0.69 Hz.

Optically-Referenced Femtosecond Laser Frequency Comb fb = fL - f(N) = fL – (fo + N frep ) Phase Locks fb fo fo fr fL (reference laser) Femtosecond Laser Frequency Comb f no frep frep = ( fL - fceo - fb )/N

Femtosecond Laser Frequency Combs Albrecht Bartels (lasers), Bob Windeler (fiber) Conventional 1 GHz Laser Ti:Sapphire Gain 532 nm Pump input ~20 mm Broadband 1 GHz Laser Ti:Sapphire Gain convex 532 nm Pump Two things must be controlled: rep rate, optical frequency Both Systems have: PZT for fRep. control AOM for f0 control

Configuration of Transportable Comb RF Synthesizer H-maser RF Synthesizer RF band pass filter fceo PLL fceo P RF band pass filter frep PLL frep HV Amp RF Amp AOM D Ti SHG 532 nm M3 Mp λ/2 Periscope λ/2 λ/2 1064 nm 600 to 900 nm M2 M1 PCF

Configuration of Broadband Comb RF Synthesizer H maser RF Synthesizer Cavity stabilized laser f657 PLL fb D frep D Delay stage fceo THG PLL fceo PMT BBO Single mode UV optical fiber 960 nm HV Amp 480 nm 320 nm λ/2 960 nm KNbO3 SHG SHG Delay stage PZT 640 nm BBO AOM λ/2 Pump laser ( 532 nm ) RF Amp

Link the Beating between Two Combs by synchronization of optical pulse Femtosecond Laser Frequency Comb 1 Optical Frequency Reference fL Filter Femtosecond Laser Frequency Comb 2 counter Photodiode

frep1 = ( fL - fceo1 - fb1 )/N1 (1) When N1 = N2 = N Δf rep is independent of fL Δf = f1(N) - f2(N) = Δf ceo + N × Δf rep frep2 = ( fL - fceo2 - fb2 )/N2 (2) f1(N1) = fceo1 + N1 × frep1 (3) f2(N2) = fceo2 + N2 × frep2 (4) Any small difference of repetition rate between two combs is enhanced by N in optical beating. ( N ~ 5 × 105 ) When frep1 = frep2 and the relative phase between the optical trains from the two combs is set to zero, all the modes that are appropriately phased generate a strong beat signal with signal-to-noise as high as 60 db within a 300 kHz bandwidth.

Optical-to-optical Comparison of Four combs Ma, et al. Science 303, 1843 (2004) 2003 Confidence level is 95%

Testing the Optical pulse train Femtosecond Laser frequency Comb 1 nonlinear cross-correlation Optical Frequency Reference fL PMT counter Femtosecond Laser Frequency Comb 2

Comparisons of Repetition Rate using Nonlinear Cross-correlation

Summary The uncertainty (potential limitation) of an optically-referenced femtosecond laser synthesizer has been measured Optical-to-optical: <110-19 Optical-to-microwave (pulse train): 2  10-18 2. The uncertainty (“accuracy”) of an H maser-referenced femtosecond laser comb has been measured Microwave-to-optical: < 1 Hz (~10-15 level ) For optical frequency metrology Limitation is due to the noise of RF synthesizer

飞秒激光光梳 f(N) = fo + N frep f Time Frequency t E(t) t Pump 532 nm Ti:Sapphire t E(t) f Time t f(N) = fo + N frep frep frep Frequency f f0 f(N)×2 - f(2N) = 2 fo + 2N frep- fo - 2N frep = fo

Why test the femtosecond laser frequency comb? It will be the “gears” of future optical clocks with projected fractional uncertainties approaching 110-18 It is used for calibration of world length standards to provide traceability to the SI second. Different type of the combs now exist and their merits should be compared Microstructure fiber systems vs. broadband lasers At what level will noise from the microstructure fiber affect the performance of the synthesizer? It can be used in comparisons of frequency standards for searches of possible drifts in fundamental constants.