Ultraprecise Measurement of Optical Frequency Ratios

Abstract

We developed a novel technique for frequency measurement and synthesis, based on the operation of a femtosecond comb generator as transfer oscillator. The technique can be used to measure frequency ratios of any optical signals throughout the visible and near-infrared part of the spectrum. Relative uncertainties of 10 −18 for averaging times of 100 s are possible. Using a Nd:YAG laser in combination with a nonlinear crystal we measured the frequency ratio of the second harmonic νSH at 532 nm to the fundamental ν0 at 1064 nm, νSH/ν0 = 2.000 000 000 000 000 001 × (1 ± 7 × 10 −19 ).The development of optical frequency comb generators based on Kerr-lens mode-locked femtosecond lasers [1,2] has enormously stimulated the field of optical frequency synthesis and metrology. Using this technique, the absolute frequencies of a number of narrow transitions in cold atoms or single stored ions such as H, Ca, Yb + or Hg + have been measured by phase-coherently linking those signals to primary cesium-clock controlled hydrogen masers [3][4][5][6]. The measurement instabilities approached those of the hydrogen masers, indicating that neither the optical frequency standards nor the frequency combs themselves were limiting parts of the setups.Any absolute frequency measurement is finally limited by the frequency instability of the device realizing the unit of frequency, Hertz, such as a radio or microwave reference like the hydrogen maser. A possibility to avoid this limitation is the measurement of optical frequency ratios, which are unitless. Thus, frequency ratios for oscillators with better stability than that of the radio or microwave reference can be determined with smaller uncertainty than the absolute frequencies if a technique is available to realize the frequency ratio without introducing additional noise.Such a technique is the transfer oscillator concept, which has been realized with a harmonic frequency chain [7]. However, the measured frequency ratios were restricted to small integer numbers. In this Letter, we describe a novel technique based on the operation of a femtosecond frequency comb generator as a transfer oscillator. Our technique has the capability of generating arbitrary ratios of any optical frequencies throughout the visible and near-infrared part of the spectrum, while frequency fluctuations of the comb modes do not enter the measurement but cancel out.We demonstrate the superior short-term instability by two measurements: first, we measured the frequency ratio of signals from a single-Yb + -ion frequency standard [8] and from an I 2 -frequency-stabilized Nd:YAG laser [9]. Second, we used the Nd:YAG laser and measured the frequency ratio of the second harmonic at 532 nm to its fundamental at 1064 nm, thereby testing how accurately the 2:1 frequency ratio is realized by second harmonic generation. We demonstrate the capability of our technique of frequency-ratio measurements with relative uncertainty better than 10 −18 . Kerr-lens mode-locked femtosecond lasers emit a periodic train of short pulses. The...

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