Optical frequency chain

Fig. 9.85 Optical frequency chain that connects the frequency of stabilized optical lasers with the Cs frequency standard [1317]...

The optical frequency chains discussed in the previous section are difficult to build. Many lasers and optical harmonic generators have to be phase-locked and frequency-stabilized, and the whole setup can easily fill a large laboratory. Furthermore, each of these chains is restricted to a single optical frequency, which is linked to the cesium clock, just like the present frequency standard. 

The next big advance towards higher precision was the 1997 phase-coherent measurement of the frequency gap with an optical frequency interval divider chain [27]. The 2.1 THz gap was no longer measured by counting cavity fringes, but divided down to the radio frequency domain by a phase-locked chain of five optical frequency interval dividers [56] (see Fig. 5). The accuracy of this approach was limited by the secondary frequency standard to 3.4 parts in 1013, exceeding the accuracy of the best previous measurements by almost two orders of magnitude. 

In order to test the measurements of the 2S — 8S and 2S — 8D transitions, the frequencies of the 2S — 12D intervals have also been measured in Paris [49]. This transition yields complementary information, because the 12D levels are very sensitive to stray electric fields (the quadratic Stark shift varies as n7), and thus such a measurement provides a stringent test of Stark corrections to the Rydberg levels. The frequency difference between the 2S — Y2D transitions (A 750 nm, u 399.5 THz) and the LD/Rb standard laser is about 14.2 THz, i.e. half of the frequency of the CO2/OSO4 standard. This frequency difference is bisected with an optical divider [56] (see Fig. 5). The frequency chain (see Fig. 11) is split between the LPTF and the LKB the two optical fibers are used to transfer the CO2/OSO4 standard from the LPTF to the LKB, where the hydrogen transitions are observed. This chain includes an auxiliary source at 809 nm (u 370.5 THz) such that the laser frequencies satisfy the equations ... 

Abstract. A suitable femtosecond (fs) laser system can provide a broad band comb of stable optical frequencies and thus can serve as an rf/optical coherent link. In this way we have performed a direct comparison of the IS — 2S transition in atomic hydrogen at 121 nm with a cesium fountain clock, built at the LPTF/Paris, to reach an accuracy of 1.9 x 10-14. The same comb-line counting technique was exploited to determine and recalibrate several important optical frequency standards. In particular, the improved measurement of the Cesium Di line is necessary for a more precise determination of the fine structure constant. In addition, several of the best-known optical frequency standards have been recalibrated via the fs method. By creating an octave-spanning frequency comb a single-laser frequency chain has been realized and tested. 

Being able to control u>0 and uir is not sufficient if we don t know their values. The repetition rate u>r is simply measured by a photo detector at the output of either the laser or the fiber. To measure the offset frequency oj0, a mode nu>r + u>0 on the red side of the comb is frequency doubled to 2(nu>r + oj0). If the comb contains more than an optical octave there will be a mode with the mode number 2n oscillating at 2nu>r+u>0. As sketched in Fig. 3 we take advantage of the fact that the offset frequency is common to all modes3 by creating the beat frequency (=difference frequency) between the frequency doubled red mode and the blue mode to obtain u>0. This method allowed the construction of a very simple frequency chain [14,15,16,17,18,19] that eventually operated with a single laser. It occupies only 1 square meter on our optical table with considerable potential for further miniaturization. At the same time it supplies us with a reference frequency grid across much of the visible and infrared spectrum. 

Fig. 4. The first self-referenced frequency chain that has been used in Refs. [16,19,31] uses an optical frequency interval divider (oval symbol) [34] that fixes the relation between the frequencies /, 4/ and 7/ by locking f + 7f to 2 x 4/. The 3.39 /Am laser at / is locked through the divider after the frequency comb locked the difference between 3.5/ and 4/...

Previously we have shown that the repetition rate of a mode locked laser equals the mode spacing to within the experimental uncertainty of a few parts in 1016 [26] by comparing it with a second frequency comb generated by an efficient electro-optic modulator [41]. Furthermore the uniform spacing of the modes was verified [26] even after further spectral broadening in a standard single mode fiber on the level of a few parts in 1018 [13]. To check the integrity of the femtosecond approach we compared the / 2/ interval frequency chain as sketched in Fig. 3 with the more complex version of Fig.4 [19]. We used the 848 nm laser diode of Fig. 4 and a second 848 nm laser diode locked to the frequency comb of the / 2/ chain. The frequencies of these two laser diodes measured relative to a quartz oscillator, that was used as a radio frequency reference for the frequency combs, are 353 504 624 750 000 Hz and 353 504 494 400 000 Hz for the / 2/ and the 3.5/ 4/ chain respectively. We expect a beat note between the two 848 nm laser diodes of 130.35 MHz which was measured with a radio frequency... 

The femtosecond frequency chain does also provide us with the long awaited compact optical clockwork that can serve in future optical clocks. Possible candidates for precise optical reference frequencies derived from narrow transitions in Ca, Hg+ [52] and In+ [53] are currently investigated using the femtosecond comb technology. 

In extension to this frequency chain we installed an optical frequency interval divider [23] to extrapolate to 1064 nm (see Fig. 3). The center frequency of the optical divider stage is given by the Nd YAG laser at 946 nm laser with its frequency determined via the beat note with the comb locked laser diode at 946 nm. The higher input frequency of the divider stage is set by a diode laser at 852 nm which is heterodyned with another diode laser at 852 nm, also phase locked to the frequency comb. The lower input frequency of the divider stage is determined by the iodine stabilized Nd YAG laser at 1064 nm. While scanning the frequency doubled 1064 nm Nd YAG laser over the iodine line the two beat notes at 852 nm and 946 nm are measured with a rf-counter. They are then used to determine the absolute frequency of the 1064 nm Nd YAG laser. 

One way an optical standard could be provided is by harmonic multiplication of a microwave frequency standard in a synthesis chain. By use of this technique, a laser at 88 THz (3.39 pm) has been made phase coherent with a microwave oscillator. - The best optical frequency standards may be made by locking a local oscillator (laser) to an atomic or molecular resonance line. State-of-the-art accuracies are characterized by measurements on methane stabilized He-Ne lasers in which reproducibilities in the 10— -- range have... 

Th. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hansch, Phase-Coherent Measurement of the Hydrogen 15-2 5 Transition Frequency with an Optical Frequency Interval Divider Chain, Physical Review Letters 79, 2646-2649 (1997). 

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