Frequency chains

Precision frequency metrology is now compatible for the search of a variation of the constants [38]. A new generation of frequency chains [8] allows to easily do two kind of frequency measurements which were hardly available previously ... 

Another metrological application of simple atoms is the determination of values of the fundamental physical constants. In particular, the use of the new frequency chain for the hydrogen and deuterium lines [6] provided an improvement of a value of the Rydberg constant (Roc)- But that is not the only the constant determined with help of simple atoms. A recent experiment on g factor of a bound electron [27,11] has given a value of the proton-to-electron mass ratio. This value now becomes very important because of the use of photon-recoil spectroscopy for the determination of the fine structure constant [41] (see also [8])-... 

Fig. 4. The first 1992 Garching frequency chain for the measurement of the IS — 2S transition in atomic hydrogen (0 phase-locked loop, SHG second harmonic generation)...

The first frequency measurement of the 15 — 25 resonance made use of a transportable ClU-stabilized HeNe infrared frequency standard at 88 THz [24], built at the Institute of Laser Physics in Novosibirsk/Russia. For calibration it was transported repeatedly to the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig/Germany where it could be compared with a Cs atomic clock using the PTB frequency chain [25]. 

Fig. 6. Comparison of the hydrogen IS1 — 25 transition frequency with a Cs clock using a femtosecond comb. This is a simplified version of the frequency chain shown in Fig. 4 Ref. [6] in this volume...

The frequencies of the three LD/Rb lasers stabilized on the 5Si/2(F = 3) — 5D /2(F = 5) two-photon transition of 85Rb were measured in 1996. The LPTF frequency chain connects the LD/Rb laser at 385 THz to a standard at 29 THz, namely a CO2 laser stabilized to an osmium tetraoxyde line (CO2/OSO4) [48]. This standard had been previously measured in 1985 with respect to the Cs clock with an uncertainty of 70 Hz. In 1998, the measurement of the CO2/OSO4 standard was remade with an uncertainty of 20 Hz (i.e. a relative uncertainty of 7xl0-13) [55]. Taking into account this last measurement, the frequency of the LD/Rb standard of LKB is, after correction of the light shift vKb = 385 285 142 376.7(1.0) kHz. 

Fig. 11. Outline of the frequency chain between the 2S — 12D hydrogen frequencies and the LD/Rb and CO2/OSO4 standards. The details are explained in the text (Ti-Sa titanium sapphire laser, LD/Rb rubidium stabilized laser diode, LD(int) intermediate laser diode, CO2/OSO4 osmium tetraoxyde stabilized CO2 laser, SHG second harmonic generation, SFG sum frequency generation)...

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 ... 

A New Type of Frequency Chain and Its Application to Fundamental Frequency Metrology... 

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... 

Fig. 6. Left Deviation of the averaged beat note between the two frequency chains from the expected value for various counter gate times. Right Measured Allan standard deviation between the two chains as a function of the counter gate time...

Fig. 7. Frequency chain used for the determination of the cesium Di line...

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. 

We have improved the signal to noise ratio of the experiment by a factor 15, this allows us to determine very precisely the 1S-3S transition frequency with a reasonnable integration time. The preliminary results for the second order Doppler effect are very stimulating. We plan to make more precise measurements of this effect. The frequency chain to make an absolute frequency measurement is in preparation in the Laboratoire Primaire du Temps et des Frequences. The determination of the absolute frequency of the 1S-3S transition is planed within one year. 

Abstract. We present a frequency comparison and an absolute frequency measurement of two independent -stabilized frequency-doubled Nd YAG lasers at 532 nm, one set up at the Institute of Laser Physics, Novosibirsk, Russia, the other at the Physikalisch-Technische Bundesanstalt, Braunschweig, Germany. The absolute frequency of the l2-stabilized lasers was determined using a CH4-stabilized He-Ne laser as a reference. This laser had been calibrated prior to the measurement by an atomic cesium fountain clock. The frequency chain linking phase-coherently the two frequencies made use of the frequency comb of a Kerr-lens mode-locked Ti sapphire femtosecond laser where the comb mode separation was controlled by a local cesium atomic clock. A new value for the R.(56)32-0 aio component, recommended by the Comite International des Poids et Mesures (CIPM) for the realization of the metre [1], was obtained with reduced uncertainty. Absolute frequencies of the R(56)32-0 and P(54)32-0 iodine absorp tion lines together with the hyperfine line separations were measured. 

We present a frequency comparison of two independent -stabilized Nd YAG lasers at 532 nm and an absolute frequency measurement of the laser frequencies which were locked to different HFS components of the R(56)32-0 and P (54)32-0 iodine absorption line. The absolute frequencies have been determinded using a phase-coherent frequency chain which links the 12-stabilized laser frequency to a CH4-stabilized He-Ne laser at 3.39 pm. This laser had been calibrated before the measurements against an atomic cesium fountain clock. 

In order to measure the absolute frequencies of the iodine spectrometers, we employed a frequency chain which links the Nd YAG laser frequencies to a CH4 stabilized He-Ne laser at 3.39 /rm (Fig. 3). This laser was set up at the Institute of Laser Physics in Novosibirsk, Russia [17], and has been calibrated previously (1996) for a measurement of the hydrogen IS - 2S absolute frequency [18]. In... 

The frequency chain works as follows to the second harmonic of the He-Ne laser at 3.39 jum a NaCl OH color center laser at 1.70 pm is phase locked. To the second harmonic of the color center laser a laser diode at 848 nm is then phase locked. This is accomplished by first locking the laser diode to a selected mode of the frequency comb of a Kerr-lens mode-locked Ti sapphire femtosecond laser (Coherent model Mira 900), frequency-broadened in a standard single-mode silica fiber (Newport FS-F), and then controlling the position of the comb in frequency space [21,11]. At the same time the combs mode separation of 76 MHz is controlled by a local cesium atomic clock [22]. With one mode locked to the 4th harmonic of the CH4 standard and at the same time the pulse repetition rate (i.e. the mode separation) fixed [22], the femtosecond frequency comb provides a dense grid of reference frequencies known with the same fractional precision as the He-Ne S tandard [23,21,11]. With this tool a frequency interval of about 37 THz is bridged to lock a laser diode at 946 nm to the frequency comb, positioned n = 482 285 modes to lower frequencies from the initial mode at 848 nm. 

Fig. 3. Set-up of the frequency chain used to measure the absolute frequency of the two iodine spectrometers. The chain links the 532 nm radiation of the frequency doubled Nd YAG lasers (563 THz) to a methane-stabilized He-Ne laser at 3.39 /rm (88 THz). The two input frequencies of the frequency interval divider stage at 852 nm and 946 nm determine the frequency of the NdtYAG lasers at 1064 nm. The input frequencies are phase-coherently linked to the methane-stabilized He-Ne laser at 3.39 /xm by use of a frequency comb generated with a Kerr-lens mode-locked femtosecond laser...

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. 

With the frequency chain in lock the unknown frequencies f532 of the investigated iodine lines at 532 nm are related to the known frequency of the He-Ne standard fHe-Ne and the comb mode separation frep through ... 

In order to verify this result, we measured the frequency gap using a different technique while one ILP laser was locked to the R(56)32-0 aio transition another ILP Nd YAG laser with slightly worse characteristics was first locked to the same transition to subtract frequency shifts due to the use of different iodine cells and then alternately locked to the ai, aio and ai5 component of the P(54)32-0 line. The beat frequency between the two lasers of about 47 GHz was detected by a fast photodetector (New Focus model 1006) and measured by mixing the signal down with a Rb-clock synchronized high-frequency synthesizer. Within the uncertainty of the two measurements, the results of the absolute frequency measurement using the frequency chain were confirmed (see Fig. 4). According to this measurement, the frequency differences between the aio HFS component of the (R56)32-0 line and the ai, aio and ai5 HFS component of the (P54)32-0 line are ... 

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