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Optical setup for the experiment on the thorium nuclear clock.

Frequency measurement of the Yb+reference transitions

In optical frequency standards, the frequency of a laser is stabilised on an atomic reference transition whose frequency lies in the optical spectral range. To measure the transition frequency in the SI base unit "second", we measure the ratio of the laser frequency to a reference frequency that is controlled by a caesium atomic clock. The reference frequency typically lies in the radiofrequency (rf) range. Through such measurements, the frequencies of  some optical reference transitions are known with an accuracy that is limited only by employed the caesium reference clocks. The BIPM recommends a number of precisely measured optical transition frequencies, including those of the E2 and E3 transitions of 171Yb+, as "secondary representations of the second".

Frequencies in the optical spectral range can not be measured by electronic frequency counters. Instead, optical frequencies are measured by means of a special type of laser which simultaneously oscillates in many longitudinal cavity modes. If the modes are suitably coupled with each other, a periodic pulse train is emitted. The corresponding optical spectrum is a "frequency comb" and consists of lines with frequencies fi exactly given by the relation fi = ifrep + fCEO (i: mode order number, frep: pulse repetition rate, fCEO: offset frequency). Thus the optical comb spectrum is completely determined by the frequencies frep and fCEO, which lie in the rf range. This enables the highly accurate measurement of optical frequencies relative to a rf reference.

Schematic of setup for optical frequency measurements.

Fig. 1 Scheme of the setup for optical frequency
measurements. The optical frequency fopt is
determined using a frequency comb generator. The
reference frequency fref is derived from a hydrogen
maser that is controlled by a caesium fountain clock.
For a given value of fref, , fopt is calculated from the
synchronized readout of three rf frequency counters.

Fig. 2: Calculation of the optical frequency fopt using the measurement scheme shown in Fig. 1 (left).

The setup employed in our optical frequency measurements is shown in Fig. 1. A photodetector and an electronic counter is used to register the frequency difference (beat frequency) between the measured frequency fopt and the nearest-lying component of the comb spectrum. Two other counters register the frequency fCEO and the difference between a harmonic of frep and the rf reference fref . With this information, fopt can be calculated for a given value of fref (Fig. 2). In this scheme, the stability of the optical frequency measurement is independent of the short-time stability of the comb frequencies fi and is determined alone by the stability of fopt and fref. Therefore a simple "slow" stabilisation of frep and fCEO is sufficient in order to suppress long-term drifts of fx and fCEO