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 f_i exactly given by the relation f_i = i_frep + f_CEO (i: mode order number, f_rep: pulse repetition rate, f_CEO: offset frequency). Thus the optical comb spectrum is completely determined by the frequencies f_rep and f_CEO, which lie in the rf range. This enables the highly accurate measurement of optical frequencies relative to a rf reference.

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 f_opt and the nearest-lying component of the comb spectrum. Two other counters register the frequency f_CEO and the difference between a harmonic of f_rep and the rf reference f_ref . With this information, f_opt can be calculated for a given value of f_ref (Fig. 2). In this scheme, the stability of the optical frequency measurement is independent of the short-time stability of the comb frequencies f_i and is determined alone by the stability of f_opt and f_ref. Therefore a simple "slow" stabilisation of frep and f_CEO is sufficient in order to suppress long-term drifts of f_x and f_CEO