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We report a clock transition spectrum approach, which is used to calibrate the zero-crossing temperature and frequency drift of an ultralow expansion (ULE) cavity with a Hertz level resolution. With this approach, the linear and nonlinear drifts of the ULE cavity along a variety of controlled temperatures are clearly presented. When the controlled temperature of ULE cavity is tuned away from the zero-crossing temperature of the ULE cavity, the cavity shows larger and larger nonlinear drift. According to our theoretical analysis and experimental results, we investigate more details of the drift property of the ULE cavity around the zero-crossing temperature, which has seldom been explored before. We can definitely conclude that the zero-crossing temperature of our ULE cavity used in an ytterbium (Yb) lattice clock is around 31.7 °C.
The second is currently defined by the transition between the two hyperfine levels of the ground state of cesium 133 atom at the General Conference of Weights and Measures in 1967 and its accuracy has reached
Usually one uses an optical frequency comb phase-locked to the reference frequency for the zero-crossing temperature measurement. The optical frequency comb links the microwave and the optical frequency domain. It is a powerful tool with which the inter-comparison of various clocks of different atomic species is very straightforward. But we know that a frequency reference with higher stability is also required when measuring the clock transition frequency with the optical frequency comb. Normally its center frequency and repetition frequency are both locked to the H-maser as a reference. When the clock transition frequency to be measured is beating with the frequency component of the optical frequency comb, we can obtain
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Another method is to use a similar ULE cavity with lower thermal noise instability as a reference. The change in the resonant frequency of the test cavity mode is measured by observing the driving frequency change of an additional acousto-optic modulator (AOM) for the reference ULE cavity while the test cavity temperature is ramped.[10] Without a systematic study of the reference cavity, one cannot give the long-term drift of the reference cavity or thermal calibrations. This method can be utilized to roughly estimate the zero-crossing temperature of the test cavity where the limitation arises from the long-term instability of the reference cavity and the variability of room temperature.
In this paper, we will demonstrate a much easier and more sensitive method to determine the zero-crossing temperature of the ULE cavity. Here the ultra-narrow clock transition spectra are used as a much better reference. With the help of the narrow clock transition spectrum, we can easily discern the frequency drifts around the zero crossing temperature of the ULE cavity.
In our experiment, ultra-cold atoms were confined in an optical lattice created by a retro-reflected high power 759 nm laser beam. Our clock laser (578 nm) was aligned along the direction of tight lattice confinement to stimulate the ultra-narrow clock transition of ytterbium (Yb) 171 fermion isotopes. The details of our setup are described elsewhere.[12] We have obtained the Hertz-level clock spectrum already. The clock laser is locked to the clock transition frequency by applying a correction frequency to the relevant AOM as shown in Fig.
The controlled temperature and its fluctuation will change the length of the ULE cavity, and the relative change of the length of the ULE
In the experiment, we set the controlled temperatures of the ULE cavity to be at several points along 30–35 °C. For each point, the ULE cavity stays in thermal equilibrium for more than five days. We measure the zero-crossing temperature of the ULE cavity with the help of an optical frequency comb as shown in Fig.
From the fitting of the frequency drifts of the ULE cavity at different temperatures, we can obtain the zero-crossing temperature of our ULE cavity to be around 31.7 ± 0.36 °C. In order to judge which method is more precise, now we record the clock transition spectra along every temperature point, respectively. We adopt the Rabi excitation, and the clock duration time is 50 ms, with a Fourier-limited linewidth of about 17.8 Hz. We scan the AOM driving frequency in steps of 2 Hz and the normalized excitation ratio of the clock transition is monitored. So, the long-term drift of resonant frequency can also be determined by continuous measurement over several days, and the results are shown in Fig.
In Fig.
In order to consider the influence of the nonlinear frequency drift on the linewidth of the clock transition spectrum, we choose the condition that the ULE cavity is controlled at 34 °C, at which the ULE cavity has the maximum nonlinear drift. Moreover, we record the linewidths of the different times during one day as shown in Fig.
![]() | Fig. 4. (color online) Normalized excitation spectra of clock transition. Differences in linewidth is corresponding to different drift rates of ULE cavity. |
Over 24 hours, spectral linewidths according to the different drift rates are recorded. We can obtain a Fourier-limited linewidth of 17.8 Hz with the proper choice of the clock laser intensity when ignoring the drift of the cavity. However, considering the contribution of cavity drift, we can record different linewidths. Figure
We change the controlled temperature to the zero-crossing temperature, 31.7 °C. We can see that only linear drifts exist there over the entire time. The linewidth of the clock transition is 17 Hz under the same Rabi excitation condition as shown in Fig.
As to the frequency drift, it seems that the method with the optical frequency comb is much noisier than that with clock transition spectra (see Figs.
In this work, we have described a method to precisely measure the zero-crossing temperature of the ULE cavity with the help of narrow Yb clock transition spectra. Compared with the traditional optical frequency comb method, the clock transition spectra method has higher resolution to reveal more details about the spectral linewidth and nonlinear frequency drift of the ULE cavity to precisely determine the zero-crossing temperature.
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