World record for two optical clocks

Optical clocks are deemed the clocks of the future. In optical clocks, the atoms, which act as a “pendulum”, are resonantly excited by means of optical radiation. Compared to cesium atomic clocks (10¹⁰ Hz) – on which the SI base unit, the second, is currently based – their excitation frequency (10¹⁴ Hz to 10¹⁵ Hz) is much higher. Therefore, the resonance quality is much better, which implies considerably increased clock accuracy (i.e. lower deviation from the true frequency) and higher stability (i.e. the required averaging period for one measurement is reduced). In both fields, PTB's optical atomic clocks are currently one step ahead.

PTB's ytterbium clock is approximately a hundred times more accurate than the best cesium clocks and is currently the world's most accurate single-ion clock. To develop this clock, the researchers from PTB exploited particular physical properties of Yb⁺: this ion has two reference transitions with which an optical clock can be realized. The clock is actually based on the excitation into the so-called “F_7/2 state” which, due to its extremely long natural lifetime (approx. 6 years), provides exceptionally narrow resonance. Due to the particular electronic structure of the F_7/2 state, the shifts of the resonance frequency caused by electric and magnetic fields are exceptionally small. The other reference transition (into the D_3/2 state) exhibits higher frequency shifts and is therefore used as a sensitive “sensor” to optimize and control the operating conditions.

The decisive factor for the last leap in accuracy was the combination of two measures: firstly, a special procedure was developed for the excitation of the reference transition. With this procedure, the “light shift” of the resonance frequency caused by the exciting laser is measured separately. This information is then used to immunize the excitation of the reference transition against the light shift and its possible variation. Secondly, the frequency shift induced by the thermal infrared radiation of the environment (which is relatively small for the F state of Yb⁺ anyway) was determined with an uncertainty of only 3 %.

Another particular property of the F state of Yb⁺ is the strong dependence of the state energy on the value of the finestructure constant (the elementary fundamental constant of electromagnetic interaction) and on violations of the Lorentz invariance for photons or electrons, as expected in some presently discussed theories on the unification of the fundamental interactions. Comparisons between Yb⁺ clocks and other highly accurate optical clocks (such as the strontium clock) are currently probably the most promising way of verifying theories from this area of “New Physics” in the lab.

Contrary to ion clocks, a strontium clock uses laser cooling to slow a gas of neutral atoms down to temperatures near absolute zero. Then, an extremely narrow transition between long-lived eigenstates of the atoms is excited in order to stabilize the frequency of the excitation laser to that of the atoms. The simultaneous interrogation of numerous atoms leads to a particularly high signal-to-noise ratio and, thus, to higher stability. However, since an atomic cloud must be prepared after each comparison between the laser and the atomic frequency, interruptions in the observation of the laser frequency occur. The laser itself hence serves as a “flywheel” and is commonly pre-stabilized to a resonance frequency of an optical resonator which keeps the laser frequency stable over short periods of time.

For PTB's strontium clock, a resonator was developed whose frequency is among the most stable worldwide. Due to its length of 48 cm and ingenious thermal and mechanical isolation from its environment, it reaches a fractional frequency instability of only 8 ⋅ 10⁻¹⁷. When analyzing the individual contributions to noise of the detected excitation probability, it turned out that the clock reaches the physically determined fundamental quantum projection noise limit as soon as with 130 atoms.

A model based on the data obtained for the noise was supplemented by the known influence of the laser frequency noise, and its prediction was experimentally verified by a self-comparison of the clock. From this, a fractional instability in normal operation amounting to 1.6 ⋅ 10⁻¹⁶/τ^1/2 was .derived as a function of the averaging time τ in seconds. This is the best published value for an atomic clock so far. This is expected to considerably facilitate the further reduction of the total measurement uncertainty of the strontium clock down to a few parts in 10¹⁸.

Apart from testing the “big issues” of fundamental physics, possible applications of highest-precision clocks arise in geodesy where they enable direct and accurate measurement of the gravitational potential of the Earth.