Tricks for Ticks

measure for measure Tricks for ticks Optical-lattice clocks have pushed the limits of frequency measurement — to such an extent that a tiny difference in altitude affects the clock’s tick rate, asHidetoshi Katori elucidates.

o measurement can be simpler These frequency ratios, which are than the counting of ticks, making considered to be dimensionless constants, Nfrequency — and hence time — should remain the same whenever and the most accurately measurable quantity. wherever measurements are carried out. To establish a reference tick rate, people If, from measurements with hitherto have always been seeking stable naturally unexplored precision, the ratio would turn occurring periodic phenomena. The motion out to vary temporally or spatially, new of celestial bodies was used for a long time questions would open up — the possibility to define an ‘astronomical second’. However, of questioning the foundations of physics is with the invention of the atomic clock, an important stimulus for the development which uses a microwave transition of Cs as of ever better clocks. a pendulum, the astronomical second was Moreover, ultraprecise clocks allow revealed to display a drift. This led to the investigating the curvature of spacetime redefinition of the SI Système( International) This way, the precise determination of indicated by Einstein’s theory of general second in 1967, based on fixing the an atomic pendulum’s frequency is a relativity. On Earth, a clock placed one aforementioned Cs frequency to time-consuming task. centimetre higher than another ticks SI –18 νCs = 9,192,631,770 Hz. Observing a million atoms at once would faster by a factor of 10 . Networked The invention of the laser in 1960 complete the measurement in one second. clocks, therefore, can serve as geopotential stimulated physicists to search for a An ‘optical lattice’ was developed in the meters5. So far, the geoid (the gravitational better pendulum, oscillating at an optical early 1990s, enabling the confinement of equipotential surface that coincides with

frequency: a higher frequency ν0 would millions of neutral atoms in a standing the average sea level) has been stable improve the clock’s uncertainty Δν/ν0 for wave of light (pictured schematically) by enough to maintain international atomic a given measurement uncertainty Δν. In spatially modulating the energy of atoms. time (TAI) with an uncertainty of ~5 × 10–16 1981, Hans Dehmelt proposed the ‘optical A trick ensuring that all clock states have by correcting the constant relativistic time clock’, with an envisioned uncertainty of the same energy shift, so that lattice- dilation of primary Cs clocks. Dynamic –18 Δν/ν0 = 10 , based on a single ion in a trap perturbations effectively cancel out, tidal perturbation arising from the Sun Paul trap1. A Paul trap confines an ion in the allowed the optical lattice to become a novel and the Moon, which is an order of minimum of a harmonic potential created by platform for building clocks3. magnitude smaller than the uncertainty an oscillating quadrupole electric field, where So far, optical-lattice clocks have achieved of TAI, has never been a limitation to

the oscillation frequency ν0 = (E2 – E1)/h of an uncertainty two orders of magnitude better maintain this global time scale. Measured the associated atomic pendulum (with h the than that realized by the SI second, showing with advanced clocks, however, what we

Planck constant and E1 and E2 the energies the inherent limitation of the SI definition. expected to be constant may no longer be of the ‘clock states’) remains unperturbed by Frequency measurements essentially rely on constant: present-day clocks are ready to the trapping field. However, like all atomic ratio measurements. For example, to describe uncover semidiurnal variation of tides and

clocks, this ideally designed single-ion the frequency νSr of a strontium pendulum, may test the stability of constants and the optical clock is fundamentally limited by the the SI definition requires measuring the ratio isotropy of space. ❐ 2 quantum nature of the measurement . R = νSr/νCs against the caesium pendulum, SI The frequency uncertainty νΔ is given followed by multiplying with νCs. To date, HIDETOSHI KATORI is in the Department SI SI by the inverse of the observation time of νSr = RνCs = 429,288,004,229,873.2(2) Hz is the of Applied Physics, Graduate School of the clock transition. For a single atom, this best described frequency within the SI, where Engineering, University of Tokyo, uncertainty can be statistically improved the 16-digit number is solely limited by the Tokyo 113-8656, Japan. by √N by repeating the measurements realization of the definition. Once a reliable e-mail: hkatori@riken.jp and increasing the total number of atomic link between a novel clock and the SI second References measurements N. Assuming a singly trapped is established, scientists are free to describe 1. Dehmelt, H. G. IEEE Trans. Instrum. Meas. IM-31, 83–87 (1982). 15 ion with ν0 ≈ 10 Hz and an observation any frequencies beyond the SI uncertainty 2. Itano, W. M. et al. Phys. Rev. A 47, 3554–3570 (1993). –18 4 3. Katori, H., Takamoto, M., Pal’chikov, V. G. & Ovsiannikov, V. D. time of 1 s, Δν/ν0 = 10 is achievable by measuring other ratios , such as νYb/νSr, 6 Phys. Rev. Lett. 91, 173005 (2003). after repeatingN = 10 measurements, while maintaining consistency with the prior 4. Nemitz, N. et al. Nat. Photon. 10, 258–261 (2016). 6 SI which would take 10 s (about 10 days). definition through νSr, for example. 5. Takano, T. et al. Nat. Photon. 10, 662–666 (2016).