Trapped Ion Optical Clocks Quantum Logic

Short answer: Quantum logic spectroscopy lets an ion with a very stable clock transition, such as aluminium-27, be probed using a second ion trapped alongside it that cools it and reads out its state. Published experiments report aluminium-ion optical clocks with a systematic uncertainty below 10^-18 in 2019. They are laboratory standards, and the figures are the authors' own.

The idea

A 2010 Physical Review Letters paper describes an optical clock based on quantum logic spectroscopy of an ion, where a simultaneously trapped ion sympathetically laser-cools the clock ion and detects its quantum state. This is useful for ions like aluminium whose clock transition cannot be cooled and read out directly. A 2019 New Journal of Physics paper describes the aluminium clock line as having an extremely narrow linewidth of about 8 mHz at 267.4 nm, a quality factor near 10^17, and high immunity to external fields, with a low second-order Zeeman shift, a very small black-body radiation shift and a negligibly small electric quadrupole shift.

Two clocks compared, 2010

In 2010 the authors report an optical clock built this way with a stated fractional frequency inaccuracy, and compare its frequency with that of a previously constructed aluminium clock. They report that the two clocks show relative stability and a fractional frequency difference consistent with the accuracy limit of the older clock. The exact values are in the paper.

Below 10^-18, 2019

A 2019 Physical Review Letters paper describes an aluminium-27 quantum-logic clock with a systematic uncertainty of 9.4 x 10^-19 and a frequency stability of 1.2 x 10^-15 divided by the square root of averaging time. A magnesium-25 ion is trapped with the aluminium ion for sympathetic cooling and state readout. Improvements in a new trap reduced secular motion heating compared with earlier aluminium clocks, so the clock can run with the ion's secular motion near the three-dimensional ground state. A lower trap drive frequency reduced excess micromotion. Both lowered the time-dilation shift uncertainty. The paper also addresses other systematics such as blackbody radiation.

A mixed-crystal measurement, 2019

A separate 2019 paper in New Journal of Physics performs quantum logic spectroscopy with an aluminium-27 and calcium-40 mixed ion crystal in a linear Paul trap. It uses Ramsey spectroscopy in interleaved measurements, with the calcium clock transition as a frequency reference, and reports the aluminium intercombination line frequency as 1 122 842 857 334 736 (85) Hz, together with the g-factor of the excited state, 0.428 133(2).

Limits

These are laboratory clocks, run by specialist groups. Systematic uncertainty and stability are different measures, and the papers use different companion ions. None reports a clock in routine service.

Why two ions

Both the 2010 and 2019 clocks rely on a pair of ions with different roles: one provides the clock transition, the other provides cooling and readout. That split is the reason quantum logic spectroscopy exists, because it lets researchers use a clock ion with excellent frequency properties even though it cannot itself be laser cooled or read out directly. The 2019 trap improvements, lower heating and lower micromotion, show how much of the accuracy budget depends on how well the ions' motion is controlled.

FAQ

What is quantum logic spectroscopy?

Using a second, co-trapped ion to cool and read out the clock ion.

Why aluminium?

Its clock transition is very narrow and insensitive to external fields, according to the 2019 NJP paper.

How accurate was the 2019 clock?

A systematic uncertainty of 9.4 x 10^-19.

Which ions were paired with it?

Magnesium-25 in the Physical Review Letters work, and calcium-40 in the mixed-crystal measurement.

Are these clocks used operationally?

The papers describe laboratory measurements.