27 September 2023

Big idea: How a portable clock is measuring the Earth

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Chris Lee* says researchers in Japan have demonstrated possibly the most expensive altitude sensor in the history of humanity.

When it comes to measuring our position on the Earth, we tend to turn to one of the global positioning satellite (GPS) constellations.

For standard commercial devices, the absolute position accuracy is a few metres, though it can be reduced to a few centimetres with more advanced techniques.

But there are applications where satellite-based measurements aren’t right for the job.

Luckily, the Earth supplies its own measuring stick: gravity.

For instance, if you want to measure subsidence and swelling around a volcano, an accuracy of a few centimetres would be highly desirable, and standard GPS isn’t accurate enough without some specialised hardware.

To get around this problem, researchers in Japan have demonstrated possibly the most expensive altitude sensor in the history of humanity.

Fortunately, it comes with a bonus feature: it will continuously test general relativity.

Shining a light on time

Einstein’s general theory of relativity tells us that clocks tick a little slower in a gravitational field.

So, if one clock is a centimetre higher than another clock, it will speed up.

How much?

Not a lot: a clock needs to be accurate to within a few attoseconds (10–18s) to be able to detect centimetre differences in height.

As it happens, optical lattice clocks can achieve this accuracy.

However, these clocks are rare and delicate flowers.

They tend to be rare enough to have names and be looked after by the sort of people who keep their pencils organised by lead type.

The idea of hauling one of these clocks outside the lab seemed laughable.

Yet this is exactly what researchers have done.

Why is this so complex?

An optical lattice clock uses the change of a quantum superposition state over time to measure the progression of time.

Let’s break that down.

The electrons in an atom have a set of energies that they occupy.

Take hydrogen, for example: it has one electron, and that electron is usually in the lowest possible energy state.

However, higher energy states are available.

If we provide energy, the electron can absorb it and pop up to the higher energy state.

At some later point, it will drop back to the lowest energy state by releasing that energy.

The electron can equally ignore the energy and stay in the lowest energy state.

So, if we provide some energy, the electron enters a state of being both excited and unexcited at the same time.

We have no way of knowing without measuring.

This is a superposition state, which we describe by the probability that the electron absorbed energy and is excited.

If we provide more energy, we increase that chance.

This being quantum mechanics, however, nothing is straightforward.

If we continue supplying energy, the chance will reach a peak, then decay back to zero, and then increase again in a regular cycle.

We call these Rabi cycles.

By measuring the Rabi frequency — that is, how many Rabi cycles are completed in a second — we also obtain a measure of how fast time is progressing.

Sculpting a trap with light

The whole process is very cool.

First, strontium atoms are cooled to a few micro-Kelvins.

The cold atoms are pushed into two laser beams that are travelling opposite of each other.

The electric fields from the laser beams interact.

In some places, the fields add to a higher value to make very bright light; in others they cancel, creating a dark patch.

The strontium atoms drift into the dark areas, where they are trapped.

The lasers are then tuned so that the dark areas slowly move, transporting the atoms into a space shielded from thermal radiation.

Once in the shielded space, the atoms are cooled even more so they are in the ground state of the trap.

This essentially means that the motion of the atoms within the trap is minimised.

The researchers then clout the strontium with a laser that puts the atoms in a superposition state.

The atoms are transported out of the shielded area, where the amount of light they emit is measured.

If the exciting laser has exactly the right frequency for strontium to absorb energy, all of the strontium atoms will emit light.

This laser frequency then becomes our measure of time (the number of light cycles per unit of time is inverted to provide the progression of time).

Many boxes in the back of a Honda Civic

To achieve all of this, the researchers built a system with six high-precision lasers, a set of controllers to distribute the laser light, and all of the magnetic field coils, etc., to provide full control of the strontium atoms.

This kit has been reduced to occupy four boxes, which can fit in the trunk of a smallish hatchback with the seats down … though I doubt the researchers would let you transport their clock in a VW.

The researchers showed that they could transport their clocks and make measurements by measuring the height of the observation room in the Tokyo SkyTree tower (pictured), which is nominally 450 m high.

They also compared their measurements to laser ranging measurements and to GNSS measurements.

The optical clock was able to measure the height to … well, as far as I can tell, the researchers don’t actually give this information.

The gravitationally induced frequency shift is 21.18Hz (the laser frequency is over 400THz, so this is a remarkably accurate frequency measurement), which corresponds to that expected for 450 m.

But turning that into a proper height change didn’t seem to happen.

However, the accuracy of the frequency measurement tells us that the height measurement is accurate to within about 10 cm, while the other techniques are accurate to about 1 cm.

Regardless of the height measurement, the variation in frequency they saw is the one predicted by general relativity, so physics still isn’t broken.

I’m most impressed by the fact that this can be achieved at all.

Take one of the highest precision bits of machinery on the planet, put it in the back of a truck, haul it up the external elevator on a broadcasting tower, and have it not break — simply amazing.

That is the key message of the paper: robust optical clocks with attosecond precision are here and ready for use (even if they aren’t tiny or low-power yet).

* Chris Lee writes for Ars Technica’s science section.

This article first appeared at arstechnica.com.

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