### To Measure Gravity, Scientists Drop Individual Atoms

Since interferometry was developed in the 19th century, physics has not been the same. The technique, which relies on manipulating a wave’s path, has been used to measure everything from the speed of light to gravitational waves with remarkable precision. Now, physicists are applying it to an entirely different type of problem: determining the acceleration that matter experiences thanks to the gravitational pull of the Earth.

This might seem outdated and boring—after all, every high school student can tell you that the acceleration due to gravity on the surface of the Earth is 9.8 m/s2. Some might even be able to rattle off the more general equation from which this value is calculated:
That is: the acceleration due to gravity on the surface of the Earth, g, is equal to the gravitational constant G (6.674 x 10-11 m3/kg s2) times the mass of the Earth M, divided by the Earth’s radius r squared.

But there’s a problem. Several, in fact. To begin with, this equation relies on accurate values for three different constants that can only be derived experimentally—an error in any one of those constants will propagate and return an inaccurate value for g. Further complicating the matter, the radius of the Earth isn’t a constant at all! In fact, the Earth is too smushed to be a sphere, with a circumference ranging from 40,008 km around the poles to 40,075 km at the equator. Finally, the Earth’s density isn’t constant either; pockets of minerals and air also affect the local mass calculation, causing gravitational acceleration to vary across locations. In other words, this formula and the 9.8 m/s2 value serve as helpful approximations, but they’re just that—approximations.

Nevertheless, an accurate measurement of the local g can be incredibly useful. If the gravitational field is larger than expected, for example, it can clue miners in to the presence of valuable deposits hidden underground. It can also alert researchers to earthquakes and sinkholes, not to mention the fact that many experiments require precise values for the acceleration due to gravity. In the search for ever more portable and precise gravimeters, researchers are working on refining a technique known as atomic interferometry.

Although interferometers come in many flavors, the basic premise remains constant across models: by measuring the interference patterns where two waves interact, researchers can deduce something about the system. It’s how Albert Michelson and Edward Morley proved that the Earth was not floating through a mysterious substance called the aether, and it’s how LIGO measured the distortions caused by incoming gravitational waves, confirming a key aspect of Einstein’s theory of general relativity.

Usually, the interacting waves used in interferometry are some form of light, manipulated via a series of lenses and mirrors. However, quantum physics tells us that the wave-particle duality also applies to matter! This means that although we usually think of a particle as having a precise shape and location, on the quantum level that isn’t really the case. Normally we don’t notice because the “wavelengths” of matter are typically tiny—and yet, University of Otaga researcher Shijie Chai and his colleagues, Dr. Mikkel Andersen and Dr. Julia Fekete, have found a way to manipulate them into yielding a precise measurement of the gravitational field.

The team’s matter of choice is Rubidium-85 thanks to its specific energy structure; 85Rb electrons can pass between several hyperfine energy states in response interactions with light. These energy levels are relatively easy to measure, since the higher-energy state quickly decays, releasing a telltale photon in the process. This characteristic holds even under normal conditions, but for the quantum wave nature of 85Rb to really come into play (which is critical for atomic interferometry), Chai uses a laser to cool the atoms to just above absolute zero. This is important because the wavelength of a matter wave depends on its temperature. By cooling the rubidium to just 5 µK, Chai is able to boost the wavelength from several hundredths of a nanometer to around 90 nm, which is large enough to be detected.

 The main vacuum chamber, where the free-falling atoms are measured. Image Credit: Shijie Chai
Once the rubidium is sufficiently cool, it’s time to invite gravity in. Up until this point, the radiation pressure from the laser has held the rubidium in place, but now the laser is switched off and the material starts on its free fall. Just before it reaches the base of the gravimeter, the laser is turned back on to create a series of vertical standing waves that the rubidium passes through.

Here’s where 85Rb’s hyperfine states come into play. As the wavelike rubidium interacts with the wavelike light pulses, interference fringes begin to emerge where parts, but not all, of the rubidium are boosted into the higher-energy state. Remarkable as it sounds, Chai is able to record those interference patterns and from them deduce the rubidium’s final speed—and thus its average acceleration, our good friend g.

Although Chai is not the first to develop a high-precision gravimeter based on atomic interferometry, his prototype is unique in that it requires only a single laser for the cooling and measurement. Chai sees this increased simplicity leading to a lower consumer cost down the road. While his research currently outlines only a proof-of-concept, Chai is happy with his 1 milliGalileo (10-5 m/s2) precision, and is already making plans to move into the next phase of testing.

If all goes well, Chai hopes to see the fruits of his research translating into inexpensive, highly portable atomic gravimeters available on the market. Although it’s unlikely you’ll ever find yourself clipping a gravimeter to your keychain, this advance does seem to tantalize industry and academia alike with the promise of an exciting new tool!

—Eleanor Hook

1. I really want someone to actually try this Un g=G^2M/r^2 as this will assist in your calculation of measurement of gravity and as such Einstein’s theory of general relativity (G^2R)needs this to make it exactly precise.

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### Ask a Physicist: Phone Flash Sharpie Shock!

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### The Science of Ice Cream: Part One

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