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Precision timekeeping

An atom interferometer provides most precise test yet of Einstein's gravitational redshift
Provided by the University of California, Berkeley
Albert Einstein
Albert Einstein.
Library of Congress
February 17, 2010
While airplane and rocket experiments have proved that gravity makes clocks tick more slowly — a central prediction of Albert Einstein's general theory of relativity — a new experiment in an atom interferometer measures this slowdown 10,000 times more accurately than before, and finds it to be exactly what Einstein predicted.

The result shows once again how well Einstein's theory describes the real world, said Holger Mueller, an assistant professor of physics at the University of California, Berkeley.

"This experiment demonstrates that gravity changes the flow of time, a concept fundamental to the theory of general relativity," Mueller said. The phenomenon is often called the gravitational redshift because the oscillations of light waves slow down or become redder when tugged by gravity.

Treating Particles as Waves
Mueller tested Einstein's theory by taking advantage of a tenet of quantum mechanics: that matter is both a particle and a wave. The cesium atoms used in the experiment can be represented by matter waves that oscillate 3 x 10^25 times per second — that is, about 30 million billion billion times per second.

When the cesium atom matter wave enters the experiment, it encounters a carefully tuned flash of laser light. The laws of quantum mechanics step in, and each cesium atom enters two alternate realities, Mueller said. In one, the laser has pushed the atom up 4/1000 of an inch (one-tenth of a millimeter) — giving it a tiny lift to where Earth's gravitational field is slightly weaker. In the other, the atom remains unmoved inside Earth's gravitational well, where time flies by less quickly.

While the frequency of cesium matter waves is too high to measure, Mueller and his colleagues used the interference between the cesium matter waves in the alternate realities to measure the resulting difference between their oscillations, and thus the redshift.

The equations of general relativity predicted precisely the measured slowing of time to an accuracy of about one part in 100 million — 10,000 times more accurate than the measurements made 30 years ago using two hydrogen maser clocks, one on Earth and the other launched via rocket to a height of 6,200 miles (10,000 kilometers).

"Two of the most important theories in all of physics are quantum mechanics and the general theory of relativity," said Mueller's collaborator, Steven Chu, a former University of California, Berkeley professor of physics and former director of Lawrence Berkeley National Laboratory (LBNL). Chu was one of the originators of the atom interferometer, which is based on his Nobel Prize-winning development of cold laser traps. "The paper that we are publishing uses two fundamental aspects of the quantum description of matter to perform one of the most precise tests of the general theory of relativity."

Precision Timekeeping
Far from merely theoretical, the results have implications for Earth's global positioning satellite system, for precision timekeeping, and for gravitational wave detectors, Mueller said.

"If we used our best clocks, with 17-digit precision, in global positioning satellites, we could determine position to the millimeter," Mueller said. "But lifting a clock by 3.4 feet (1 meter) creates a change in the 16th digit. So, as we use better and better clocks, we need to know the influence of gravity better."

Mueller also noted that the experiment demonstrates very clearly "Einstein's profound insight that gravity is a manifestation of curved space and time, which is among the greatest discoveries of humankind."

This insight means that what we think of as the influence of gravity — planets orbiting stars, for example, or an apple falling to Earth — is really matter following the quickest path through space-time. In a flat geometry, the quickest route is a straight line. But in Einstein's theory, the flow of time becomes a function of location, so the quickest path could now be an elliptical orbit or a plumb line to the ground.

Experiments have tested the theory to higher and higher precisions, but direct measurements of the gravitational redshift have had to struggle with the minimal size of the effect in Earth's gravitational field. These measurements culminated in the 1976 experiment by NASA and the Harvard Smithsonian Astrophysical Observatory using hydrogen maser clocks.

Atom Interferometers
Just as an optical interferometer uses interfering light waves to measure time or distance to within to a fraction of a wavelength, an atom interferometer uses interfering matter waves. Because matter waves oscillate at a much higher frequency than light waves, they can be used to measure correspondingly smaller times and distances.

Since 1991, when Chu was at Stanford University, California, he and former members of his lab have used Chu's technique of cooling and trapping atoms with lasers to build the most precise atom interferometers. In 1999, one of those students, Achim Peters, now at Humboldt University in Berlin, performed such an experiment on cesium atoms in free fall to precisely measure the acceleration of gravity.

After joining the UC Berkeley faculty in July 2008, Mueller attended a conference on frequency and time measurement where he realized that Peters' experimental data could also yield the most precise measure yet of the gravitational redshift. Mueller approached Chu about the experiment and received an enthusiastic response.

Peters' experiment involved capturing a million cesium atoms in a cold laser trap chilled to a few millionths of a degree above absolute zero and zapping them with a vertical laser beam tuned to give them a kick upwards, with 50 percent probability. A split second later, a second laser pulse sends the high-flying matter waves downward and the stationary ones upward to merge. A third laser pulse recombines the two. Measuring the amplitude of the recombined matter waves reveals the phase difference between the two.

Mueller and Chu noted that the contribution of the rest mass to the frequency of matter wave oscillations is normally ignored in quantum mechanical calculations because the resulting frequencies are too fast to measure. But in this experiment, that high "Compton" frequency allowed an extremely precise measurement of the different clock rates.

"In conceiving of this research, we realized that relativity theory demands that the energy, E, also includes the energy due to the rest mass of the atom, given by Einstein's famous equation E = mc^2," Chu wrote in an e-mail. "The energy due to the rest mass of the atoms is enormous, resulting in an atomic clock that ticks at 3 x 10^25 Hertz."

Freefall
During the approximately 0.3 second of free fall, the matter waves on the higher route feel that a little more time elapsed: just 2 x 10^-20 second compared to the lower route. But because of the sheer magnitude of the Compton frequency, Mueller said, they oscillated about a million times more often. Because the atom interferometer could measure the difference to within a thousandth of an oscillation, the experiment produced a 9-digit accuracy.

"If the time of free fall was extended to the age of the universe, 14 billion years, the time difference between the upper and lower routes would be a mere 1/100th second, and the accuracy of the measurement would be 60 picoseconds, the time it takes for light to travel about 1/2 inch," Mueller said.

Mueller is building evermore precise atom interferometers, and he hopes this year to measure the gravitational redshift more precisely with a millimeter separation. One future milestone will be a separation of a meter or more.

"If we could separate the atoms by a meter, we could build an experiment to observe gravity waves," he said. Gravity waves are generated by interactions between massive stars or black holes.

To filter out noise from Earth's gravity and other perturbations, like a passing truck, such an experiment would have to involve at least two atom interferometers separated by a large distance. An ideal spot for the experiment, he said, would be the Deep Underground Science and Engineering Laboratory at the former Homestake mine in South Dakota.
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