Atomic Tests of GR

Testing General Relativity with Atom Interferometry

Savas Dimopoulos, Peter W. Graham, Jason M. Hogan, and Mark A. Kasevich

PRL 98, 111102 (2007)

URL: http://link.aps.org/abstract/PRL/v98/e111102

Wild! The authors demonstrate how an atomic physics experiment could be used to probe non-Newtonian effects predicted by general relativity. They are not the first to propose using the methods of atomic physics for this purpose, but claim to be the first to have really worked out all the details of their setup.

The setup is similar to the initial stage of a fountain clock. A cold cloud of atoms is launched upward, then falls under the influence of gravity back down to the bottom of the chamber. The authors propose using a series of laser pulses to make an atomic version of a Mach-Zehnder interferometer.

The interferometer works by splitting a beam of coherent light. One part of the beam passes through a sample while the other does not. In the absence of a sample, the two paths are identical, and there is no phase shift between the two beams. The sample alters the path of one of the beams, and information about the sample is obtained from the phase difference.

In the atomic version described by the authors, a photon is used as the beam splitter. An atom on its way up interacts with a photon which puts it into a superposition of velocity eigenstates. According to GR, the geodesics an atom follows are determined by its initial position and velocity. As a result, the atom follows two geodesics simultaneously and interferes with itself when it recombines!

The geodesics can be calculated by solving the equations of general relativity. The phase difference can then be calculated. The metric from which the geodesics are derived contains Newtonian gravity and higher order terms. By studying the effects of these higher order terms on the phase difference of the two paths, one can test GR's predictions of non-Newtonian phenomena.

Table II in the text lists 8 different contributions to the phase difference in the proposed experiment. Four of these are terms from general relativity that are not present in Newton's theory of gravity.

The current precision of atomic interferometry are not good enough to probe these effects, but they could provide more precise tests of the equivalence principle. The authors believe that technical developments in the field will make the precision good enough to eventually probe the other effects.

One big improvement would come in the signal to noise ratio. For uncorrelated atoms, this scales with the square root of the number of atoms. If the atoms are entangled, however, the ratio scales linearly with the number of atoms. This could improve the precision by several orders of magnitude.

The benefits of atomic experiments over astrophysical tests of GR are two-fold. First, their is the accuracy. Clocks can be synchronized to a part in 10^16. More important is control. In an atomic physics experiment, you can modify the setup to isolate some effect you wish to observe. If you're looking through a telescope, you simply collect data on the setup Nature has provided.

I find the idea of using entangled quantum states to probe general relativity very interesting. Popularizations would have you believe the two theories are totally incompatible. If that's the case, then the experiments proposed simply won't work. If not, then Brian Greene and his buddies need to do a better job of explaining exactly where the two theories clash.