Physicists in the US and Germany have used two fundamental tenets of quantum mechanics to perform a high-precision test of Einstein’s general theory of relativity. The researchers exploited wave-particle duality and superposition within an atom interferometer to prove that an effect known as gravitational redshift – the slowing down of time near a massive body – holds true to a precision of seven parts in a billion. The result is important in the search for a theory of quantum gravity and could have significant practical implications, such as improving the accuracy of global positioning systems.

Gravitational redshift follows on from the equivalence principle that underlies general relativity. The equivalence principle states that the local effects of gravity are the same as those of being in an accelerated frame of reference. So the downward force felt by someone in a lift could be equally due to an upward acceleration of the lift or to gravity. Pulses of light sent upwards from a clock on the lift floor will be Doppler shifted, or redshifted, when the lift is accelerating upwards, meaning that this clock will appear to tick more slowly when its flashes are compared at the ceiling of the lift to another clock. Because there is no way to tell gravity and acceleration apart, the same will hold true in a gravitational field; in other words the greater the gravitational pull experienced by a clock, or the closer it is to a massive body, the more slowly it will tick.

Confirmation of this effect supports the idea that gravity is a manifestation of space–time curvature because the flow of time is no longer constant throughout the universe but varies according to the distribution of massive bodies. Reinforcing the idea of space–time curvature is important when distinguishing between different theories of quantum gravity because there are some versions of string theory in which matter can respond to something other than the geometry of space–time.

Universality of freefall

Gravitational redshift, however, as a manifestation of local position invariance (the idea that the outcome of any non-gravitational experiment is independent of where and when in the universe it is carried out) is the least well confirmed of the three types of experiment that support the equivalence principle. The other two, the universality of freefall and local Lorentz invariance, have been verified with precisions of 10–13 or better, whereas gravitational redshift had previously been confirmed only to a precision of 7 × 10–5. This was achieved in 1976 by recording the difference in elapsed time as measured by two atomic clocks – one on the surface of the Earth and the other sent up to an altitude of 10,000 km in a rocket.

This kind of redshift measurement is limited by the degree of gravitational pull provided by the Earth’s mass. The new research, carried out by Holger Müller of the University of California Berkeley, Achim Peters of Humboldt University in Berlin and Steven Chu, previously at Berkeley but now US secretary of energy, is limited in the same way but manages to dramatically increase precision thanks to an ultrafine clock provided by quantum mechanics.

In 1997 Peters used laser trapping techniques developed by Chu to capture caesium atoms and cool them to a few millionths of a degree above absolute zero (in order to reduce their velocity as much as possible), and then used a vertical laser beam to impart an upward kick to the atoms in order to measure gravitational freefall.

Now, Chu and Müller have re-interpreted the results of that experiment to give a measurement of the gravitational redshift.

In the experiment each of the atoms was exposed to three laser pulses. The first pulse placed the atom into a superposition of two equally probable states – either leaving it alone to decelerate and then fall back down to Earth under gravity’s pull or giving it an extra kick so that it reached a greater height before descending. A second pulse was then applied at just the right moment so as to push the atom in the second state back faster toward Earth, causing the two superposition states to meet on the way down. At this point the third pulse measured the interference between these two states brought about by the atom’s existence as a wave, the idea being that any difference in gravitational redshift as experienced by the two states existing at difference heights above the Earth’s surface would be manifest as a change in the relative phase of the two states.

Enormous frequency

The virtue of this approach is the extremely high frequency of a caesium atom’s de Broglie wave – some 3 × 1025 Hz. Although during the 0.3 s of freefall the matter waves on the higher trajectory experienced an elapsed time of just 2 × 10–20 s more than the waves on the lower trajectory did, the enormous frequency of their oscillation, combined with the ability to measure amplitude differences of just one part in 1000, meant that the researchers were able to confirm gravitational redshift to a precision of 7 × 10–9.

As Müller puts it, “If the time of freefall was extended to the age of the universe – 14 billion years – the time difference between the upper and lower routes would be a mere one thousandth of a second, and the accuracy of the measurement would be 60 ps, the time it takes for light to travel about a centimetre.”

This extreme precision could become useful as global positioning systems become ever more accurate. As Müller points out, to determine the position of an object on the ground to millimetre accuracy the atomic clocks on GPS satellites would need to operate with a precision of 10–17, a figure in fact achieved recently by a clock developed at the National Institute of Standards and Technology in the US (see “New optical clock breaks accuracy record”). But at the satellites’ altitude of 20,000 km, such clocks will experience a speeding up of time of about one part in 1010 thanks to gravitational redshift. Recovering the precision of 10–17 would therefore require knowing the redshift effect to a precision of 10–7.

Müller hopes to further improve the precision of the redshift measurements by increasing the distance between the two superposition states of the caesium atoms. The distance achieved in the current research was a mere 0.1 mm, but, he says, by increasing this to 1 m it should be possible to detect gravitational waves, miniscule ripples in the fabric of space–time predicted by general relativity but never before observed.

The work is described in Nature 463 926.