A precision measurement of the gravitational redshift by the interference of matter waves

One of the central predictions of metric theories of gravity, such as general relativity, is that a clock in a gravitational potential U will run more slowly by a factor of 1 + U/c(2), where c is the velocity of light, as compared to a similar clock outside the potential(1). This effect, known as gravitational redshift, is important to the operation of the global positioning system(2), timekeeping(3,4) and future experiments with ultra-precise, space-based clocks(5) (such as searches for variations in fundamental constants). The gravitational redshift has been measured using clocks on a tower(6), an aircraft(7) and a rocket(8), currently reaching an accuracy of 7 x 10(-5). Here we show that laboratory experiments based on quantum interference of atoms(9,10) enable a much more precise measurement, yielding an accuracy of 7 x 10(-9). Our result supports the view that gravity is a manifestation of space-time curvature, an underlying principle of general relativity that has come under scrutiny in connection with the search for a theory of quantum gravity(11). Improving the redshift measurement is particularly important because this test has been the least accurate among the experiments that are required to support curved space-time theories(1).