Circumventing Heisenberg’s Uncertainty Principle in Atom Interferometry Tests of the Equivalence Principle

Atom interferometry tests of universality of free fall based on the differential measurement of two different atomic species provide a useful complement to those based on macroscopic masses. However, when striving for the highest possible sensitivities, gravity gradients pose a serious challenge. Indeed, the relative initial position and velocity for the two species need to be controlled with extremely high accuracy, which can be rather demanding in practice and whose verification may require rather long integration times. Furthermore, in highly sensitive configurations gravity gradients lead to a drastic loss of contrast. These difficulties can be mitigated by employing wave packets with narrower position and momentum widths, but this is ultimately limited by Heisenberg’s uncertainty principle. We present a promising scheme that overcomes these problems by compensating the effects of the gravity gradients and circumvents the fundamental limitations due to Heisenberg’s uncertainty principle. Furthermore, it relaxes the experimental requirements on initial colocation by several orders of magnitude.

Figure 1

Sketch of an atom interferometry setup for differential acceleration measurements of two different atomic species. The various laser beams driving the diffraction processes for both species share a common retroreflection mirror so that vibration noise is highly suppressed in the differential phase-shift measurement.

Figure 2

Central trajectories for a Mach-Zehnder interferometer in the presence of gravity gradients as seen in a suitable freely falling frame. The tidal forces tend to open up the trajectories compared to the case without gravity gradients (dashed lines). The momentum transfer from the laser pulses is also indicated for the different branches. The picture on the left shows the tidal forces experienced by objects in a freely falling frame (the Einstein elevator) as a consequence of the gravity gradient.

Figure 3

Central trajectories for the same situation depicted in Fig. 2 but with a suitable adjustment of the momentum transfer from the second laser pulse so that a closed interferometer, with vanishing relative displacement between the interfering wave packets in each port, is recovered.