Gravitational wave detectors based on matter wave interferometers (MIGO) are no better than laser interferometers (LIGO)

We show that a recent claim that matter wave interferometers have a much higher sensitivity than laser interferometers for a comparable physical setup is unfounded. We point out where the mistake in the earlier analysis is made. We also disprove the claim that only a description based on the geodesic deviation equation can produce the correct physical result. The equations for the quantum dynamics of nonrelativistic massive particles in a linearly perturbed spacetime derived here are useful for treating a wider class of related physical problems. A general discussion on the use of atom interferometers for the detection of gravitational waves is also provided.

Figure 1

Schematic spacetime diagram representing the two trajectories employed to compute the phase shift in an atom interferometer with a Michelson-type configuration. The vertical axis corresponds to time and the horizontal axis represents the positions along the two arms. Each side of the time axis represents a different direction in space corresponding to the two different arms. The continuous lines are the unperturbed trajectories, and the dashed line is a perturbed one. In this particular example, the perturbed trajectory is identical to the unperturbed one before bouncing off the mirror, but its velocity is lower after the reflection, which would be the case for a mirror moving away from the source and the detector.