Possible latitude effects of Chern-Simons gravity on quantum interference

It has been recently suggested that, as a gravitational Aharonov-Bohm effect due to a gravitomagnetic potential, possible effects of Chern-Simons gravity on a quantum interferometer are dependent on the latitude and direction of the interferometer on Earth in orbital motion around the Sun. Continuing work initiated in an earlier publication [H. Okawara, K. Yamada, and H. Asada, Phys. Rev. Lett. 109, 231101 (2012)], we perform numerical calculations of time variation in the induced phase shifts for nonequatorial cases. We show that the maximum phase shift at any latitude might occur at 6, 0 (and 12), and 18 hours (in local time) of each day, when the normal vector to the interferometer is vertical, eastbound, and northbound, respectively. If two identical interferometers were located at different latitudes, the difference between two phase shifts measured at the same local time would be O(sin delta phi) for a small latitude difference delta phi. It might thus become maximally similar to 20% for delta phi similar to 10 degrees, for instance. DOI: 10.1103/PhysRevD.87.084038