Yu-Jie Tan, Cheng-Gang Shao,* and Zhong-Kun Hu†
MOE Key Laboratory of Fundamental Physical Quantities Measurement,
School of Physics, Huazhong University of Science and Technology,
1037 Luo Yu Road, Wuhan 430074, People’s Republic of China
(Received 18 October 2016; published 4 January 2017)
Atom interferometry is currently developing rapidly, which is now reaching sufficient precision to motivate laboratory tests of general relativity. Thus, it is extremely significant to develop a general relativistic model for atom interferometers. In this paper, we mainly present an analytical derivation process and first give a complete vectorial expression for the relativistic interferometric phase shift in an atom interferometer. The dynamics of the interferometer are studied, where both the atoms and the light are treated relativistically. Then, an appropriate coordinate transformation for the light is performed crucially to simplify the calculation. In addition, the Bordé ABCD matrix combined with quantum mechanics and the “perturbation” approach are applied to make a methodical calculation for the total phase shift. Finally, we derive the relativistic phase shift kept up to a sensitivity of the acceleration ∼10−14 m/s2 for a 10-m-long atom interferometer.
DOI: 10.1103/PhysRevD.95.024002
