Relativistic Center-of-mass and Relative Coordinates in Curved Spacetime – Relativistic Signatures in Atom Interferometry

Recently, quantum clock interferometry has been suggested for tests of the universality of free fall and the universality of gravitational redshift [1, 2]. The relativistic mass defect, i.e., the atomic mass depending on the internal state, plays a crucial role in these interferometer schemes. Sonnleitner and Barnett [3] calculated first-order relativistic corrections and included them into the multipolar atom-light Hamiltonian. They used (special) relativistic center-of-mass (COM) and relative coordinates first presented by Osborn and Close [4, 5] to decouple the COM and relative dynamics so that all remaining cross terms in the Hamiltonian can be interpreted as a state-dependent atomic mass. Schwartz [6] extended this work to curved spacetime and showed that these special-relativistic COM and relative coordinates do not remove all cross terms between the internal and external dynamics. Since these coordinates are determined by the generators of the Poincaré group for flat spacetime only, we show how to generalize them to curved spacetime. With explicit examples, we apply our results to calculate general-relativistic correction terms for atom interferometric sequences in a straight-forward manner.

References:

[1] Roura, Phys. Rev. X, 10:021014, Apr 2020.

[2] Ufrecht et al., Phys. Rev. Research, 2:043240, Nov 2020.

[3] Sonnleitner and Barnett, Phys. Rev. A, 98:042106, Oct 2018.

[4] Osborn, Phys. Rev., 176:1514–1522, Dec 1968.

[5] Close and Osborn, Phys. Rev. D, 2:2127–2140, Nov 1970.

[6] Schwartz, PhD thesis, Gottfried Willhelm Leibniz Universität Hannover, 2020.