We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a sum rule that explicitly relates them to the corresponding geometric phase of the whole system. The marginal geometric phases in the Zeeman and Paschen-Back limits are analyzed. We point out the existence of nodal points in the marginal phases that may be detected by topological means.We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a sum rule that explicitly relates them to the corresponding geometric phase of the whole system. The marginal geometric phases in the Zeeman and Paschen-Back limits are analyzed. We point out the existence of nodal points in the marginal phases that may be detected by topological means.

arXiv:quant-ph/0505058Physical Review ANov 1, 200516 citations

Geometric Phase of Polarized Hydrogenlike Atoms in an External Magnetic Field

Zhong Feng Tang, David Finkelstein

We show that the motion of polarized hydrogenlike atoms in an external magnetic field $B$ is a cyclic evolution. The geometric phase they exhibit is dependent on both the initial state and the Hamiltonian. Properties of the geometric phase in the cases of weak (called Zeeman limit) and strong (called Paschen-Back limit) magnetic fields are presented. We point out that the results of the two limits are interpolated in the intermediate $B$ region. Some observable effects in a specially devised interferometer are predicted.We show that the motion of polarized hydrogenlike atoms in an external magnetic field $B$ is a cyclic evolution. The geometric phase they exhibit is dependent on both the initial state and the Hamiltonian. Properties of the geometric phase in the cases of weak (called Zeeman limit) and strong (called Paschen-Back limit) magnetic fields are presented. We point out that the results of the two limits are interpolated in the intermediate $B$ region. Some observable effects in a specially devised interferometer are predicted.

Physical Review LettersApr 17, 199510 citations

We show that the motion of polarized hydrogenlike atoms in an external magnetic field

B

is a cyclic evolution. The geometric phase they exhibit is dependent on both the initial state and the Hamiltonian. Properties of the geometric phase in the cases of weak (called Zeeman limit) and strong (called Paschen-Back limit) magnetic fields are presented. We point out that the results of the two limits are interpolated in the intermediate

B

region. Some observable effects in a specially devised interferometer are predicted.