Zeeman shift of an electron trapped near a surface

Bennett, R. and Eberlein, C. (2014) Zeeman shift of an electron trapped near a surface. Physical Review A: Atomic, Molecular and Optical Physics, 89(4), 042107. (doi: 10.1103/PhysRevA.89.042107)

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Boundary-dependent corrections to the spin energy eigenvalues of an electron in a weak magnetic field and confined by a harmonic trapping potential are investigated. The electromagnetic field is quantized through a normal-mode expansion obeying the Maxwell boundary conditions at the material surface. We couple the electron to this photon field and a classical magnetic field in the Dirac equation, to which we apply the unitary Foldy-Wouthuysen transformation in order to generate a nonrelativistic approximation of the Hamiltonian to the desired order. We obtain the Schrödinger eigenstates of an electron subject to double confinement by a harmonic potential and a classical magnetic field, and then use these within second-order perturbation theory to calculate the spin energy shift that is attributable to the surface-modified quantized field. We find that a pole at the eigenfrequency of a set of generalized Landau transitions gives dominant oscillatory contributions to the energy shift in the limit of tight harmonic confinement in a weak magnetic field, which also make the energy shift preferable to the magnetic moment for a physically meaningful interpretation.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Bennett, Dr Robert
Authors: Bennett, R., and Eberlein, C.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:Physical Review A: Atomic, Molecular and Optical Physics
Publisher:American Physical Society
ISSN (Online):1094-1622
Published Online:15 April 2014

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