Zeeman shift of an electron trapped near a surface

Eberlein, Claudia and Bennett, Robert (2014) Zeeman shift of an electron trapped near a surface. Physical Review A, 89. 042107. ISSN 1050-2947

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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: Article
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Subjects: Q Science > QC Physics > QC0170 Atomic physics. Constitution and properties of matter Including molecular physics, relativity, quantum theory, and solid state physics
Q Science > QC Physics > QC0501 Electricity and magnetism > QC0522 Electricity > QC0680 Quantum electrodynamics
Depositing User: Claudia Eberlein
Date Deposited: 01 May 2014 09:21
Last Modified: 22 Jul 2019 13:44
URI: http://sro.sussex.ac.uk/id/eprint/48321

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