Quantum magnetic field effects in atom-surface van der Waals interaction

This paper provides the theoretical basis for experimentation on van der Waals atom-surface energy as a manifestation of quantum zero-point energy, with a continuously variable parameterization by a Landau-quantizing magnetic field applied normal to the surface. Quantum magnetic field effects in the second-order van der Waals (vdW) atom-surface energy are fully analyzed. Focusing on the electrostatic nonretarded limit, we employ a random phase approximation (RPA) description of the dynamic, nonlocal polarizability of the mobile semi-infinite Landau quantized plasma behind a semiconductor surface. Our initial examination is carried out using a general low-wave-number approximation of the bounded plasma dielectric function both parallel and perpendicular to the surface, to expeditiously determine quantum magnetic field effects in the second-order vdW energy. Since the formulation calls for an integration over all wave numbers perpendicular to the surface, pz, we subsequently eliminate the reasonable approximation of the RPA polarizability expanded in powers of pz, and carry out a more accurate study in this respect. Explicit analytic results for quantum magnetic field effects in vdW energy due to a neutral atom in Coulombic interaction with a semi-infinite nonlocal, dynamic semiconductor plasma are obtained and presented in full detail