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Physical Review A

Atomic energy-level shifts near a dielectric microsphere

W. Jhe, Jae‐Wook Kim

Published Feb 1, 1995• 27 citations
Publisher

Abstract

We calculate the energy-level shifts of an atom near a dielectric microsphere. With the quantum electrodynamic linear-response formalism and the exact field susceptibility satisfying the boundary conditions, the energy shifts of a ground-state atom are calculated numerically. From the numerical results, in particular, we are able to identify the short-range instantaneous van der Waals interaction energy and the long-range Casimir-Polder retarded interaction energy between two polarizable objects (atom and cavity).

DOI
10.1103/physreva.51.1150

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We calculate the energy-level shifts of an atom near a dielectric microsphere. With the quantum electrodynamic linear-response formalism and the exact field susceptibility satisfying the boundary conditions, the energy shifts of a ground-state atom are calculated numerically. From the numerical results, in particular, we are able to identify the short-range instantaneous van der Waals interaction energy and the long-range Casimir-Polder retarded interaction energy between two polarizable objects (atom and cavity).
We calculate the atomic energy-level shift and the modified dipolar radiation rate inside a hollow dielectric cylinder and outside a solid cylinder using a quantum-mechanical linear-response formalism in the dipole approximation. We first derive the electromagnetic fields scattered by the cylindrical surface for an oscillating dipole inside and outside the cylinder. When an atom is located on the axis of the cylindrical hollow, we obtain analytic expressions of the atomic level shifts in two limiting cases: when bbb (radius of hollow) is very small, the level shift is proportional to ${b}^{\ensuremath{-}2}$ which is associated with the kinetic-energy change of the atomic electron, whereas when bbb is very large, the shift is proportional to ${b}^{\ensuremath{-}4}$ which is identified as the retarded (Casimir-Polder) interaction energy. Moreover, we calculate the atomic potentials as a function of the position of atoms in the hollow region, which is important for the atom-guiding experiment. We also calculate the decay rates and find enhanced rates inside and outside the cylinder. In particular, we compare the radiative properties of an atom inside the hollow cylinder with those between two plates, and those near a cylinder with near a single surface.
We have made a quantitative study of quantum electrodynamic corrections to the atomic energy levels between parallel conducting mirrors. Within the framework of simple two-level atoms, we evaluate the level shifts numerically and discuss the van der Waals, Casimir, and cavity-resonant radiative shifts as their asymptotic forms. In particular, we find that the level shifts of an excited state are substantially different not only from those of a classical dipole radiator but also from those of an excited atom near a single mirror. For the ground state, however, the shifts are qualitatively similar to those near a single mirror. We also apply the results to some simple atomic systems that may be used to test the cavity QED theory.
The energy–level shifts and the change in the rate of spontaneous emission are calculated for an atom located at a distanceZ from a dielectric half–space. The dielectric is a non–dispersive and non–absorbing medium characterized by a constant real refractive indexn. The explicit analytic formulae derived are applicable for arbitrary values ofn. All results are analysed in the non-retarded and retarded limits, which apply to the atom being close to or far from the interface, respectively, i.e. toZ being small or large on the scale of a wavelength of a typical atomic transition. For ground-state atoms, the energy–level shift varies as 1/Z3 in the non–retarded regime and as 1/Z4 in the retarded regime, which agrees with the Casimir–Polder result for the limitn→α. For excited–state atoms, the energy–level shifts receive additional contributions that oscillate with the distanceZ from the interface.
Within the frame of macroscopic quantum electrodynamics in causal media, a rigorous derivation of the van der Waals energy of an atomic system in the presence of an arbitrary arrangement of dispersing and absorbing dielectric bodies is given. As an application, the van der Waals potential of an atom in the presence of a dispersing and absorbing sphere is derived. Closed expressions for the long-distance (retardation) and short-distance (non-retardation) limits are given, and the effect of material absorption is discussed.
The 1%-accurate calculations of the van der Waals interaction between an atom and a cavity wall are performed in the separation region from 3nmto150nm3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}150\phantom{\rule{0.3em}{0ex}}\mathrm{nm}3nmto150nm. The cases of metastable He∗{\mathrm{He}}^{*}He∗ and Na atoms near metal, semiconductor, and dielectric walls are considered. Different approximations to the description of wall material and atomic dynamic polarizability are carefully compared. The smooth transition to the Casimir-Polder interaction is verified. It is shown that to obtain accurate results for the atom-wall van der Waals interaction at short separations with an error less than 1% one should use the complete optical-tabulated data for the complex refractive index of the wall material and the accurate dynamic polarizability of an atom. The obtained results may be useful for the theoretical interpretation of recent experiments on quantum reflection and Bose-Einstein condensation of ultracold atoms on or near surfaces of different kinds.