Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Cavity quantum electrodynamics for a cylinder: Inside a hollow dielectric and near a solid dielectric cylinder

Hyunchul Nha, W. Jhe

Published Sep 1, 1997• 68 citations
Publisher

Abstract

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 $b$ (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 $b$ 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.

DOI
10.1103/physreva.56.2213

Related papers

Cavity quantum electrodynamics inside a hollow spherical cavity

W. Jhe, K. Jang

We present a general formalism for studying the cavity quantum electrodynamics for an atom or a radiating dipole inside a hollow spherical cavity. The atomic-energy-level shifts and the modified dipolar decay rates are calculated in specific cases. In particular, the energy shifts for an atom located at the center of an empty sphere (radius a) vary as 1/${\mathit{a}}^{4}$ for large ka and 1/${\mathit{a}}^{2}$ for small ka, where k is the wave number. We attribute these variations to the retarded Casimir-Polder interaction and the state-independent vacuum-field contribution, respectively. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Feb 1, 1996•28 citations

Atomic energy-level shifts near a dielectric microsphere

W. Jhe, Jae‐Wook Kim

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).

Physical Review A•Feb 1, 1995•27 citations

Quantum electrodynamics of an atom in front of a non–dispersive dielectric half–space

Shin-Tza Wu, Claudia Eberlein

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.

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Jul 8, 1999•38 citations

Submicron rectangular cylinders as atom guides

S. Al‐Awfi, M. Babiker

The guiding of atoms by laser light is investigated for atoms inside a long hollow cylinder with a rectangular cross section of subwavelength dimensions $a\ifmmode\times\else\texttimes\fi{}b.$ The cavity modes are quantized, allowing the position-dependent spontaneous emission rate to be evaluated for an electric dipole inside the cylinder. Useful limits of the spontaneous rate are derived. In particular, results appropriate for the parallel-plate case are recovered when side a of the rectangular cross section becomes large, while side b is kept fixed. In the limit of the small cross section, especially when both a and b are less than \ensuremath{\lambda} (the atom electric dipole transition wavelength), the spontaneous emission process is possible only via a few cavity modes. If a cavity mode is now excited with sufficient intensity, the atoms become subject to a transverse dipole potential and an axial dissipative force, both of which vary across the cylinder and are also functions of the atom axial velocity. The dipole potential is responsible for the transverse trapping (and hence the channeling) of atoms at specific regions of the cross section, while the dissipative force controls the axial motion of the channeled atoms. The conditions facilitating atom guiding are explored using typical parameters for sodium atoms in rectangular cylinders of subwavelength dimensions.

Physical Review A•Dec 1, 1998•16 citations

Enhancement of energy relaxation rates near metal-coated dielectric cylinders

G. D. Banyard, C. R. Bennett, M. Babiker

The electromagnetic modes and their field distributions are evaluated for a dielectric cylindrical structure embedded in another dielectric, with a thin metallic film at the cylinder/dielectric interface. These modes provide energy relaxation channels for excited dipole emitters located inside or outside the cylinder. Significantly, we find that the emission rate is sensitive to the magnitude of the electron density of the metallic film coating. For typical parameter values, we find large enhancements of the emission rate, which can be in excess of three orders of magnitude, relative to the case in the absence of the film, arising at specific ranges of electron density. The theory is shown to conform with known limits, including the high density (perfect conductor) limit and the large distance (unbounded bulk) limit. The implications of the predicted enhancement due to the metal coating for the purpose of guiding atoms within such microstructures are pointed out. PACS Numbers: 34.50.Dy, 32.80.-t, 41.20.Jb, 42.50.-p 1 There is at present much interest in small (micrometre to nanometre) scale spherical

•Jan 1, 2001•11 citations

The Casimir-Polder interaction between atoms and hollow-core fibers

Bettina Beverungen, Daniel Reiche, Kurt Busch +1 more

The Casimir-Polder force acts on polarizable particles due to quantum fluctuations of the electromagnetic field that are modified by the presence of material bodies. We investigate the Casimir-Polder interaction for atoms near cylindrical fibers with hollow cores. This geometry represents one of the archetypal configurations encountered in numerous experimental setups designed to control and manipulate atoms in fundamental and quantum technological applications. Specifically, we analyze how the interplay of both geometrical and material-related length scales characterize the interaction, emphasizing the impact of the shell thickness. We develop a flexible and fast-converging numerical scheme for evaluating the interaction over a wide range of atom-cylinder separations at both zero and finite temperature. Furthermore, we provide a detailed analytical investigation of how various material properties modify the Casimir-Polder potential. Finally, we analyze and discuss a number of limiting cases and compare numerical computations with corresponding analytical asymptotic expressions. In particular, in this geometry the Casimir-Polder potential is able to distinguish between an ohmic and non-ohmic description of conductors. One of the most significant outcomes of our work is that the shell thickness emerges as a useful parameter for controlling the interaction, opening avenues for both fundamental physics and applications in quantum technologies.

quant-pharXiv:2512.11603•Dec 15, 2025
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{b}^{\ensuremath{-}2}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{b}^{\ensuremath{-}4}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 present a general formalism for studying the cavity quantum electrodynamics for an atom or a radiating dipole inside a hollow spherical cavity. The atomic-energy-level shifts and the modified dipolar decay rates are calculated in specific cases. In particular, the energy shifts for an atom located at the center of an empty sphere (radius a) vary as 1/a4{\mathit{a}}^{4}a4 for large ka and 1/a2{\mathit{a}}^{2}a2 for small ka, where k is the wave number. We attribute these variations to the retarded Casimir-Polder interaction and the state-independent vacuum-field contribution, respectively. \textcopyright{} 1996 The American Physical Society.
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).
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.
The guiding of atoms by laser light is investigated for atoms inside a long hollow cylinder with a rectangular cross section of subwavelength dimensions $a\ifmmode\times\else\texttimes\fi{}b.$ The cavity modes are quantized, allowing the position-dependent spontaneous emission rate to be evaluated for an electric dipole inside the cylinder. Useful limits of the spontaneous rate are derived. In particular, results appropriate for the parallel-plate case are recovered when side a of the rectangular cross section becomes large, while side b is kept fixed. In the limit of the small cross section, especially when both a and b are less than \ensuremath{\lambda} (the atom electric dipole transition wavelength), the spontaneous emission process is possible only via a few cavity modes. If a cavity mode is now excited with sufficient intensity, the atoms become subject to a transverse dipole potential and an axial dissipative force, both of which vary across the cylinder and are also functions of the atom axial velocity. The dipole potential is responsible for the transverse trapping (and hence the channeling) of atoms at specific regions of the cross section, while the dissipative force controls the axial motion of the channeled atoms. The conditions facilitating atom guiding are explored using typical parameters for sodium atoms in rectangular cylinders of subwavelength dimensions.
The electromagnetic modes and their field distributions are evaluated for a dielectric cylindrical structure embedded in another dielectric, with a thin metallic film at the cylinder/dielectric interface. These modes provide energy relaxation channels for excited dipole emitters located inside or outside the cylinder. Significantly, we find that the emission rate is sensitive to the magnitude of the electron density of the metallic film coating. For typical parameter values, we find large enhancements of the emission rate, which can be in excess of three orders of magnitude, relative to the case in the absence of the film, arising at specific ranges of electron density. The theory is shown to conform with known limits, including the high density (perfect conductor) limit and the large distance (unbounded bulk) limit. The implications of the predicted enhancement due to the metal coating for the purpose of guiding atoms within such microstructures are pointed out. PACS Numbers: 34.50.Dy, 32.80.-t, 41.20.Jb, 42.50.-p 1 There is at present much interest in small (micrometre to nanometre) scale spherical
The Casimir-Polder force acts on polarizable particles due to quantum fluctuations of the electromagnetic field that are modified by the presence of material bodies. We investigate the Casimir-Polder interaction for atoms near cylindrical fibers with hollow cores. This geometry represents one of the archetypal configurations encountered in numerous experimental setups designed to control and manipulate atoms in fundamental and quantum technological applications. Specifically, we analyze how the interplay of both geometrical and material-related length scales characterize the interaction, emphasizing the impact of the shell thickness. We develop a flexible and fast-converging numerical scheme for evaluating the interaction over a wide range of atom-cylinder separations at both zero and finite temperature. Furthermore, we provide a detailed analytical investigation of how various material properties modify the Casimir-Polder potential. Finally, we analyze and discuss a number of limiting cases and compare numerical computations with corresponding analytical asymptotic expressions. In particular, in this geometry the Casimir-Polder potential is able to distinguish between an ohmic and non-ohmic description of conductors. One of the most significant outcomes of our work is that the shell thickness emerges as a useful parameter for controlling the interaction, opening avenues for both fundamental physics and applications in quantum technologies.