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arXiv:2501.03077 · Physica Scripta

Impact of cut-off frequency effect on resonance energy transfer and Casimir–Polder interaction

Nguyen Dung Chinh, Vinh N. T. Pham, Nguyen Duy Vy

Published Nov 8, 2024• 2 citations
arXivHTMLPDF

Abstract

Abstract Using the Green’s function approach, we investigate the resonance energy transfer (RET) rate between two parallel, identical two-level atoms in the presence of three types of cylindrical system: a distributed Bragg reflector (DBR), a perfectly reflecting wall (PRW), and a two-layer silicon fiber. Our analysis, incorporating the cut-off frequency condition, reveals significant suppression of the RET rate for atoms positioned along the axis of the cylinder with the PRW. In contrast, for atoms located within the DBR, the RET rate is enhanced in the far zone. Additionally, we find that for atoms oriented radially are placed inside or near the surface of the silicon fiber, the RET rate is entirely inhibited. We also investigate the Casimir–Polder (CP) interaction between a cut-off-frequency DBR and an excited atom, discovering a fully attractive potential towards the surface for the atom within the waveguide.

DOI
10.1088/1402-4896/ad908f

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Abstract Using the Green’s function approach, we investigate the resonance energy transfer (RET) rate between two parallel, identical two-level atoms in the presence of three types of cylindrical system: a distributed Bragg reflector (DBR), a perfectly reflecting wall (PRW), and a two-layer silicon fiber. Our analysis, incorporating the cut-off frequency condition, reveals significant suppression of the RET rate for atoms positioned along the axis of the cylinder with the PRW. In contrast, for atoms located within the DBR, the RET rate is enhanced in the far zone. Additionally, we find that for atoms oriented radially are placed inside or near the surface of the silicon fiber, the RET rate is entirely inhibited. We also investigate the Casimir–Polder (CP) interaction between a cut-off-frequency DBR and an excited atom, discovering a fully attractive potential towards the surface for the atom within the waveguide.
Abstract We consider how the rate of resonance energy transfer (RET) between an excited atom and a ground-state one is affected by the presence of a cylindrical photonic band-gap waveguide by using the Green’s function approach. Both positions inside and outside the wall and three types of atomic dipole moment orientations, namely radial, azimuthal and axial orientations, are examined. Results for the photonic band-gap structure and those for the perfectly reflecting one are compared. Differences between the two are found to be significant near the surfaces. Frequency dependence of the rate, which is beyond the perfectly reflecting wall model, is investigated. It is shown that when the waveguide is located in between two atoms which have transition dipole moments parallel with the axis and transition frequency falling within the gap region, the RET is suppressed.
Abstract Spontaneous decay rate and Casimir–Polder interaction of an excited two-level atom enclosed in a distributed-Bragg-reflector cylindrical waveguide are studied. Conditions for resonances to exist are established by comparing the distributed-Bragg-reflector-waveguide results with those of a perfectly reflecting hollow waveguide, and taking advantage of the simplicity of the Green tensor of the latter. The Casimir–Polder potential is obtained and found to exhibit a potential well along the cylinder axis. The results remain valid when realistic frequency-dependent permittivities of Si and SiO 2 are used.
Abstract The resonance energy transfer rate between an excited atom and a ground-state one depends on various factors such as the matching between the donor and acceptor wavelengths, location of the atoms, and the environment that surrounds them. We investigate the interatomic resonance energy transfer rate in the presence of a cylindrical dielectric multi-layer structure using the Green’s tensor formalism. The permittivities of the layers are interchanged periodically between low and high values, so as to create a photonic band-gap system in the radial direction. We present results for atoms situated in a cross section normal to the cylinder axis. The contrast between low and high permittivities is varied to elucidate the effect of the band-gap structure. Furthermore, the results are compared with those for atoms located near a perfectly reflecting c-ylinder.
Abstract We derive a formula for computing the resonance energy transfer (RET) rate between two two-level atoms—one in the excited state (donor) and the other in the ground state (acceptor)—oriented along the axial direction near a finite-length dielectric cylinder, which can be regarded as a finite optical fiber. By employing a truncated Born expansion of the homogeneous Green’s tensor and using numerical solutions, we identify a range of parameters for which the finite cylinder can be well approximated by an infinite one, whose Green’s tensor is known in closed form. Beyond the validity of the infinite-cylinder approximation, we find that the effect of the fiber tip on the RET rate becomes significant, particularly when the donor–acceptor pair is located above the top edge of the fiber.
We consider the energy transfer process between two identical atoms placed inside a perfectly conducting cylindrical waveguide. We first introduce a general analytical expression of the energy transfer amplitude in terms of the electromagnetic Green's tensor; we then evaluate it in the case of a cylindrical waveguide made of a perfect conductor, for which analytical expressions of the Green's tensor exist. We numerically analyze the energy transfer amplitude when the radius of the waveguide is such that the transition frequency of both atoms is below the lower cutoff frequency of the waveguide, so that the resonant photon exchange is strongly suppressed. We consider both cases of atomic dipoles parallel and orthogonal to the axis of the guide. In both cases, we find that the energy transfer is modified by the presence of the waveguide. In the near zone, that is when the atomic separation is smaller than the atomic transition wavelength, the change, with respect to the free-space case, is small for axial dipoles, while it is larger for radial dipoles; it grows when the intermediate region between near and far zone is approached. In the far zone, we find that the energy transfer amplitude is strongly suppressed by the waveguide, becoming virtually zero. A physical interpretation of these results is discussed. Finally, we discuss the resonance interaction energy and force between two identical correlated atoms in the waveguide, one excited and the other in the ground state, prepared in their symmetric or antisymmetric superposition.
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.