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Applied Physics B

Waveguide-induced dispersion interaction between two two-level atoms with orthogonal in-transverse-plane dipoles

Fam Le Kien, Lewis Ruks, Thomas Busch

Published Oct 16, 2019• 3 citations
Publisher

Abstract

Abstract We study the dispersion interaction between two ground-state two-level atoms near a cylindrical vacuum-clad optical waveguide. We focus on the case where the electric-dipole matrix-element vectors of the atoms are perpendicular to each other and to the interatomic axis. When these atoms are in free space, the dispersion interaction between them vanishes. In the presence of a waveguide aligned parallel to the interatomic axis, the energy of the dispersion interaction between the atoms may become nonzero and comparable to the average energy of the dispersion interaction between two atoms with arbitrarily oriented dipoles in free space. This waveguide-induced dispersion interaction is a consequence of the anisotropy of the medium around the atoms.

DOI
10.1007/s00340-019-7321-x

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Abstract We study the dispersion interaction between two ground-state two-level atoms near a cylindrical vacuum-clad optical waveguide. We focus on the case where the electric-dipole matrix-element vectors of the atoms are perpendicular to each other and to the interatomic axis. When these atoms are in free space, the dispersion interaction between them vanishes. In the presence of a waveguide aligned parallel to the interatomic axis, the energy of the dispersion interaction between the atoms may become nonzero and comparable to the average energy of the dispersion interaction between two atoms with arbitrarily oriented dipoles in free space. This waveguide-induced dispersion interaction is a consequence of the anisotropy of the medium around the atoms.
Abstract We consider dispersion interaction between two ground-state atoms positioned inside a hollow cylindrical waveguide or outside a solid cylindrical waveguide. In the case of atoms having radial dipole moments and being located outside a waveguide, the dispersion interaction is found to be strongly enhanced as compared with that in free space. Results for a perfectly reflecting wall and walls made of a conductor (gold) and a dielectric (undoped silicon) are compared. It is shown that though the perfectly reflecting waveguide model can predict qualitatively correctly the main features of the interatomic dispersion interaction, taking into account realistic permittivities is important because the difference can amount to a few orders of magnitudes.
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.
Spontaneous emission of an atom with two close upper levels and one lower level in a multilayer dielectric medium, and quantum interference between transitions from the upper levels to the lower one, are considered. Since the medium is inhomogeneous along the direction normal to the interfaces of the dielectric layers, the vacuum has an anisotropic spatial structure, and quantum intereference between the two decay channels can appear even if the two dipole matrix elements are orthogonal to each other. If the atom is placed in a three-layer dielectric plate cavity, a strong quantum interference similar to that for an atom with two nearly parallel dipole moments in free space arises due to the influence of anisotropic vacuum. Putting the atom in a three-layer dielectric waveguide and a one-dimensional photonic crystal, there appears a strong quantum interference similar to that for an atom with nearly antiparallel dipole moments.
We study the resonance interaction between two quantum electric dipoles immersed in optically active surroundings. Quantum electrodynamics is employed to deal with dipole-vacuum interaction. Our results show that the optical activity of surroundings will not change the single atom behaviors while it can change the collective behaviors of the two dipoles, as well as greatly affect the dipole-dipole resonance interaction. Especially, if the orientations of two dipoles are orthogonal and respectively perpendicular to the interdipole axis, the interdipole resonance interaction can be established with the help of optically active surroundings while there is no resonance interaction in vacuum.
In this work we study the spontaneous emission of a two-level atom placed inside a hollow cylindrical waveguide of infinite length and with perfectly electric conducting walls. The atom, whose electric dipole moment is assumed to be oriented along the symmetry axis of the waveguide, couples to a photonic band structure with a non-linear dispersion relation. We address two different regimes of coupling between the atom and the photonic band structure. In particular, we refer to the regime where the internal frequency of the a.tom is close to a band edge as the strong coupling regime and to the regime where the internal frequency is far from a band edge as the weak coupling regime. In the weak coupling regime, we find that the a.tom decays exponentially with a modified decayed rate due to the presence of the waveguide, and that the line-shape of the emitted photons within every band takes the form of a Lorentzian. In the strong coupling regime, we find a non-exponential decay of the atom, which is due to non-Markovian dynamics of the system. Moreover, the population of the atom presents oscillations in time and it converges to a non-zero positive value, indicating that the a.tom never fully decays. In this regime the spectrum of the emitted photons becomes more involved.
We investigate spontaneous emission of a two-level atom with an arbitrarily polarized electric dipole in front of a flat dielectric surface. We treat the general case where the atomic dipole matrix element is a complex vector, that is, the atomic dipole can rotate with time in space. We calculate the rates of spontaneous emission into evanescent and radiation modes. We systematically study the angular densities of the rates in the space of wave vectors for the field modes. We show that the asymmetry of the angular density of the spontaneous emission rate under central inversion in the space of in-plane wave vectors occurs when the ellipticity vector of the atomic dipole polarization overlaps with the ellipticity vector of the field mode polarization.