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arXiv:1709.06700 · Physical Review A

Enhancement of the quadrupole interaction of an atom with the guided light of an ultrathin optical fiber

Fam Le Kien, Tridib Ray, Thomas Nieddu, Thomas Busch, Síle Nic Chormaic

Published Jan 16, 2018• 34 citations
arXivHTMLPDF

Abstract

We investigate the electric quadrupole interaction of an alkali-metal atom with guided light in the fundamental and higher-order modes of a vacuum-clad ultrathin optical fiber. We calculate the quadrupole Rabi frequency, the quadrupole oscillator strength, and their enhancement factors. In the example of a $^{87}\mathrm{Rb}$ atom, we study the dependencies of the quadrupole Rabi frequency on the quantum numbers of the transition, the mode type, the phase circulation direction, the propagation direction, the orientation of the quantization axis, the position of the atom, and the fiber radius. We find that the root-mean-square (rms) quadrupole Rabi frequency reduces quickly but the quadrupole oscillator strength varies slowly with increasing radial distance. We show that the enhancement factors of the rms Rabi frequency and the oscillator strength do not depend on any characteristics of the internal atomic states except for the atomic transition frequency. The enhancement factor of the oscillator strength can be significant even when the atom is far away from the fiber. We show that, in the case where the atom is positioned on the fiber surface, the oscillator strength for the quasicircularly polarized fundamental mode ${\mathrm{HE}}_{11}$ has a local minimum at the fiber radius $a\ensuremath{\simeq}107$ nm, and is larger than that for quasicircularly polarized higher-order hybrid modes, transverse electric modes, and transverse magnetic modes in the region $a<498.2$ nm.

DOI
10.1103/physreva.97.013821

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We investigate the electric quadrupole interaction of an alkali-metal atom with guided light in the fundamental and higher-order modes of a vacuum-clad ultrathin optical fiber. We calculate the quadrupole Rabi frequency, the quadrupole oscillator strength, and their enhancement factors. In the example of a 87Rb^{87}\mathrm{Rb}87Rb atom, we study the dependencies of the quadrupole Rabi frequency on the quantum numbers of the transition, the mode type, the phase circulation direction, the propagation direction, the orientation of the quantization axis, the position of the atom, and the fiber radius. We find that the root-mean-square (rms) quadrupole Rabi frequency reduces quickly but the quadrupole oscillator strength varies slowly with increasing radial distance. We show that the enhancement factors of the rms Rabi frequency and the oscillator strength do not depend on any characteristics of the internal atomic states except for the atomic transition frequency. The enhancement factor of the oscillator strength can be significant even when the atom is far away from the fiber. We show that, in the case where the atom is positioned on the fiber surface, the oscillator strength for the quasicircularly polarized fundamental mode HE11{\mathrm{HE}}_{11}HE11​ has a local minimum at the fiber radius a\ensuremath≃107a\ensuremath{\simeq}107a\ensuremath≃107 nm, and is larger than that for quasicircularly polarized higher-order hybrid modes, transverse electric modes, and transverse magnetic modes in the region a<498.2a<498.2a<498.2 nm.
We study the directional dependence of the coupling between a nanofiber-guided light field and a two-level atom with an electric quadrupole transition. We examine the situation where the nanofiber is aligned along the zzz axis, the atom lies on the fiber transverse xxx axis, the quantization axis for the atomic internal states is the other orthogonal transverse yyy axis, the atomic upper and lower levels are the magnetic sublevels ${M}^{\ensuremath{'}}$ and MMM of hyperfine-structure levels of an alkali-metal atom, and the field is in a quasilinearly polarized fundamental guided mode HE11{\mathrm{HE}}_{11}HE11​ with the polarization $\ensuremath{\xi}=x$ or yyy. We find that the absolute value of the quadrupole Rabi frequency depends on the propagation direction of the light field in the cases of (${M}^{\ensuremath{'}}\ensuremath{-}M=\ifmmode\pm\else\textpm\fi{}1, \ensuremath{\xi}=y$) and (${M}^{\ensuremath{'}}\ensuremath{-}M=\ifmmode\pm\else\textpm\fi{}2, \ensuremath{\xi}=x$). We show that the directional dependence of the coupling leads to the directional dependence of spontaneous emission into guided modes. We find that the directional dependence of the atom-field coupling in the case of quadrupole transitions is not entirely due to spin-orbit coupling of light: there are some other contributions resulting from the gradient of the spatial phase factor of the field.
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We study the transfer of angular momentum of guided photons to a two-level atom with an electric quadrupole transition near an optical nanofiber. We show that the generation of the axial orbital torque of the driving guided field on the atom is governed by the internal-state selection rules for the quadrupole transition and by the angular momentum conservation law with the photon angular momentum given in the Minkowski formulation. We find that the torque depends on the photon angular momentum, the change in the angular momentum of the atomic internal state, and the quadrupole-transition Rabi frequency. We calculate numerically the torques for the quadrupole transitions between the sublevel M=2M=2M=2 of the hyperfine-structure level 5S1/2F=25{S}_{1/2}F=25S1/2​F=2 and the sublevels ${M}^{\ensuremath{'}}=0$, 1, 2, 3, and 4 of the hyperfine-structure level $4{D}_{5/2}{F}^{\ensuremath{'}}=4$ of a 87Rb^{87}\mathrm{Rb}87Rb atom. We show that the absolute value of the torque for the higher-order mode HE21{\mathrm{HE}}_{21}HE21​ is larger than that of the torque for the fundamental mode HE11{\mathrm{HE}}_{11}HE11​ except for the case ${M}^{\ensuremath{'}}\ensuremath{-}M=2$, where the torque for the mode HE21{\mathrm{HE}}_{21}HE21​ is vanishing.
Abstract We evaluate the rate of the absorption of an optical nanofibre mode by a Cs atom in an electric quadrupole transition. With the Cs atom localised near the outer surface of the optical nano-fibre, an interaction occurs between the atomic quadrupole tensor components and the gradients of the vector components of the electric field of a hybrid fibre mode. The absorption rate is evaluated as a function of the radial position of the atom from the fibre axis, assuming a specific value of the laser power and we use experimentally accessible parameters. We find that the absorption of the hybrid modes by the Cs atom decreases as the atom recedes away from the fibre axis and it formally vanishes at sufficiently large radial distances. Close to the fibre, however, the absorption rate for the input power chosen can be two orders of magnitude larger than the quadrupole de-excitation rate despite the moderate power used.
We study the force of light on a two-level atom near an ultrathin optical fiber using the mode function method and the Green tensor technique. We show that the total force consists of the driving-field force, the spontaneous-emission recoil force, and the fiber-induced van der Waals potential force. Due to the existence of a nonzero axial component of the field in a guided mode, the Rabi frequency and, hence, the magnitude of the force of the guided driving field may depend on the propagation direction. When the atomic dipole rotates in the meridional plane, the spontaneous-emission recoil force may arise as a result of the asymmetric spontaneous emission with respect to opposite propagation directions. The van der Waals potential for the atom in the ground state is off-resonant and opposite to the off-resonant part of the van der Waals potential for the atom in the excited state. Unlike the potential for the ground state, the potential for the excited state may oscillate depending on the distance from the atom to the fiber surface.