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arXiv:2205.12440 · Physical Review A

Transfer of angular momentum of guided light to an atom with an electric quadrupole transition near an optical nanofiber

Fam Le Kien, Síle Nic Chormaic, Thomas Busch

Published Jul 18, 2022• 10 citations
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Abstract

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 $M=2$ of the hyperfine-structure level $5{S}_{1/2}F=2$ 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 $^{87}\mathrm{Rb}$ atom. We show that the absolute value of the torque for the higher-order mode ${\mathrm{HE}}_{21}$ is larger than that of the torque for the fundamental mode ${\mathrm{HE}}_{11}$ except for the case ${M}^{\ensuremath{'}}\ensuremath{-}M=2$, where the torque for the mode ${\mathrm{HE}}_{21}$ is vanishing.

DOI
10.1103/physreva.106.013712

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We calculate analytically and numerically the axial orbital and spin torques of guided light on a two-level atom near an optical nanofiber. We show that the generation of these torques is governed by the angular momentum conservation law in the Minkowski formulation. The orbital torque on the atom near the fiber has a contribution from the average recoil of spontaneously emitted photons. Photon angular momentum and atomic spin angular momentum can be converted into atomic orbital angular momentum. The orbital and spin angular momenta of the guided field are not transferred separately to the orbital and spin angular momenta of the atom.
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.
We calculate analytically and numerically the axial orbital and spin torques of guided light on a two-level atom near an optical nanofiber. We show that the generation of these torques is governed by the angular momentum conservation law in the Minkowski formulation. The orbital torque on the atom near the fiber has a contribution from the average recoil of spontaneously emitted photons. Photon angular momentum and atomic spin angular momentum can be converted into atomic orbital angular momentum. The orbital and spin angular momenta of the guided field are not transferred separately to the orbital and spin angular momenta of the atom.
Photons carry one unit of angular momentum associated with their spin~\cite{Beth1936}. Structured vortex beams carry additional orbital angular momentum which can also be transferred to matter~\cite{Allen1992}. This extra twist has been used for example to drive motion of microscopic particles in optical tweezers as well as to create vortices in degenerate quantum gases~\cite{He1995,Andersen2006}. Here we demonstrate the transfer of optical orbital angular momentum from the transverse spatial structure of the beam to the internal (electronic) degrees of freedom of an atom. Probing a quadrupole transition of a single trapped 40^{40}40Ca+^++ ion localized at the center of the vortex, we observe strongly modified selection rules, accounting for both the photon spin and the vorticity of the field. In particular, we show that an atom can absorb two quanta of angular momentum from a single photon even when rotational symmetry is conserved. In contrast to previous findings~\cite{Araoka2005,Loeffler2011a,Mathevet2013}, our experiment allows for conditions where the vorticity of the laser beam determines the optical excitation, contributing to the long-standing discussion on whether the orbital angular momentum of photons can be transferred to atomic internal degrees of freedom~\cite{VanEnk1994,Babiker2002,Jauregui2004, Schmiegelow2012, Mondal2014, Scholz-Marggraf2014} and paves the way for its use to tailor light-matter interactions.
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 $a\ensuremath{\simeq}107$ nm, and is larger than that for quasicircularly polarized higher-order hybrid modes, transverse electric modes, and transverse magnetic modes in the region a<498.2a<498.2a<498.2 nm.
Recent experiments involving the interaction of optical vortices with atoms in quadrupole transitions have shown it to be accompanied by the exchange of orbital angular momentum (OAM) between the electronic states of the atom and the optical vortex field. Earlier work, both theoretical and experimental, had ruled out the transfer of a vortex OAM to the electronic degrees of freedom in an electric dipole atomic transition and it has been confirmed that the lowest multipolar order involving an OAM transfer to the electronic motion is indeed the electric quadrupole. Hitherto, the quadrupole transition involving optical vortices has not been quantified and we thus set out to evaluate the absorption rate accompanied by an OAM transfer with reference to the $6^{2}S_{1/2}\ensuremath{\rightarrow}5^{2}D_{5/2}$ in Cs when cesium atoms are subject to the field of a linearly polarized optical vortex. Our results assuming typical experimentally accessible parameters indicate that the absorption rate for moderate light intensities is lower than the quadrupole spontaneous emission rate but should still be within the measurement capabilities of modern spectroscopic techniques.