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Frontiers in Optics

Optical Angular Momentum Transfer to Sub-Wavelength Quantum Systems

Andrei V. Afanasev, Maria Solyanik‐Gorgone

Published Jan 1, 2019• 0 citations
Publisher

Abstract

Twisted light, or optical vortices, can transfer angular momentum both to internal excitation of a target and to its center-of-mass (CM) motion. We use an example of electric dipole (E1) and electric quadrupole (E2) photoexcitation in a single atom to demonstrate that the internal vs CM transfer of optical angular momentum depends on atom’s location with respect to the optical vortex center and multipolarity of the quantum transition.

DOI
10.1364/fio.2019.jw4a.22

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Twisted light, or optical vortices, can transfer angular momentum both to internal excitation of a target and to its center-of-mass (CM) motion. We use an example of electric dipole (E1) and electric quadrupole (E2) photoexcitation in a single atom to demonstrate that the internal vs CM transfer of optical angular momentum depends on atom’s location with respect to the optical vortex center and multipolarity of the quantum transition.
In the interaction of molecules with light endowed with orbital angular momentum, an exchange of orbital angular momentum in an electric dipole transition occurs only between the light and the center of mass motion; i.e., internal "electronic-type" motion does not participate in any exchange of orbital angular momentum in a dipole transition. A quadrupole transition is the lowest electric multipolar process in which an exchange of orbital angular momentum can occur between the light, the internal motion, and the center of mass motion. This rules out experiments seeking to observe exchange of orbital angular momentum between light beams and the internal motion in electric dipole transitions.
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.
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.
Photons can carry angular momentum, not only due to their spin, but also due to their spatial structure. This extra twist has been used, for example, to drive circular motion of microscopic particles in optical tweezers as well as to create vortices in quantum gases. Here we excite an atomic transition with a vortex laser beam and demonstrate the transfer of optical orbital angular momentum to the valence electron of a single trapped ion. We observe strongly modified selection rules showing that an atom can absorb two quanta of angular momentum from a single photon: one from the spin and another from the spatial structure of the beam. Furthermore, we show that parasitic ac-Stark shifts from off-resonant transitions are suppressed in the dark centre of vortex beams. These results show how light's spatial structure can determine the characteristics of light-matter interaction and pave the way for its application and observation in other systems.
The exchange of orbital angular momentum between a Laguerre-Gaussian beam of light and the center-of-mass motion of an atom or molecule is well known. We show that the orbital angular momentum of light can also be transferred to the internal electronic or rotational motion of an atom or a molecule provided the internal and center-of-mass motions are coupled. However, this transfer does not happen directly to the internal motion, but via center-of-mass motion. If atoms or molecules are cooled down to the recoil limit, then an exchange of angular momentum between the quantized center-of-mass motion and the internal motion is possible during the interaction of cold atoms or molecules with the Laguerre-Gaussian beam. The orientation of the exchanged angular momentum is determined by the sign of the winding number of the Laguerre-Gaussian beam. We present selective results of numerical calculations for the quadrupole transition rates in the interaction of the Laguerre-Gaussian beam with an atomic Bose-Einstein condensate to illustrate the underlying mechanism of light orbital angular momentum transfer. We discuss how the alignment of diatomic molecules will facilitate exploration of the effects of light orbital angular momentum on the electronic motion of molecules.
Twisted light beams, or optical vortices, have been used to drive the circular motion of microscopic particles in optical tweezers and have been shown to generate vortices in quantum gases. Recent studies have established that electric quadrupole interactions can mediate an orbital angular momentum exchange between twisted light and the electronic degrees of freedom of atoms. Here we consider a quadrupole atomic transition mediated by a circularly-polarized optical vortex. We evaluate the transfer rate of the optical angular momentum to a Ca+ ion involving the 42S1∕2→32D5∕2 quadrupole transition and explain how the polarization state and the topological charge of the vortex beam determine the selection rules.