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arXiv:1703.01844 · Physical Review A

Twisted molecular excitons as mediators for changing the angular momentum of light

Xiaoning Zang, Mark T. Lusk

Published Jul 11, 2017• 12 citations
arXivHTMLPDF

Abstract

Molecules with ${C}_{N}$ or ${C}_{Nh}$ symmetry can absorb quanta of optical angular momentum to generate twisted excitons with well-defined quasiangular momenta of their own. Angular momentum is conserved in such interactions at the level of a paraxial approximation for the light beam. A sequence of absorption events can thus be used to create a range of excitonic angular momenta. Subsequent decay can produce radiation with a single angular momentum equal to that accumulated. Such molecules can thus be viewed as mediators for changing the angular momentum of light. This sidesteps the need to exploit nonlinear light-matter interactions based on higher-order susceptibilities. A tight-binding paradigm is used to verify angular momentum conservation and demonstrate how it can be exploited to change the angular momentum of light. The approach is then extended to a time-dependent density functional theory setting where the key results are shown to hold in a many-body, multilevel setting.

DOI
10.1103/physreva.96.013819

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Molecules with CN{C}_{N}CN​ or CNh{C}_{Nh}CNh​ symmetry can absorb quanta of optical angular momentum to generate twisted excitons with well-defined quasiangular momenta of their own. Angular momentum is conserved in such interactions at the level of a paraxial approximation for the light beam. A sequence of absorption events can thus be used to create a range of excitonic angular momenta. Subsequent decay can produce radiation with a single angular momentum equal to that accumulated. Such molecules can thus be viewed as mediators for changing the angular momentum of light. This sidesteps the need to exploit nonlinear light-matter interactions based on higher-order susceptibilities. A tight-binding paradigm is used to verify angular momentum conservation and demonstrate how it can be exploited to change the angular momentum of light. The approach is then extended to a time-dependent density functional theory setting where the key results are shown to hold in a many-body, multilevel setting.
A class of centrosymmetric molecules support excitons with a well-defined quasi-angular momentum. Cofacial arrangements of these molecules can be engineered so that quantum cutting produces a pair of excitons on sandwiching acceptors with angular momenta that are maximally entangled. These Bell state constituents can subsequently travel in opposite directions down molecular chains as ballistic wave packets. This is a direct excitonic analog to the entangled polarization states produced by the spontaneous parametric downconversion of light. As in optical settings, the ability to produce Bell states should enable experiments and technologies based on non-local excitonic quantum correlation. The idea is elucidated with a combination of quantum electrodynamics theory and numerical simulations.
molecules support excitons with a well-defined quasi-angular momentum. Cofacial arrangements of these molecules can be engineered so that quantum cutting produces a pair of excitons with angular momenta that are maximally entangled. The Bell state constituents can subsequently travel in opposite directions down molecular chains as ballistic wave packets. This is a direct excitonic analog to the entangled polarization states produced by the spontaneous parametric down-conversion of light. As in optical settings, the ability to produce Bell states should enable foundational experiments and technologies based on non-local excitonic quantum correlation. The idea is elucidated with a combination of quantum electrodynamics theory and numerical simulation.
Theoretical work has already established the existence of a light-induced torque acting on the centre of mass of an atom, ion or molecule immersed in twisted light, where the transition frequency is suitably detuned from that of the twisted light beam. The twisted beam carries l units of orbital angular momentum per photon, and the steady-state saturation form of the torque is also determined by the width of the upper state in the atomic transition. It has been shown that, to leading order, the transfer of orbital angular momentum can only occur between the twisted light and the centre of mass motion. We argue here that, for small linewidth, the full time-dependence of the torque is needed to account correctly for the dynamics of atoms in a twisted light beam. We outline the theoretical framework needed to derive this full time-dependence, applying the theory to the motion in a twisted light beam of Eu3+ ions, which possess a particularly narrow linewidth state. For relatively large linewidth, the steady-state forces and torque are appropriate, but the processes of cooling and trapping require the application of several suitably oriented twisted beams. The description of atomic motion in multiple twisted beams demands the application of special coordinate transformations. We show how to construct the appropriate transformation matrices to represent a twisted light beam propagating in an arbitrary direction, and we proceed to investigate the cooling and trapping of Mg+ ions in sets of pairs of counter-propagating twisted beams in two-dimensional and three-dimensional molasses configurations.
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.
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.