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arXiv:1511.07206

Excitation of an Atomic Transition with a Vortex Laser Beam

Christian Tomás Schmiegelow, J. Schulz, Henning Kaufmann, Thomas Ruster, Ulrich Poschinger, Ferdinand Schmidt‐Kaler

Published Nov 23, 2015• 6 citations
arXivHTMLPDF

Abstract

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 $^{40}$Ca$^+$ 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.

DOI
10.48550/arxiv.1511.07206

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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.
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.
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.
We study the interaction of a light beams carrying angular momentum with a single, trapped and well localized ion. We provide a detailed calculation of selection rules and excitation probabilities for quadrupole transitions. The results show the dependencies on the angular momentum and polarization of the laser beam as well as the direction of the quantization magnetic field. In order to observe optimally the specific effects, focusing the angular momentum beam close to the diffraction limit is required. We discuss a protocol for examining experimentally the effects on the S1/2_{1/2}1/2​ to D5/2_{5/2}5/2​ transition using a 40^{40}40Ca+^++ ion. Various applications and advantages are expected when using light carrying angular momentum: In quantum information processing, where qubit states of ion crystals are controlled, parasitic light shifts could be avoided as the ion is excited in the dark zone of the beam at zero electric field amplitude. Such interactions also open the door to high dimensional entanglement between light and matter. In spectroscopy one might access transitions which have escaped excitation so far due to vanishing transition dipole moments.
We consider transfer of optical vortices between laser pulses carrying orbital angular momentum in a cloud of cold atoms characterized by the $\mathrm{\ensuremath{\Lambda}}$ configuration of the atom-light coupling. The atoms are initially prepared in a coherent superposition of the lower levels, creating a so-called phaseonium medium. If a single vortex beam initially acts on one transition of the scheme, an extra laser beam is subsequently generated with the same vorticity as that of the incident vortex beam. The absorption of the incident probe beam takes place mostly at the beginning of the atomic medium within the absorption length. The losses disappear as the probe beam propagates deeper into the medium where the atoms are transferred to their dark states. The method is extended to a tripod atom-light coupling scheme and a more general (n+1n+1n+1)-level scheme containing nnn ground states and one excited state, allowing for creation of multiple twisted light beams. We also analyze generation of composite optical vortices in the scheme using a superposition of two initial vortex beams and study lossless propagation of such composite vortices.
In this paper we analyze the novel quantum properties of atomic photo-excitations generated by Orbital Angular Momentum (OAM) photons. It was previously predicted for Bessel beams (BB), that transitionsin atomic systems driven by twisted laser beams obey a modified set of position-dependent angular-momentum selection rules. It was also shown, that in the case of perfect alignment of the atom on the beam axis, total angular momentum of the photon must be fully transferred to the internal degrees of freedom of the target, which causes dramatic enhancement of higher-multipole processes. As a result, weak atomic transitions, which are hardly observable in interactions with simple states of light, become accessible with OAM photons. In the current paper, we extend the earlier developed theory to describe atomic photoexcitations by Bessel-Gauss (BG) and Laguerre-Gauss (LG) modes. It allowed us to infer the information about the phase structure of the beam, such as mode content and topological charge. The formalism exhibits a high level of sensitivity to the polarization content of the laser beam, which is on the order of 0.005% of the polarization admixture. The theoretical predictions are confirmed experimentally for photo-excitation of Ca40+ ions, trapped in a micro-structured, segmented Paul trap. The full set of quadrupole transitions from the S-state were generated by 729nm OAM laser beam shaped with a holographic phase-plate with a fork-dislocation. The experiment was conducted by Ferdinand Schmidt-Kaler's group at the University of Mainz.