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arXiv:2407.05080 · Physical Review Letters

Observation of Space-Dependent Rotational Doppler Shifts with a Single Ion Probe

Nicolás A. Nuñez Barreto, Muriel Bonetto, Marcelo Alejandro Luda, Cecilia Cormick, Christian Tomás Schmiegelow

Published Oct 29, 2024• 5 citations
arXivHTMLPDF

Abstract

We present an experiment investigating the rotational Doppler effect using a single trapped ion excited by two copropagating vortex laser beams. The setup isolates the azimuthal gradients of the fields, eliminating longitudinal and curvature effects. We provide a detailed characterization of the phenomenon by deterministically positioning a single ion across the beams and measuring fluorescence spectra with sharp "dark resonances" whose features depend on the angular velocity of the ion and the difference of optical orbital angular momentum between the two beams. The interpretation of the measurements is supported by numerical simulations and by a simplified analytical model. Our results reveal key properties of the rotational Doppler effect, showing that it increases approaching the center of the beam and that it is independent of the waist of the beam. This offers insights into the feasibility of superkicks or super-Doppler shifts for sensing and manipulating atomic motion transverse to the beams' propagation direction.

DOI
10.1103/physrevlett.133.183601

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We present an experiment investigating the rotational Doppler effect using a single trapped ion excited by two copropagating vortex laser beams. The setup isolates the azimuthal gradients of the fields, eliminating longitudinal and curvature effects. We provide a detailed characterization of the phenomenon by deterministically positioning a single ion across the beams and measuring fluorescence spectra with sharp "dark resonances" whose features depend on the angular velocity of the ion and the difference of optical orbital angular momentum between the two beams. The interpretation of the measurements is supported by numerical simulations and by a simplified analytical model. Our results reveal key properties of the rotational Doppler effect, showing that it increases approaching the center of the beam and that it is independent of the waist of the beam. This offers insights into the feasibility of superkicks or super-Doppler shifts for sensing and manipulating atomic motion transverse to the beams' propagation direction.
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Single, rf-trapped ions find various applications ranging from metrology to quantum computation. High-resolution interrogation of an extremely weak transition under best observation conditions requires an ion almost at rest. To avoid line-broadening effects such as the second order Doppler effect or rf heating in the absence of laser cooling, excess micromotion has to be eliminated as far as possible. We have tested a novel method to probe the motional state of a confined three-level ion. Actually, dark resonances observed with two counterpropagating laser beams are very sensitive to the trapped ion's velocity. Their contrast increases with reduced micromotion and allows in this way to control the oscillation amplitude of the stored ion. The influence of different parameters such as laser linewidth and power has been investigated experimentally and numerically.
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.
Using a structured light beam carrying orbital angular momentum, we demonstrate excitation of the center-of-mass motion of a single atom in the transverse direction to the beam's propagation. This interaction enables quantum control of atomic motion in all axes with a single beam direction, which leads to applications in quantum computing and simulations with ion crystals. Here we demonstrate all the key features required for these applications, namely, coherent dynamics and strong carrier suppression in a configuration with the ion centered in the beam, which allows for single ion addressing and also provides robustness against pointing instabilities. To quantify transverse momentum transfer, we observe coherent dynamics on the sidebands of the S_{1/2} to D_{5/2} transition near 729 nm of a singly charged ^{40}Ca^{+} ion, cooled near the ground state of motion in the 3D harmonic potential of a Paul trap, and placed at the center of a first-order Laguerre-Gaussian beam. Exchange of quanta in the perpendicular direction to the beam's wave vector k is observed with a centered vortex shaped beam, together reduction of the parasitic carrier excitation by a factor of 40. This is in sharp contrast to the vanishing spin-motion coupling at the center of the Gaussian beam. Further, we characterize the coherent interaction by an effective transverse Lamb-Dicke factor η_{⊥}^{exp}=0.0062(5) which is in agreement with our theoretical prediction η_{⊥}^{theo}=0.0057(1).
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.