Excitation of an Electric Octupole Transition by Twisted Light

Open Access

Excitation of an Electric Octupole Transition by Twisted Light

R. Lange, N. Huntemann, A. A. Peshkov, A. Surzhykov, and E. Peik

Phys. Rev. Lett. 129, 253901 – Published 12 December 2022

Abstract

We study the coherent excitation of the ${}^{2}{S_{1 / 2}} \to {}^{2}{F_{7 / 2}}$ electric octupole ( $E 3$ ) transition by twisted light modes with a single ${}^{171}{Yb}^{+}$ ion in the dark center of a vortex beam. The intensity distribution of the beam is mapped as a function of the ion’s position by measuring the light shift on an auxiliary electric quadrupole transition. In the center of the vortex beam, we observe excitation of the $E 3$ transition with a fivefold reduced light shift in comparison to excitation by plane wave radiation for the same Rabi frequency. We measure the excitation probabilities for Laguerre-Gaussian twisted light modes of first and second order for different polarization patterns at various orientations of the ion quantization axis with respect to the beam propagation vector. We compare the experimental results with theoretical predictions and find good qualitative agreement.

Received 20 June 2022
Accepted 14 November 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.253901

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Angular momentum of light Atomic & molecular processes in external fields Atomic, optical & lattice clocks Coherent control Electronic transitions Laser spectroscopy Quantum sensing Spatial profiles of optical beams Stark effect Time & frequency standards

Atomic, Molecular & OpticalGeneral PhysicsQuantum Information, Science & Technology

Authors & Affiliations

R. Lange¹, N. Huntemann ^1,*, A. A. Peshkov ^1,2, A. Surzhykov^1,2,3, and E. Peik ¹

¹Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
²Institut für Mathematische Physik, Technische Universität Braunschweig, Mendelssohnstraße 3, 38106 Braunschweig, Germany
³Laboratory for Emerging Nanometrology, Langer Kamp 6a/b, 38106 Braunschweig, Germany

^*nils.huntemann@ptb.de

Article Text

Click to Expand

References

Click to Expand

Issue

Vol. 129, Iss. 25 — 16 December 2022

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The electric octupole ( $E 3$ ) probe light is fiber guided to the experiment (a) and focused using a high-NA objective. The optical setup is mounted on a motorized $x y z$ stage for submicrometer control of the displacement between beam focus and ion position. The ion is confined in a Paul trap inside a vacuum chamber. The partial level scheme of ${Yb}^{+}$ (b) shows the cooling, the electric quadrupole ( $E 2$ ) and the $E 3$ transition. The experimental geometry is depicted in (c). The probe beam with wave vector $\vec{k}$ propagates along $x$ and the magnetic field $\vec{B}$ defining the ion quantization axis is moved either in the $x z$ plane ( ${\vec{B}}_{∥}$ , red) or the $x y$ plane ( ${\vec{B}}_{⊥}$ , green). In the case of linearly polarized light, we choose the polarization vector ${\vec{ε}}_{lin} | | {\hat{e}}_{z}$ .
Reuse & Permissions
Figure 2
Transverse intensity patterns of the focused ${LG}_{rad}$ (a) and ${LG}_{20}$ (b) vortex beams. The patterns are inferred from the light shift (LS) measured on the ${}^{2}{S_{1 / 2}} \to {{}^{2}D}_{3 / 2}$ $E 2$ transition at the position of the ion. A cut through the center of the patterns, denoted by the dark blue dots, provides the beam profiles shown in the lower graphs of (a) and (b). Based on these profiles we determine the radii of the ring of maximum intensity to be $r_{tw} ({LG}_{rad}) = 1.6 (1) μ m$ and $r_{tw} ({LG}_{20}) = 1.5 (1) μ m$ . A comparison to the ideal LG modes (blue lines) taking into account tip-tilt aberrations yields good agreement in the vicinity of the beam center. For the ${LG}_{rad}$ beam, a 4% admixture of plane wave radiation is included in the theoretical description that results in nonvanishing intensity at the beam center.
Reuse & Permissions
Figure 3
Excitation spectrum (a) and Rabi oscillation (b) for the ion in the dark center of the ${LG}_{20}$ mode. The blue dots are experimental data points and the blue lines are fits to the data, where the full width at half maximum of the excitation spectrum of 20 Hz is fixed by the Rabi pulse time of 40 ms. The light shift $Δ ν = 38 (1) Hz$ from the unperturbed transition frequency in combination with the Rabi frequency $Ω = 2 π \times 11.4 (2) Hz$ are used to determine the light shift suppression factor $S = 4.5 (2)$ over optimal excitation with plane wave radiation. The damping of the Rabi oscillations is attributed to a limited coherence of the laser beam due to pointing fluctuations. For each data point, 20 and 30 interrogations were taken in (a) and (b), respectively.
Reuse & Permissions
Figure 4
Excitation probability of the $E 3$ transition for different vortex beams at experimental parameters shown in Table 1. The magnetic field orientation is scanned in the $x z$ ( $θ_{∥}$ ) and the $x y$ plane ( $θ_{⊥}$ ) as defined in Fig. 1. Employing the theory explained in [16], we present calculations for an ion spatial spread of 100 nm (blue solid lines) and 25 nm (purple dashed lines), scaled to the experimental data (red dots). The ${LG}_{rad}$ vortex beam does not feature a strong dependence on the ion spatial spread, but exhibits an asymmetry for the two orientations due to an admixture of plane wave radiation. Without this admixture (light blue dashed lines) the theory curve for $θ_{∥}$ remains unchanged. The uncertainties of the experimental data points result from measurement instability and systematic effects.
Reuse & Permissions

Physical Review Letters