Trapping, shaping, and isolating of an ion Coulomb crystal via state-selective optical potentials

Pascal Weckesser, Fabian Thielemann, Daniel Hoenig, Alexander Lambrecht, Leon Karpa, and Tobias Schaetz

Phys. Rev. A 103, 013112 – Published 21 January 2021

Abstract

For conventional ion traps, the trapping potential is close to independent of the electronic state, providing confinement for ions dependent primarily on their charge-to-mass ratio $Q / m$ . In contrast, storing ions within an optical dipole trap results in state-dependent confinement. Here we experimentally study optical dipole potentials for ${}^{138}{Ba}^{+}$ ions stored within two distinctive traps operating at 532 and 1064 nm. We prepare the ions in either the electronic ground ( $6 S_{1 / 2}$ ) or one of the metastable excited states ( $5 D_{3 / 2}$ or $5 D_{5 / 2}$ ) and probe the relative strength and polarity of the potential. On the one hand, we apply our findings to selectively remove ions from a Coulomb crystal, despite all ions sharing the same $Q / m$ . On the other hand, we deterministically purify the trapping volume from parasitic ions in higher-energy orbits, resulting in reliable isolation of Coulomb crystals down to a single ion within a radio-frequency trap.

Received 26 October 2020
Accepted 23 December 2020

DOI:https://doi.org/10.1103/PhysRevA.103.013112

Physics Subject Headings (PhySH)

Trapped ions

Atom & ion trapping & guiding

Atomic, Molecular & Optical

Authors & Affiliations

Pascal Weckesser ¹, Fabian Thielemann ¹, Daniel Hoenig ¹, Alexander Lambrecht¹, Leon Karpa ^1,2, and Tobias Schaetz ^1,3

¹Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
²Leibniz University Hannover, Institute of Quantum Optics, Welfengarten 1, 30167 Hannover, Germany
³EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, 79085 Freiburg, Germany

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Issue

Vol. 103, Iss. 1 — January 2021

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Images

Figure 1
Overview of the experimental setup (not to scale) and the ${}^{138}{Ba}^{+}$ level scheme. (a) Indicated are the Doppler cooling lasers (including the cooler and the repumper), both optical dipole traps (VIS and NIR) along the axial direction of the Paul trap, as well as the shelving laser being perpendicularly aligned to the ion Coulomb crystal. dc electrodes are used for axial confinement, axial transport, and stray-field compensation. Further electrodes for radial stray-field compensation are not shown. (b) Simplified level scheme: A total of four different lasers are used to control the internal state of the ion. Doppler cooling is performed with the 493- and 650-nm lasers. Additional lasers at 455 nm (614 nm) are used for shelving into (out of) the $5 D_{5 / 2}$ manifold.
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Figure 2
Protocol for intermediate ion trapping within an ODT in the absence of rf fields. The presented protocol (not to scale) can be divided into three stages: (1) In preparation within the rf trap, we prepare one to four ions close to Doppler temperature. During this stage we can optionally pump dedicated ions into the metastable $5 D_{5 / 2}$ manifold by illuminating a target ion with 455 nm. (2) In optical trapping, the ions are transferred into the ODT. We turn off the rf fields, while the electrostatic axial potential remains unchanged. (3) In detection in the rf trap, we switch on the rf fields again and detect the ions while Doppler cooling.
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Figure 3
Demonstration and probing state-dependent averaged trap depths in the NIR ODT. Illustrated are the trapping probability for a single ion depending on NIR laser intensity expressed as $U_{0}^{NIR} (6 S_{1 / 2})$ . Solid circles: Experimental data of ions being prepared in the $6 S_{1 / 2}$ state. Fitting a radial cutoff model [42] with orthogonal distance regression (upper solid line) results in a temperature of $T_{ion} (6 S_{1 / 2}) = 355 (29) μ K$ . Open squares: Data for an ion being prepared in the $5 D_{3 / 2}$ state. The lower solid line results from fitting the data with a modified radial cutoff model $p_{opt} = 1 - e^{- 2 κ_{0} ξ} - 2 κ_{0} ξ e^{- κ_{0} ξ}$ while keeping the temperature fixed to the value obtained from the $6 S_{1 / 2}$ evaluation. Bootstrapping the uncertainty of the temperature allows to extract an upper $1 σ$ uncertainty for $κ_{0}$ , yielding $κ_{0} = 0.12 (1)$ . Shaded regions, bounds corresponding to the fit standard errors. Error bars: (trap depth) upper bounds of $1 σ$ uncertainty extracted from bootstrapping our experimental uncertainties and ( $p_{opt}$ ) upper bounds of $1 σ$ confidence intervals calculated from the underlying binomial distribution.
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Figure 4
Demonstration of state-dependent trapping with the VIS ODT. (a) Optical trapping efficiency for $N = {1, 2, 3, 4}$ ions being prepared in the $6 S_{1 / 2}$ state. Top: Exemplary fluorescence images of ion Coulomb crystals before and after optical trapping. Bottom: Corresponding measured optical trapping probability. The error bars denote the statistical uncertainty given by the calculated $1 σ$ Wilson score interval. The gray dashed line indicates the theoretical prediction of the loss rate by off-resonant scattering into the metastable $D$ manifolds. The gray dashed area represents the bounds of the theoretical prediction based on our experimental uncertainties. (b) Performance of state-selective removal normalized to the optical trapping efficiency. Top: Exemplary fluorescence images of ion Coulomb crystals before and after state-selective removal. The orange circles within the fluorescence images mark the dark ions prepared in the $5 D_{5 / 2}$ manifold. Experimental results are shown below. The color code of the bars equals the color code of the final ion number $M$ in (a). The measured values were normalized to the overall trapping performance of the final crystal size $p (M \to M)$ , to obtain the efficiency of state-selective removal only; therefore, some values are larger than 1, but consistent with unity within their respective uncertainties.
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Figure 5
Efficient loading and isolation of a single ion in an rf trap by cutting off parasitic ions using an intermediate step of optical trapping in the VIS ODT. Dashed blue curve: We apply ablation loading and photoionization in the first 3 s of the experiment and without further ablation or photoionization we track the number of bright ${}^{138}{Ba}^{+}$ ions over 20 min. Even after 20 min the size of the Coulomb crystal still increases, revealing the presence of former hidden ions within the rf trap. Solid red curve: We apply ablation loading for 3 s. Unlike before, once two ions form a Coulomb crystal, we immediately remove one ion by state-selective removal. The shallow depth and the small volume of the VIS ODT allows the storage of a finite number of ions, while parasitic ions on higher-energy trajectories are effectively removed from the former trapping volume of the rf trap. Transferring the ions from the ODT into the rf trap again can be understood as deterministic loading and purification of the rf trap.
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