Optical Trapping of Ion Coulomb Crystals

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Optical Trapping of Ion Coulomb Crystals

Julian Schmidt, Alexander Lambrecht, Pascal Weckesser, Markus Debatin, Leon Karpa, and Tobias Schaetz

Phys. Rev. X 8, 021028 – Published 1 May 2018

Abstract

The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems. Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields. We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal. As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap. Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion. Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one- and two-dimensional crystals.

Received 22 December 2017
Revised 20 February 2018

DOI:https://doi.org/10.1103/PhysRevX.8.021028

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)

Hybrid quantum systems Quantum information with trapped ions Ultracold collisions

Trapped ions

Atom & ion trapping & guiding

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Julian Schmidt, Alexander Lambrecht, Pascal Weckesser, Markus Debatin, Leon Karpa, and Tobias Schaetz^*

Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Straße 3, 79104 Freiburg, Germany

^*tobias.schaetz@physik.uni-freiburg.de

Popular Summary

At temperatures near absolute zero, clouds of ions can crystallize when held in ion traps. Such “Coulomb crystals” have allowed physicists to explore the frontiers of physics in a variety of fields, from the cores of white dwarf stars to architectures for quantum computing. However, ions in conventional traps, which use electric and magnetic fields to hold the ions in place, are subject to a continuous swirling motion driven by the trapping fields. This disturbance masks intriguing effects that are predicted to arise in Coulomb crystals. Recently, our group trapped a single ion for several seconds using light, a process in which this driven motion is negligible. But light traps are thought to be too weak to counteract the Coulomb repulsion between multiple ions. Overcoming this challenge, we have now trapped six ions inside a laser beam without the aid of the confinement fields that disturb ions in conventional traps.

Our work relies on precise knowledge and control of the electrostatic and optical potentials inside the trap, which allows us to transfer multiple ions from a conventional trap into an optical dipole trap. We then show that the ions remain crystallized in the optical trap even in the absence of cooling. In addition, we observe the collective motion of the ions on their lattice sites in a simple crystal. These sound waves are also a characteristic signature of conventional solid-state crystals.

Our findings pave the way for studies of quantum dynamics in Coulomb crystals, such as the transition from linear strings to two-dimensional zigzag structures or the quantum superposition of such structures across the phase transition.

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Issue

Vol. 8, Iss. 2 — April - June 2018

Subject Areas

Atomic and Molecular Physics

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Images

Figure 1
Schematic of the apparatus and contributions to the total trapping potential. (a) We load chains of up to six Doppler-cooled barium ions, with lengths of up to $135 μ m$ (the 5-ion crystal in (d) has a length of $115 μ m$ ), into a linear rf trap. dc electrodes are used to adjust the external electrostatic potential. The ions are then transferred from the rf trap into either a visible (VIS) or near-infrared (NIR) optical dipole trap by ramping up the optical potential and simultaneously turning off the rf fields. Axial dc confinement in the external electrostatic potential [grey surfaces in (b) and (d)], as well as the ions’ mutual Coulomb interaction (c), lead to additional defocusing forces in the radial directions. In our experiment, defocusing is chosen to predominantly lie in the $x$ direction [red arrows in (b)] while defocusing in the $y$ direction is negligible (thin gray arrows). With Rayleigh lengths $z_{R}^{VIS} = 40 μ m$ and $z_{R}^{NIR} = 74 μ m$ for the respective dipole laser beams, the radial optical potential depicted by the blue surfaces in (d) also depends on the ion position along the $z$ -axis.
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Figure 2
Demonstrating the persistence of Coulomb order for an increasing number of optically trapped ions. (a) Fluorescence images of Coulomb crystals with $N_{ini} = 1 \dots 6$ ${Ba}^{+}$ ions are recorded before and after optical trapping of $N_{opt}$ . For $N_{ini} \geq 4$ , the gaps marked by orange circles reveal the presence of dark ions, which appear at initial random lattice sites after Doppler and sympathetic cooling. (b) The experimental protocol (not to scale) consists of three steps: (1) we detect the initial configuration and ion number $N_{ini}$ while Doppler cooling the ions; (2) the ions are transferred into the dipole trap by turning off the rf field and cooling lasers for the optical trapping duration $Δ t_{opt}$ , keeping the electrostatic potential; and (3) we again detect the number and final configuration of all remaining ions in the rf trap. An intermittent gaseous phase followed by recrystallization or enhanced diffusion should be observable with high fidelity via changes of the positions of the dark ions within the crystal.
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Figure 3
Measuring the temperature of multiple ions in the single-beam VIS dipole trap. (a) We measure the trapping probability $p_{opt}$ for $N_{ini} = 1 \dots 5$ ions as a function of $P_{opt}^{VIS}$ (red, blue, green, yellow, and black squares). The solid lines indicate fits with the radial-cutoff model [29], which relates the trapping probability and finite trap depth for atoms or a single ion to their temperature. We observe that trapping $N_{ini} > 1$ ions requires increased laser power. Still applying the single-particle model yields a ten times larger temperature or decreased trap depth. In (b), we reanalyze the data shown in (a), taking into account the axial extent of the ensemble, electrostatic fields, and mutual Coulomb interaction to calculate the local radial trap depth at the axial positions of the outermost ions $Δ U_{tot} (z_{1, N_{ini}}^{0})$ . Solid lines depict fits assuming the altered radial-cutoff model for $Δ U_{tot} (z_{i}^{0})$ (see text). We obtain temperatures of $T_{N_{ini}} = (0.7 \pm 0.1) mK$ for $N_{ini} \leq 3$ , as well as $T_{4} = (1.3 \pm 0.5) mK$ and $T_{5} = (1.8 \pm 0.5) mK$ (inset).
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Figure 4
Spectrometry of normal modes, demonstrating access to the axial phonons of the crystal during optical trapping. In (a), we show typical fluorescence images of ions in the rf trap with dc axial confinement, resonantly modulated with oscillating electric fields (the two-ion distance is $43 μ m$ , with other images to scale). For $N_{ini} = 1$ , we observe a single resonance for the axial motion at $ω_{ax}^{COM}$ . For $N_{ini} = 2$ , 3, an additional resonance at $ω_{ax}^{str} = \sqrt{3} ω_{ax}^{COM}$ , corresponding to out-of-phase motion, appears. (b) Optical trapping probability for $N_{ini} = 1$ (blue squares) and $N_{ini} = 2$ (red circles) ion(s) in the NIR trap, as a function of the frequency $ω_{\mod} / 2 π$ of the oscillating electric field. We observe a drop in $p_{opt}$ at $ω_{ax}^{COM}$ for both $N_{ini} = 1$ and $N_{ini} = 2$ , in agreement with the expected axial confinement. For the COM mode, the solid lines show fits to the data. The resonance at $ω_{ax}^{str} = 2 π \times (43.3 \pm 0.15) kHz \approx \sqrt{3} ω_{ax}^{COM}$ (binned data points weighted with their statistical significance; for details on uncertainty, see text) only emerges in the case $N_{ini} = 2$ and shows access to the motional degrees of freedom of the Coulomb crystal during $Δ t_{opt}$ . In the case of the stretch mode, we modulate the harmonic confinement to excite differential motion between the ions. The electric field amplitude at the equilibrium positions of the ions amounts to $| E | = (1.8 \pm 0.1) mV / m$ , for which we numerically simulate the out-of-phase motion (no free parameters). We depict the amplitude of the stretch mode by $\max [z_{str} (t)] - \min [z_{str} (t)]$ by the solid red line (axis on the right-hand side). The nonlinearity of the Coulomb interaction leads to an asymmetric frequency response (see Supplemental Material [30]). We emphasize that the dependence of $p_{opt}$ on $\max [z_{str} (t)] - \min [z_{str} (t)]$ is nontrivial and not taken into account here.
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