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arXiv:2111.05829 · Physical Review A

Two-tone Doppler cooling of radial two-dimensional crystals in a radio-frequency ion trap

Alexander Kato, Apurva Goel, Raymond Lee, Zeyu Ye, Samip Karki, Jian Jun Liu, ANDREI NOMEROTSKI, B. B. Blinov

Published Feb 3, 2022• 13 citations
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Abstract

We study the Doppler-cooling of radial two-dimensional (2D) Coulomb crystals of trapped barium ions in a radiofrequency trap. Ions in radial 2D crystals experience micromotion of an amplitude that increases linearly with the distance from the trap center, leading to a position-dependent frequency modulation of laser light in each ion's rest frame. We use two tones of Doppler-cooling laser light separated by approximately 100 MHz to efficiently cool distinct regions in the crystals with differing amplitudes of micromotion. This technique allows us to trap and cool more than 50 ions populating four shells in a radial 2D crystal, where with a single tone of Doppler cooling light we are limited to 30 ions in three shells. We also individually characterize the micromotion of all ions within the crystals and use this information to locate the center of the trap and to determine the Matthieu parameters ${q}_{x}$ and ${q}_{y}$.

DOI
10.1103/physreva.105.023101

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We study the Doppler-cooling of radial two-dimensional (2D) Coulomb crystals of trapped barium ions in a radiofrequency trap. Ions in radial 2D crystals experience micromotion of an amplitude that increases linearly with the distance from the trap center, leading to a position-dependent frequency modulation of laser light in each ion's rest frame. We use two tones of Doppler-cooling laser light separated by approximately 100 MHz to efficiently cool distinct regions in the crystals with differing amplitudes of micromotion. This technique allows us to trap and cool more than 50 ions populating four shells in a radial 2D crystal, where with a single tone of Doppler cooling light we are limited to 30 ions in three shells. We also individually characterize the micromotion of all ions within the crystals and use this information to locate the center of the trap and to determine the Matthieu parameters qx{q}_{x}qx​ and qy{q}_{y}qy​.
We propose and demonstrate a method for Doppler cooling trapped-ion crystals where the distribution of micromotion amplitudes may be large and uneven. The technique uses pulses of Doppler cooling light synchronized with the trap rf that selectively target ions when their velocity is near a node, leading to more uniform cooling across a crystal by a single tone of cooling light. We lay out a theoretical framework that describes where this technique is practical and provides a simple experimental demonstration.
We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 ^{171}Yb^{+} ions, we demonstrate that the structural phase boundaries of such crystals are well described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced heating of the radial-2D crystal is confined to the radial plane. Finally, we verify that the transverse motional modes, which are used in most ion-trap quantum simulation schemes, are well-predictable numerically and remain decoupled and cold in this geometry. Our results establish radial-2D ion crystals as a robust experimental platform for realizing a variety of theoretical proposals in quantum simulation and computation.
An experimental study of sideband laser cooling of trapped ions in miniature radio-frequency traps is presented. In+{\mathrm{In}}^{+}In+ ions are laser cooled by exciting the narrow intercombination line ${5s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}5s5p{}^{3}{P}_{1}$, which shows resolved sidebands due to the vibrational motion of the ions in the trap. The influence of the micromotion at the frequency of the oscillating trapping field is investigated. Heating processes through coupling with the trapping field occur for certain regions of negative laser detuning. A method of bichromatic sideband cooling is introduced that combines efficient cooling from high temperatures with the possibility of reaching low mean vibrational quantum numbers 〈n〉<1〈n〉<1〈n〉<1 by using narrow optical transitions. This technique allows recording of high-resolution excitation spectra of the cooling transition in the Lamb-Dicke regime and thus determination of 〈n〉〈n〉〈n〉. Single ions as well as two-ion Coulomb crystals have been cooled to temperatures below $100 \ensuremath{\mu}\mathrm{K}$, and population of the ground state of motion to more than 50% over long time scales is demonstrated. These values are close to the lower limit for the detection of vibrational excitation with the present method.
In this paper, direct observation of micromotion for multiple ions in a laser-cooled trapped ion crystal is discussed along with a measurement technique for micromotion amplitude. Micromotion is directly observed using a time-resolving, single-photon-sensitive camera that provides both fluorescence and position data for each ion on the nanosecond time scale. Micromotion amplitude and phase for each ion in the crystal are measured, allowing this method to be sensitive to tilts and shifts of the ion chain from the null of the radio-frequency quadrupole potential in the linear trap. Spatial resolution makes this micromotion detection technique suitable for complex ion configurations, including two-dimensional geometries. It does not require any additional equipment or laser beams, and the modulation of the cooling lasers or trap voltages is not necessary for detection as it is in other methods.
We analyze the possibility of cooling ions with a single laser beam, due to the coupling between the three components of their motion induced by the Coulomb interaction. For this purpose, we numerically study the dynamics of ion clouds of up to 140 particles, trapped in a linear quadrupole potential and cooled with a laser beam propagating in the radial plane. We use molecular dynamics simulations and model the laser cooling by a stochastic process. For each component of the motion, we systematically study the dependence of the temperature on the anisotropy of the trapping potential. Results obtained using the full radio-frequency (rf) potential are compared to those of the corresponding pseudopotential. In the rf case, the rotation symmetry of the potential has to be broken to keep ions inside the trap. Then, as for the pseudopotential case, we show that the efficiency of the Coulomb coupling to thermalize the components of motion depends on the geometrical configuration of the cloud. Coulomb coupling appears to be not efficient when the ions organize as a line or a pancake and the three components of motion reach the same temperature only if the cloud extends in three dimensions.