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Optical and Quantum Sensing and Precision Metrology II

Numerical investigation of the waveform dependence in sympathetic cooling of trapped particles

Andreas Wolfgang Schell, Oskar Sund

Published Mar 19, 2025• 0 citations
Publisher

Abstract

To control the motion of a trapped particle and prevent quantum state decoherence, cooling is required. In order to trap particles that do not offer cooling transitions, sympathetic cooling can be used. We are going to investigate the effects that arise from changing the trapping waveform applied to a Paul trap. We are especially interested in the comparison of the sympathetic cooling performance of the sinusoidal wave with its alternatives. We investigate different waveforms such as normal sine driven traps, but also traps driven with a saw-tooth, triangle, or square waveforms. From the simulation results, cooling rates as well as stability parameters are extracted. Ours findings indicate potential benefits of further in-depth studies on the key properties that trap driving waveforms should possess to enhance the sympathetic cooling efficiency in Paul traps.

DOI
10.1117/12.3043056

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To control the motion of a trapped particle and prevent quantum state decoherence, cooling is required. In order to trap particles that do not offer cooling transitions, sympathetic cooling can be used. We are going to investigate the effects that arise from changing the trapping waveform applied to a Paul trap. We are especially interested in the comparison of the sympathetic cooling performance of the sinusoidal wave with its alternatives. We investigate different waveforms such as normal sine driven traps, but also traps driven with a saw-tooth, triangle, or square waveforms. From the simulation results, cooling rates as well as stability parameters are extracted. Ours findings indicate potential benefits of further in-depth studies on the key properties that trap driving waveforms should possess to enhance the sympathetic cooling efficiency in Paul traps.
Cooling of ions or other charged particles in electromagnetic traps is an essential tool to achieve control over their degrees of freedom on the quantum level. For many objects, there is no viable route for direct cooling, such as an accessible laser cooling transition. In such a case, the sympathetic cooling can be used, where a particle with such a direct route is used to cool down the other particle via Coulomb interaction. On the downside, this cooling process often is inefficient. Here, we numerically evaluate the sympathetic cooling performance in a quadrupole ion trap for different driving waveforms. We find that using different driving waveforms and optimized trap parameters the sympathetic cooling performance can be enhanced. These results will open up the way to achieve larger sympathetic cooling rates from which many techniques, such as aluminum ion clocks, might profit.
Sympathetic laser cooling is a key concept in precision spectroscopy and quantum state control of charged particles. Significant challenges arise in the metrologically relevant case where the effective interaction between the particles is weak and the particle to be cooled exhibits significant initial motional energy. Here we specifically address the most generally applicable case where the laser-cooled ion and the particle of interest are confined to two spatially separate potential wells with equal motional frequency for resonant enhancement of the cooling dynamics. We analyze the latter through numerical simulations and find that anharmonicities of the potential wells can prevent maintaining the resonance condition throughout the cooling process and thus inhibit a significant reduction in motional energy. We propose a cooling scheme that sweeps the trapping frequency of the potential wells. We show that this scheme enables efficient cooling from cryogenic temperatures all the way to the quantum regime of motion. As a specific application scenario, we analyze the sympathetic cooling of (anti-)protons into the quantum regime of motion for quantum-logic-spectroscopy-based tests of CPT invariance at the quantum limit in Penning traps. Nevertheless, our results and cooling strategies are generally applicable to other laser-inaccessible ion species.
Sympathetic laser cooling of ions stored within a linear-geometry, radio frequency, electric-quadrupole trap has been investigated using computational and theoretical techniques. The simulation, which allows five sample ions to interact with 35 laser-cooled atomic ions, revealed an instability heating mechanism, which can prevent ions below a certain critical mass from being sympathetically cooled. This critical mass can, however, be varied by changing the trapping field parameters, thus allowing ions with a very large range of masses to be sympathetically cooled using a single ion species. A theoretical explanation of this instability heating mechanism is presented which predicts that the cooling-heating boundary in trapping parameter space is a line of constant qu{q}_{u}qu​ (ion trap stability coefficient), a result supported by the computational results. The threshold value of qu{q}_{u}qu​ depends on the masses of the interacting ions. A functional form of this dependence is given.
Abstract Sympathetic laser cooling is a key concept in precision spectroscopy and quantum state control of charged particles. Significant challenges arise in the metrologically relevant case where the effective interaction between the particles is weak and the particle to be cooled exhibits significant initial motional energy. Here we specifically address the most generally applicable case where the laser-cooled ion and the particle of interest are confined to two spatially separate potential wells with equal motional frequency for resonant enhancement of the cooling dynamics. We analyze the latter through numerical simulations and find that anharmonicities of the potential wells can prevent maintaining the resonance condition throughout the cooling process and thus inhibit a significant reduction in motional energy. We propose a cooling scheme that sweeps the trapping frequency of the potential wells. We show that this scheme enables efficient cooling from cryogenic temperatures all the way to the quantum regime of motion. As a specific application scenario, we analyze the sympathetic cooling of (anti-)protons into the quantum regime of motion for quantum logic spectroscopy-based tests of charge-parity-time invariance at the quantum limit in Penning traps. Nevertheless, our results and cooling strategies are generally applicable to other laser-inaccessible ion species.
Cooling the center-of-mass motion of levitated nanoparticles provides a route to quantum experiments at mesoscopic scales. Here we demonstrate three-dimensional sympathetic cooling and detection of the center-of-mass motion of a levitated silica nanoparticle. The nanoparticle is electrostatically coupled to a feedback-cooled particle while both particles are trapped in the same Paul trap. We identify two regimes, based on the strength of the cooling: in the first regime, the sympathetically cooled particle thermalizes with the directly cooled one, while in the second regime, the sympathetically cooled particle reaches a minimum temperature. This result provides a route to efficiently cool and detect particles that cannot be illuminated with strong laser light, such as absorptive particles, and paves the way for controlling the motion of arrays of several trapped nanoparticles.