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arXiv:2406.13467

Simulation of sympathetic cooling efficiency in a linear Paul trap driven by alternative waveforms

Oskar Sund, Andreas Wolfgang Schell

Published Jun 19, 2024• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2406.13467

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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.
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.
Abstract Efficient cooling of trapped charged particles is essential in many fundamental physics experiments, for high-precision metrology, and for quantum technology. Until now, ion-ion coupling for sympathetic cooling or quantum state control has been limited to ion species with accessible optical transitions or has required close-range Coulomb interactions. To overcome this limitation and further develop scalable quantum control techniques, there has been a sustained desire to extend laser-cooling techniques to particles in macroscopically separated traps, opening quantum control techniques to previously inaccessible particles such as highly charged ions, molecular ions, and antimatter particles. Here, we demonstrate sympathetic cooling of a single proton by laser cooled Be+ ions stored in a spatially separated Penning trap. The two traps are connected by a superconducting LC circuit that enables energy exchange over a distance of 9 cm. We simultaneously demonstrate the cooling of a resonant mode of a macroscopic LC circuit with laser-cooled ions and sympathetic cooling of an individually trapped proton, reaching temperatures far below the environment temperature. Importantly, as this technique does not rely on the direct Coulomb interaction but rather on image-current interactions, it can be easily applied to an experiment with antiprotons, facilitating improved precision in matter-antimatter comparisons and dark matter searches.
Coulomb crystals, containing up to a few hundred ions of which more than 50% were cooled sympathetically by the Coulomb interaction with laser cooled Mg+ ions, have been produced in a linear Paul trap. By controlling the balance of the radiation pressure from the two cooling lasers, the Coulomb crystals could be segregated according to ion species. Previous studies of ion crystals and molecular dynamics simulations suggest that the temperature may be around 10 mK or lower. The obtained results indicate that a wide range of atomic and molecular ions, which due to their internal structures are not amenable to direct laser cooling, can be effectively cooled and localized (crystallized) in linear Paul traps. For high resolution spectroscopy of such ions this may turn out to be very useful.
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 Cooling of particles to mK-temperatures is essential for a variety of experiments with trapped charged particles. However, many species of interest lack suitable electronic transitions for direct laser cooling. We study theoretically the remote sympathetic cooling of a single proton with laser-cooled 9Be+ in a double-Penning-trap system. We investigate three different cooling schemes and find, based on analytical calculations and numerical simulations, that two of them are capable of achieving proton temperatures of about 10 mK with cooling times on the order of 10 s. In contrast, established methods such as feedback-enhanced resistive cooling with image-current detectors are limited to about 1 K in 100 s. Since the studied techniques are applicable to any trapped charged particle and allow spatial separation between the target ion and the cooling species, they enable a variety of precision measurements based on trapped charged particles to be performed at improved sampling rates and with reduced systematic uncertainties.
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.