Explicit, analytical radio-frequency heating formulas for spherically symmetric nonneutral plasmas in a Paul trap

Abstract

We present explicit, analytical heating formulas that predict the heating rates of spherical, nonneutral plasmas stored in a Paul trap as a function of cloud size $S$, particle number $N$, and Paul-trap control parameter $q$ in the low-temperature regime close to the cloud $\to$ crystal phase transition. We find excellent agreement between our analytical heating formulas and detailed, time-dependent molecular-dynamics simulations of the trapped plasmas. We also present the results of our numerical solutions of a temperature-dependent mean-field equation, which are consistent with our numerical simulations and our analytical results. This is the first time that analytical heating formulas are presented that predict heating rates with reasonable accuracy, uniformly for all $S$, $N$, and $q$.

14 pages, 1 figure

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• Frequency Comparison of Two High-Accuracy Al+ Optical Clocks
• Demonstration of a small programmable quantum computer with atomic qubits
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
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Cited by in corpus (4)

• The physics and applications of strongly coupled plasmas levitated in electrodynamic traps
• Analytical model of an ion cloud cooled by collisions in a Paul trap
• RF-induced heating dynamics of non-crystallized trapped ions
• Thermal bistability in laser-cooled trapped ions