Far-from-equilibrium noise heating and laser cooling dynamics in radio-frequency Paul traps

TL;DR

This paper develops a semiclassical theory to analyze the stochastic dynamics of laser-cooled ions in radio-frequency Paul traps, revealing regimes where cooling becomes diffusive or turns into heating, affecting ion retention.

Contribution

It introduces a comprehensive semiclassical model for laser cooling in anharmonic, time-dependent traps, extending understanding of nonequilibrium ion dynamics beyond previous harmonic approximations.

Findings

Identifies a regime where laser cooling becomes diffusive and can lead to ion heating.

Predicts high-energy ions can be lost despite cooling, but this can be mitigated with large laser detuning.

Provides a detailed analysis of stochastic dynamics in anharmonic, time-dependent traps.

Abstract

We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.