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

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