Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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



A Maitra, Dietrich Leibfried, D. Ullmo, H. Landa


We study the stochastic dynamics of a particle subject to 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 timescale of the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, that 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- dependence of the trap. We employ our approach to a detailed study of the stochastic dynamics of an ion in the different regimes of motion within an anharmonic radio-frequency Paul trap, drawing general conclusions regarding the nonequilibrium dynamics of trapped ions. We predict a regime of anharmonic motion with laser cooling becoming diffusive (i.e. it is equally likely to cool the ion as it is to heat it), and also turning into an effective heating. Such a mechanism implies that a high-energy ion would be easily lost from the trap despite being laser cooled, however we find it can be counteracted using a large laser detuning. More generally, the presented theory applies to a broad range of periodically driven systems and out-of-equilibrium stochastic dynamics.
Physical Review A


laser cooling, periodically driven potential, stochastic force, trapped ion


Maitra, A. , Leibfried, D. , Ullmo, D. and Landa, H. (2019), Far-from-equilibrium noise heating and laser cooling dynamics in radio-frequency Paul traps, Physical Review A, [online], (Accessed June 16, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created April 23, 2019, Updated October 14, 2021