Tuning nonthermal distributions to thermal ones in time-dependent Paul traps

TL;DR

This paper investigates how to achieve thermal-like phonon distributions in laser-cooled ions within time-dependent Paul traps, even under nonequilibrium conditions, by tuning laser parameters and accounting for excess micromotion.

Contribution

It introduces a Floquet-based approach to model ion distributions and demonstrates how to restore thermal distributions through laser detuning in driven traps.

Findings

Thermal-like exponential phonon distributions can be achieved despite nonequilibrium forces.

Proper laser detuning can restore exponential distributions with mean phonon numbers near the Doppler limit.

The derived relations enable experimental determination of optimal detuning and phonon number from photon scattering rates.

Abstract

We study the probability distribution of an atomic ion being laser-cooled in a periodically-driven Paul trap using a Floquet approach to the semiclassical photon scattering dynamics. We show that despite the microscopic nonequilibrium forces, a stationary thermal-like exponential distribution can be obtained in the Hamiltonian action, or equivalently in the number of quanta (phonons) of the motion linearized about the zero of the potential. At the presence of additional stray electric fields, the ion is pushed from the origin of the potential and set into a large-amplitude driven oscillation, and above a threshold amplitude of such "excess micromotion", the action distribution of excitations about the driven oscillation broadens and becomes distinctly nonthermal. We find that by a proper choice of the laser detuning the distribution can be made exponential again, with a mean phonon number close to that of the Doppler cooling limit. We derive a relation allowing to deduce just from the experimentally observable photon scattering rate both the required detuning for optimal cooling and the final mean phonon number. These results are important for quantum information processing and other applications, and in particular the derived approach can be applied to crystals of trapped ions in planar configurations, where the driven motion of ions is unavoidable.