Population dynamics in sideband cooling of trapped ions outside the Lamb-Dicke regime

TL;DR

This paper investigates the dynamics of sideband cooling for trapped ions outside the Lamb-Dicke regime, demonstrating optimized cooling sequences for efficient ground state preparation in shallow traps and extending the analysis to two-ion systems.

Contribution

It provides a detailed simulation study of sideband cooling outside the Lamb-Dicke regime, proposing optimized sequences for single and multiple ions in Penning traps.

Findings

Efficient ground state cooling is achievable outside the Lamb-Dicke regime with optimized sequences.

Two-ion cooling requires complex sequences to cool multiple motional modes simultaneously.

Sideband heating effects are also characterized in Penning traps.

Abstract

We present the results of simulations of optical sideband cooling of atomic ions in a trap with a shallow potential well. In such traps, an ion cannot be Doppler cooled near to the Lamb-Dicke regime ($\eta^2(2n+1) \ll 1$). Outside the Lamb-Dicke regime, the sideband cooling dynamics are altered by the existence of various Fock states where the cooling becomes very slow. A calcium ion trapped in our Penning trap realises such a situation, hence single stage cooling is inefficient to prepare the ion in the motional ground state. For these systems, it is necessary to study the cooling dynamics in detail and we show that it is possible to implement an optimised cooling sequence to achieve efficient ground state cooling. We also present the simulated cooling dynamics of two ions trapped in a Penning trap, where the presence of an additional motional mode requires a complicated cooling sequence in order to cool both axial modes to the ground state simultaneously. Additionally we investigate sideband heating of a single ion in a Penning trap.