Steady state phonon occupation of EIT cooling: higher order calculations

TL;DR

This paper extends the analytic understanding of EIT cooling by deriving the steady state phonon occupation formula to second order in the Lamb-Dicke parameter, improving accuracy over previous zeroth-order models.

Contribution

The authors provide a higher-order analytical expression for the steady state phonon occupation in EIT cooling, addressing limitations of earlier zeroth-order approximations.

Findings

Derived explicit second-order formula for phonon occupation.

Resolved discrepancies in previous zeroth-order results.

Enhanced understanding of EIT cooling efficiency.

Abstract

Electromagnetically induced transparency (EIT) cooling has established itself as one of the most widely used cooling schemes for trapped ions during the past twenty years. Compared to its alternatives, EIT cooling possesses important advantages such as a tunable effective linewidth, a very low steady state phonon occupation, and applicability for multiple ions. However, existing analytic expression for the steady state phonon occupation of EIT cooling is limited to the zeroth order of the Lamb-Dicke parameter. Here we extend such calculations and present the explicit expression to the second order of the Lamb-Dicke parameter. We discuss several implications of our refined formula and are able to resolve certain difficulties in existing results.