Abstract
We discuss laser cooling of a string of two-level atoms confined in a linear iontrap. The equations for the dynamics are first analysed in the Lamb–Dicke regime(i.e. when the size of the mechanical wavefunction is much smaller than the laserwavelength), and then in general, for Doppler cooling. In the latter case, usingseveral consecutive steps of averaging we derive from the full quantummechanical master equation an equation for the total mechanical energyof the one-dimensional crystal, defined on a coarse-grained energy scalewhose grid size is smaller than the linewidth of the electronic transition.This equation describes the cooling dynamics for an arbitrary number ofions in the quantum regime. We discuss the analogy and the scalabilityof the string’s laser-cooling dynamics with that of a single trapped ion.
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