Is an ion string laser-cooled like a single ion?
Giovanna Morigi, Jürgen Eschner · Journal of Physics B Atomic Molecular and Optical Physics · 2003
We discuss laser cooling of a string of two-level atoms confined in a linear ion trap. 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 laser wavelength), and then in general, for Doppler cooling. In the latter case, using several consecutive steps of averaging we derive from the full quantum mechanical master equation an equation for the total mechanical energy of the one-dimensional crystal, defined on a coarse-grained energy scale whose grid size is smaller than the linewidth of the electronic transition. This equation describes the cooling dynamics for an arbitrary number of ions in the quantum regime. We discuss the analogy and the scalability of the string's laser-cooling dynamics with that of a single trapped ion.