Berlin 2001 – scientific programme
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A: Atomphysik
A 8: Cooling and Trapping I (joint session A and Q)
A 8.4: Talk
Tuesday, April 3, 2001, 16:30–16:45, H104
Doppler Cooling of a Coulomb Crystal — •Giovanna Morigi1, Jürgen Eschner2, and Herbert Walther1 — 1Max-Planck Institut für Quantenoptik, Hans-Kopfermannstrasse 1, D-85748 Garching, Germany — 2Institut für Experimentalphysik, University of Innsbruck, Technikerstrasse 25/4, A-6020 Innsbruck, Austria
We study theoretically Doppler cooling of a cluster of 2-level atoms confined in an ion trap. Using several consecutive steps of averaging we derive, from the full quantum mechanical master equation, an ergodic equation for the total mechanical energy of the crystal, defined on a coarse-grained energy scale whose grid size is smaller than the electronic transition linewidth. This equation describes the cooling dynamics for an arbitrary number of ions and in the quantum regime. We discuss the validity of the ergodic assumption. From our equation we recover the semiclassical limit (i.e. when the mechanical motion can be treated classically) and the Lamb-Dicke limit (i.e. when the size of the mechanical state is much smaller than the laser wavelength), finding a Fokker-Planck equation for the total mechanical energy of the system, whose solution is in full agreement with previous analytical calculations which were based on different assumptions and valid only in their specific regimes.