Application of this property to the measurement of cavity fields is discussed, with particular consideration given to a possible scheme for quantum measurements of the intracavity photon number. A model for cooling a system of bosons in a harmonic trap via their interactions with a thermal bath of other particles is studied. The master equation describing the evolution of the system is derived for an arbitrary number of spatial dimensions. This equation is characterized by transition rates between trap levels. We present an analytic approximation for these rates and compare it with exact formulas, derived for the case of an even number of spatial dimensions.
Analytic expressions show very good agreement with the exact ones for a wide range of parameters.
We also discuss the cooling dynamics in terms of the approximated rates. A quantum computer can be implemented with cold ions confined in a linear trap and interacting with laser beams. Quantum gates involving any pair, triplet, or subset of ions can be realized by coupling the ions through the collective quantized motion. J. I. Cirac, M. Lewenstein, and P. Zoller, Phys. We study the dynamics of a system of atoms undergoing laser cooling in a microtrap.