  We show how to design different couplings between a single ion trapped in a
harmonic potential and an environment. This will provide the basis for the
experimental study of the process of decoherence in a quantum system. The
coupling is due to the absorption of a laser photon and subsequent spontaneous
emission. The variation of the laser frequencies and intensities allows one to
``engineer'' the coupling and select the master equation describing the motion
of the ion.
