Pointer states via Decoherence in a Quantum Measurement

We consider the interaction of a quantum system (spin-1/2) with a macroscopic quantum apparatus (harmonic oscillator) which in turn is coupled to a bath of harmonic oscillators. Exact solutions of the Markovian Master equation show that the reduced density matrix of the system-apparatus combine decoheres to a statistical mixture where up and down spins eventually correlate with pointer states of the apparatus. For the zero temperature bath these pointer states turn out to be coherent states of the harmonic oscillator for arbitrary initial states of the apparatus. For a high temperature bath pointer states are Gaussian distributions (generalized coherent states). For both cases, the off-diagonal elements in spin-space decohere over a time scale which goes inversely as the square of the "separation" between the "pointers". Our exact results also demonstrate in an unambiguous way that the pointer states in this measurement model emerge independent of the initial state of the apparatus.