  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.

Quantum Physics