Pointer states via decoherence in a quantum measurement - art. no. 012102

We consider the interaction of a quantum system (spin-1/2) with a macroscop ic quantum apparatus (harmonic oscillator) which in turn is coupled to a ba th of harmonic oscillators. Exact solutions of the Markovian master equatio n show that the reduced density matrix of the system-apparatus combination decoheres to a statistical mixture where up and down spins eventually corre late with pointer states of the apparatus (harmonic oscillator), with assoc iated probabilities in accordance with quantum principles. For the zero-tem perature bath these pointer states rum out to be coherent states of the har monic oscillator (apparatus) for arbitrary initial states of the apparatus. Further, we see that the decoherence time is inversely proportional to the square of the separation between the two coherent states with which the sp ins correlate. For a high-temperature bath, pointer states no longer remain coherent states but are Gaussian distributions (generalized coherent stare s). Spin up and down states of the system now correlate with nearly diagona l distributions in position of these generalized coherent states. The diago nalization in position increases with the temperature of the bath. The off- diagonal elements in spin space decohere over a time scale which goes inver sely as the square of the separation between the peaks of the two position distributions that correlate with the spin states. Zurek's earlier approxim ate result for the decoherence time is consistent with our exact results. O ur analysis brings out the importance of looking at a measurementlike scena rio where definite correlations are established between the system and appa ratus to determine the nature of the pointer basis of the apparatus. Furthe r, our exact results demonstrate in an unambiguous way that the pointer sta tes in this measurement model emerge independent of the initial state of th e apparatus.