Decoherence and Schrödinger-cat states in a Stern-Gerlach-type experiment

A Stern-Gerlach setup for the measurement on a quantum system (spin-1/2) with a macroscopic quantum apparatus (the particle trajectory) produces a Schrödinger-cat-like superposition in which the spin states correlate with wave packets centered around macroscopically distinguishable positions and momenta. When an interaction with an environment is included, the pure density matrix of the system-apparatus combination reduces to a statistical mixture in the spin space, and exact solutions show that the decoherence time for this reduction goes inversly as the macroscopic separation between the two parts of the superposition correlating with up- and down-spin states. This is consistent with Zurek’s approximate result for the decoherence time, and the persistence of system-meter correlations at large times makes it an interesting candidate to look at experimentally.