Progressive quantum collapse

Abstract

Instantaneous collapse of the wave function upon measurement of a single particle is one of the postulates of the Copenhagen interpretation of quantum mechanics. However, what happens when a many-body system in a macroscopic coherent state is measured one particle at a time? Here, we consider successive measurements of individual spins from a spin Bose condensate that starts in a Schrödinger cat state. When the spin measurements are done one particle at a time, the collapse of the spin condensate is not instantaneous but leads to probabilities for spin measurement that strongly depend on the previous measurements. What is surprising is that an almost complete collapse occurs in very few measurements. Even in a large system, a single cat component is emphasized quite quickly in the sequence of measurements. We examine the process by analysis of a simple two-Fock-state cat, as well as a cat state that has many components. Justification is given for our theoretical measurement process.