The Quantum to Classical Transition in Entangled Systems via Continuous Measurements.

We study the role of continuous measurement in the quantum to classical transition for a particle in a harmonic well whose motion in the well is coupled to the internal spin. This system provides a rich illustration of the quantum to classical transition in weakly measured coupled systems. We demonstrate the emergence of classically regular as well as chaotic dynamics from the measured quantum trajectories when the external and internal actions are large relative to h. We also show the breakdown of the conditions for the quantum-classical transition in a mixed quantum-classical regime where the spin is treated quantum mechanically but the motion in the well can be treated classically. The conditions for the transition can be quantified by examining the covariance matrix. We explore the behavior of entanglement between spin and motion in the (classical) limit of large actions and find that whereas the measured quantum trajectories recover classical dynamics, the conditioned evolution can lead to highly non-classical entangled states. This is due to the finite resolution of the measurement. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]