The issue of phases in quantum measurement theory

Abstract

The issue of phases is always very subtle in quantum world and many of the curious phenomena are due to the existence of the phase of the quantum mechanical wave function. We investigate the issue of phases in quantum measurement theory and predict a new effect of fundamental importance. We call a quantum system under goes a quantum Zeno dynamics (QZD) when the unitary evolution of a quantum system is interrupted by a sequence of measurements. In particular, We investigate the effect of repeated measurements on the geometric phase and show that the quantum Zeno dynamics can inhibit its development under a large number of measurement pulses. It is interesting to see that neither the total phase nor the dynamical phase goes to zero under large number of measurements. This new effect we call as the "quantum Zeno Phase effect" (QZPE) in analogous to the quantum Zeno effect (QZE) where the repeated measurements inhibit the transition probability. This "quantum Zeno Phase effect" can be proved within von Neumann's collapse mechanism as well as using a continuous measurement model. So the effect is really independent of any particluar measurement model considered. Since the geometric phase attributes a memory to a quantum system our results also proves that the path dependent memory of a system can be erased by a sequence of measurements. The QZPE provides a way to control and manipulate the phase of a wave function in an interference set up. Finally, we stress that the quantum Zeno Phase effect can be tested using neutron, photon and atom interference experiments with the presently available technology.