Observing Quantum Trajectories: From Mott's Problem to Quantum Zeno Effect and Back

TL;DR

This paper re-examines the concept of quantum trajectories in interference experiments, analyzing the role of the quantum potential and its suppression in phenomena like the quantum Zeno effect from a Bohmian perspective.

Contribution

It provides a theoretical framework for understanding quantum trajectories, highlighting the active suppression of the quantum potential and its connection to the quantum Zeno effect.

Findings

Quantum trajectories can be constructed in interference regions.

Active suppression of the quantum potential explains Mott's trajectories.

Suppression of the quantum potential accounts for the quantum Zeno effect.

Abstract

The experimental results of Kocsis et al., Mahler et al. and the proposed experiments of Morley et al. show that it is possible to construct "trajectories" in interference regions in a two-slit interferometer. These results call for a theoretical re-appraisal of the notion of a "quantum trajectory" first introduced by Dirac and in the present paper we re-examine this notion from the Bohm perspective based on Hamiltonian flows. In particular, we examine the short-time propagator and the role that the quantum potential plays in determining the form of these trajectories. These trajectories differ from those produced in a typical particle tracker and the key to this difference lies in the active suppression of the quantum potential necessary to produce Mott-type trajectories. We show, using a rigorous mathematical argument, how the active suppression of this potential arises. Finally we discuss in detail how this suppression also accounts for the quantum Zeno effect.