Reflection of a Particle from a Quantum Measurement

TL;DR

This paper generalizes continuous position measurements to include spatially inhomogeneous measurement strengths, revealing that particles can coherently reflect from measurement regions and connecting this to the quantum Zeno effect.

Contribution

It introduces a framework for inhomogeneous position measurements, demonstrating particle reflection and the quantum Zeno effect through quantum-trajectory simulations.

Findings

Particles can coherently reflect from measurement regions.

Reflection probability approaches unity with increased measurement strength.

Measurement back-action can be modeled as stochastic fluctuating potentials.

Abstract

We present a generalization of continuous position measurements that accounts for a spatially inhomogeneous measurement strength. This describes many real measurement scenarios, in which the rate at which information is extracted about position has itself a spatial profile, and includes measurements that detect if a particle has crossed from one region into another. We show that such measurements can be described, in their averaged behavior, as stochastically fluctuating potentials of vanishing time average. Reasonable constraints restrict the form of the measurement to have degenerate outcomes, which tend to drive the system to spatial superposition states. We present the results of quantum-trajectory simulations for measurements with a step-function profile (a "which-way" measurement) and a Gaussian profile. We find that the particle can coherently reflect from the measurement region in both cases, despite the stochastic nature of the measurement back-action. In addition, we explore the connection to the quantum Zeno effect, where we find that the reflection probability tends to unity as the measurement strength increases. Finally, we discuss two physical realizations of a spatially varying position measurement using atoms.