Measurement-induced crossover in quantum first-detection times

TL;DR

This paper investigates how measurement back action in quantum systems causes a crossover in the statistics of first-detection times, revealing fundamentally quantum effects absent in classical first-passage problems.

Contribution

It demonstrates a measurement-induced crossover in quantum first-detection time statistics, highlighting the quantum nature of the detection process in different potential scenarios.

Findings

Algebraic decay in free particles

Exponential decay with confining potential

Time-dependent crossover behavior

Abstract

The quantum first-detection problem concerns the statistics of the time at which a system, subject to repeated measurements, is observed in a prescribed target state for the first time. Unlike its classical counterpart, the measurement back action intrinsic to quantum mechanics may profoundly alter the system dynamics. Here we show that it induces a distinct change in the statistics of the first-detection time. For a quantum particle in one spatial dimension subject to stroboscopic measurements, we observe an algebraic decay of the probability of the first-detection time if the particle is free, an exponential decay in the presence of a confining potential, and a time-dependent crossover between these behaviors if the particle is partially confined. This crossover reflects the purely quantum nature of the detection process, which fundamentally distinguishes it from the first-passage problem in classical systems.