Monitoring the wave function by time continuous position measurement

TL;DR

This paper presents a method to continuously monitor and accurately estimate the complete wave function of a quantum particle in real-time using position measurements, even under environmental disturbances.

Contribution

It introduces a novel continuous measurement technique for full wave function monitoring, combining known potential information with real-time updates from position data.

Findings

Achieves high-accuracy wave function estimation within finite time

Demonstrates robustness against environmental perturbations

Provides real-time tracking of quantum state evolution

Abstract

We consider a single copy of a quantum particle moving in a potential and show that it is possible to monitor its complete wave function by only continuously measuring its position. While we assume that the potential is known, no information is available about its state initially. In order to monitor the wave function, an estimate of the wave function is propagated due to the influence of the potential and continuously updated according to the results of the position measurement. We demonstrate by numerical simulations that the estimation reaches arbitrary values of accuracy below 100 percent within a finite time period for the potentials we study. In this way our method grants, a certain time after the beginning of the measurement, an accurate real-time record of the state evolution including the influence of the continuous measurement. Moreover, it is robust against sudden perturbations of the system as for example random momentum kicks from environmental particles, provided they occur not too frequently.