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Abstract: We consider a single copy of a quantum particle moving in a potential andshow that it is possible to monitor its complete wave function by onlycontinuously measuring its position. While we assume that the potential isknown, no information is available about its state initially. In order tomonitor the wave function, an estimate of the wave function is propagated dueto the influence of the potential and continuously updated according to theresults of the position measurement. We demonstrate by numerical simulationsthat the estimation reaches arbitrary values of accuracy below 100 percentwithin a finite time period for the potentials we study. In this way our methodgrants, a certain time after the beginning of the measurement, an accuratereal-time record of the state evolution including the influence of thecontinuous measurement. Moreover, it is robust against sudden perturbations ofthe system as for example random momentum kicks from environmental particles,provided they occur not too frequently.



Autor: Thomas Konrad, Andreas Rothe, Francesco Petruccione, Lajos Diósi

Fuente: https://arxiv.org/



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