Monitoring the wave function by time continuous position measurement

Motivated by the technical requirements of quantum information processing and nanotechnology, the control of individual quantum systems such as single atoms, ions or even photons has become a highly desirable aim. The monitoring of quantum systems—a direct test and in many cases a prerequisite of their control—has been investigated so far only for certain observables such as the position or momentum of quantum particles. Here, we describe a method to monitor in real time the complete state of a quantum particle with unknown initial state moving in a known potential. The method is based on successively updating an estimate by the results of a continuous position measurement. We demonstrate by numerical simulations that even in a chaotic potential tracking the wave function of a particle is possible, and we show with an example that the monitoring scheme appears to be robust against sudden random perturbations. S Online supplementary data available from stacks.iop.org/NJP/12/043038/ mmedia

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