We propose a method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a "slow" detector. Such a detector is only sensitive to slowly-changing variables, e. g. energy, while its back-action can be limited solely to decoherence of the eigenstate superpositions. We apply this scheme to the problem of detection of quantum jumps between energy eigenstates in a harmonic oscillator.
@article{arxiv.cond-mat/0702068,
title = {Measurement of energy eigenstates by a slow detector},
author = {I. Martin and W. H. Zurek},
journal= {arXiv preprint arXiv:cond-mat/0702068},
year = {2009}
}