Monitoring quantum oscillations with very small disturbance

We present a new scheme to detect and visualize oscillations of a single quantum system in real time. The scheme is based upon a sequence of very weak generalized measurements, distinguished by their low disturbance and low information gain. Accumulating the information from the single measurements by means of an appropriate Bayesian estimator, the actual oscillations can be monitored nevertheless with high accuracy and low disturbance. For this purpose only the minimum and the maximum expected oscillation frequency need to be known. The accumulation of information is based on a general derivation of the optimal estimator of the expectation value of a Hermitian observable for a sequence of measurements. At any time it takes into account all the preceding measurement results