Approximate real time visualization of a Rabi transition by means of continuous fuzzy measurement

Continuous weak or fuzzy measurement of the Rabi oscillation of a two level atom subjected to a $\pi-$pulse of a resonant light field is simulated numerically. We thereby address the question whether it is possible to measure characteristic features of the motion of the state of a single quantum system in real time. We compare two schemes of continuous measurement: continuous measurement with constant fuzziness and with fuzziness changing in the course of the measurement. Because the sensitivity of the Rabi atom to the influence of the measurement depends on the state of the atom, it is possible to optimize the continuous fuzzy measurement by varying its fuzziness.