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

For the detection of gravitational waves the quantum mechanical properties of the detector have to be taken into account. Not all gravitational wave d etectors allow a quantum nondemolition (QND) measurement. Continuous weak o r fuzzy measurements are an alternative to study the evolution of a quantum mechanical system under the influence of an external field. In the present paper we investigate this alternative by applying it to a simplified syste m. We numerically simulate continuous fuzzy measurements of the oscillation s of a two-level atom subjected to a resonant external light field. We ther eby address the question whether it is possible to measure characteristic f eatures of the evolution of a single quantum system in real time without re lying on a QND scheme. We compare two schemes of continuous measurement: co ntinuous measurement with constant fuzziness and with fuzziness changing in the course of the measurement. Because the sensitivity of the two-level at om 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 fu zziness.