Time-resolved quantum measurements using active detectors

Time-resolved quantum measurements using active detectors are analyzed. It is shown that the time-resolved observation of a quantum field leads to a mode mismatch between observed field and detection device that unavoidably introduces vacuum modes into the measurement. When active detectors are used, this gives rise to considerable background noise. The same conclusion may be drawn when considering other highly resolved quantum measurements of, e.g., energy, position, etc. Special emphasis is put on the analysis of time-resolved optical homodyne detection as an important example of an active detector.