CONTINUOUS QUANTUM-NONDEMOLITION MEASUREMENT OF PHOTON NUMBER

This paper presents a general theory for a continuous quantum-nondemolition measurement of photon number. This theory treats a time-distributed measurement as a sequence of measurements in which at most one photon can be detected in an infinitesimal time, and shows that the average number of photons remaining in the measured field increases when a photon is detected and decreases when no photon is detected. The state of the measured system evolves nonunitarily and reduces continuously to a number state whose eigenvalue is uniquely determined by the average rate of photodetection and whose probability distribution coincides with the initial photon-number distribution. Applying the general theory to typical quantum states - coherent, thermal, and squeezed states - shows that the continuous-state reduction towards a number state depends strongly on the initial photon statistics. Despite the nonunitarity of state evolution, an initially pure state keeps its purity: the initial density operator becomes diagonalized only if the readout information is discarded.