An adaptive measurement aims at optimizing the acquisition of information on a system, with the help of a feedback loop on the measuring apparatus. In our cavity quantum electrodynamics setup we have achieved an adaptive measurement of a quantum system, the microwave field trapped in a high finesse superconducting cavity. Circular Rydberg atoms interact dispersively with the field and achieve a quantum nondemolition measurement of the photon number by a succession of "weak" measurements. Taking into account all measurement outcomes, the measurement back-action and all experimental imperfections, a control computer estimates the field state in real-time. The phase of the Ramsey interferometer defining the atomic measurement is then optimized so that the following detections bring maximal information. We demonstrate that the preparation of Fock states is clearly accelerated using an adaptive technique, compared to a passive protocol where the choice of measurement phase is predefined. Such an adaptive measurement is of great interest in presence of decoherence, and could be used for example in quantum feedback protocols where the speed of state estimation is crucial.
