Measurement and preparation using two probe modes

We consider the simultaneous measurement of two conjugate variables by coupling the system of interest to two independent probe modes. Our model consists of linearly coupled boson modes that can be realized by quantum optical fields in the rotating-wave approximation. We approach the setup both as a device to extract observable information and to prepare an emerging quantum state. The initial states of the probe modes and the coupling are utilized to optimize the operation in the various regimes. In contrast to the Arthurs and Kelly ideal scheme [Bell. Syst. Tech. J. 44, 725 (1965)], our more realistic coupling does not allow perfect operation but the ideal situations can be approximated closely. We discuss the conditions for maximum information transfer to the probe modes, information extraction with minimum disturbance of the system mode, and optimal state preparation for subsequent measurements. The minimum disturbance operation can be made to approximate a nondemolition measurement, especially when the information is carried in one quadrature component only. In the preparation mode, we find that the recording accuracy of the probe signals plays an essential role. We restrict the discussion to the first and second moments only, but the method can easily be generalized to any situation. Choosing all modes to be in squeezed coherent states originally, we can carry out analytical considerations; other cases can be treated numerically. The results are presented and discussed in detail as the paradigm of a class of realizable measurements.