Weak measurement: Effect of the detector dynamics

A general approach to the measurement of an observable with pre- and post-selection is presented. The limit of weak measurement is studied in detail, and it is shown that the phase of the probe, including a Hamiltonian contribution to it, gives rise to observable effects, since the coherence of the probe is essential for the concept of complex weak value to be meaningful. As a particular example, the measurement of a spin component is considered. We find that the contribution of the imaginary part of the weak value is sizeable in this case.