Abstract
A cavity quantum electrodynamical scenario is proposed for implementing a Schr\"odinger microscope capable of amplifying differences between non orthogonal atomic quantum states. The scheme involves an ensemble of identically prepared two-level atoms interacting pairwise with a single mode of the radiation field as described by the Tavis-Cummings model. By repeated measurements of the cavity field and of one atom within each pair a measurement-induced nonlinear quantum transformation of the relevant atomic states can be realized. The intricate dynamical properties of this nonlinear quantum transformation, which exhibits measurement-induced chaos, allows approximate orthogonalization of atomic states by purification after a few iterations of the protocol, and thus the application of the scheme for quantum state discrimination.