Inverted spectroscopy and interferometry for quantum-state reconstruction of systems with SU(2) symmetry

We consider how the conventional spectroscopic and interferometric schemes can be rearranged to serve for reconstructing quantum states of physical sy stems possessing SU(2) symmetry. The discussed systems include a collection of two-level atoms, a two-mode quantized radiation field with a fixed tota l number of photons, and a single laser-cooled ion in a two-dimensional har monic trap with a fixed total number of vibrational quanta. In the proposed rearrangement, the standard spectroscopic and interferometric experiments are inverted. Usually one measures an unknown frequency or phase shift usin g a system prepared in a known quantum state. Our aim is just the inverse, i.e., to use a well-calibrated apparatus with known transformation paramete rs to measure unknown quantum states.