Quantum state reconstruction
The neutron interferometer set-up S18 at the ILL reactor has been used for the ﬁrst neutron quantum state reconstruction experiment. The observed Wigner functions are directly related to the wave packet of the neutron.
The reconstruction of the Wigner functions of various quantum states is made possible by a simultaneous measurement of the coherence function and of the modulated momentum distribution behind the interferometer. This is equivalent to knowledge of the particle wave function. Its spatial dimension follows from the measurement of the coherence function, which is the autocorrelation function of the wave function and the shape in momentum space follows from momentum post-selection experiments.
Non-orthogonal traces through the(x,k)-phase space have to be measured for an unambiguous reconstruction. Nearly classical (coherent) and non-classical states in the form of Schrodinger cat-like states have been identiﬁed.
Ref.: M. Baron, H. Rauch and M.Suda, J. Opt. B: QuantumSemiclass. Opt. 5 (2003) S241–S244.