  We realize on an Atom-Chip a practical, experimentally undemanding,
tomographic reconstruction algorithm relying on the time-resolved measurements
of the atomic population distribution among atomic internal states. More
specifically, we estimate both the state density matrix as well as the
dephasing noise present in our system by assuming complete knowledge of the
Hamiltonian evolution. The proposed scheme is based on routinely performed
measurements and established experimental procedures, hence providing a
simplified methodology for quantum technological applications.
