  Quantum process tomography is used to fully characterize the evolution of the
quantum vibrational state of atoms. Rubidium atoms are trapped in a shallow
optical lattice supporting only two vibrational states, which we charcterize by
reconstructing the 2x2 density matrix. Repeating this process for a complete
set of inputs allows us to completely characterize both the system's intrinsic
decoherence and resonant coupling.
