Quantum process tomography on vibrational states of atoms in an optical lattice

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 characterize by reconstructing the $2\times 2$ density matrix. Repeating this reconstruction for a complete set of inputs allows us to completely characterize both the system’s intrinsic decoherence and resonant coupling.