Quantum-state reconstruction of atoms in optical lattices - art. no. 011405

We propose a method to reconstruct the vibrational quantum state of atoms b ound in arbitrary periodic potentials created by an optical lattice. The vi brational density matrix is determined from vibrational populations that ar e measured after translations of the optical-lattice potential. These trans lations are realized by phase shifts of the lattice laser fields. The feasi bility of the reconstruction method is shown for a typical situation realiz ed in recent experiments.