Quantum-state reconstruction of atoms in optical lattices

Abstract

We propose a method to reconstruct the vibrational quantum state of atoms bound in arbitrary periodic potentials created by an optical lattice. The vibrational density matrix is determined from vibrational populations that are measured after translations of the optical-lattice potential. These translations are realized by phase shifts of the lattice laser fields. The feasibility of the reconstruction method is shown for a typical situation realized in recent experiments.