Reconstruction of motional states of neutral atoms via maximum entropy principle

We present a scheme for a reconstruction of states of quantum systems from incomplete tomographiclike data. The proposed scheme is based on the Jaynes principle of maximum entropy. We apply our algorithm for a reconstruction of motional quantum states of neutral atoms. As an example we analyze the experimental data obtained by Salomon and co-workers and we reconstruct Wigner functions of motional quantum states of Cs atoms trapped in an optical lattice.