  We apply quantum optimal control to shape the phase-space distribution of
Bose-Einstein condensates in a one-dimensional optical lattice. By a
time-dependent modulation of the lattice position, determined from optimal
control theory, we prepare, in the phase space of each lattice site, translated
and squeezed Gaussian states, and superpositions of Gaussian states. Complete
reconstruction of these non-trivial states is performed through a maximum
likelihood state tomography. As a practical application of our method to
quantum simulations, we initialize the atomic wavefunction in an optimal
Floquet-state superposition to enhance dynamical tunneling signals.

Quantum Gases;Quantum Physics