Phase-space distributions of Bose-Einstein condensates in an optical lattice: optimal shaping and reconstruction

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.

Automated summary

We utilize quantum optimal control to manipulate the phase-space distribution of Bose-Einstein condensates in a one-dimensional optical lattice. By modulating the lattice position in a time-dependent manner, determined through optimal control theory, we prepare translated and squeezed Gaussian states, as well as superpositions of Gaussian states, in the phase space of each lattice site. These non-trivial states are fully reconstructed using maximum likelihood state tomography. As a practical application, we use our method to initialize the atomic wavefunction in an optimal Floquet-state superposition to enhance dynamical tunneling signals.