Quantum State Control of a Bose-Einstein Condensate in an Optical Lattice

We report on the efficient design of quantum optimal-control protocols to manipulate the motional states of an atomic Bose-Einstein condensate (BEC) in a one-dimensional optical lattice. Our protocols operate on the momentum comb associated with the lattice. In contrast to previous works also dealing with control in discrete and large Hilbert spaces, our control schemes allow us to reach a wide variety of targets by varying a single parameter, the lattice position. With this technique, we experimentally demonstrate a precise, robust, and versatile control: we optimize the transfer of the BEC to a single or multiple quantized momentum states with full control on the relative phase between the different momentum components. This also allows us to prepare the BEC in a given eigenstate of the lattice band structure, or superposition thereof.

Automated summary

This study presents an efficient design of quantum optimal-control protocols for manipulating the motional states of atomic Bose-Einstein condensate in a one-dimensional optical lattice. By varying the lattice position, a wide variety of targets can be reached, including single or multiple quantized momentum states with full control on the relative phase between different momentum components.