Quantum state control of a Bose-Einstein condensate in an optical lattice

TL;DR

This paper demonstrates efficient quantum optimal control of a Bose-Einstein condensate in an optical lattice, enabling precise manipulation of motional states and superpositions through a single parameter, the lattice position.

Contribution

It introduces a novel control scheme that achieves versatile and robust manipulation of BEC momentum states by varying lattice position, surpassing previous methods in flexibility.

Findings

Successful transfer of BEC to targeted momentum states

Full control over phase relations between states

Preparation of BEC in eigenstates or superpositions

Abstract

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.