Bloch-sphere rotations in driven double-well for ultracold atoms

Abstract

We show that, by using suitable protocols for a non-interacting condensate in a driven double-well, one can achieve controlled rotations about arbitrary axes in the equatorial plane of the Bloch sphere, composed with fast rotations about the $z$-axis. Specifically, we investigate the dynamics induced by a spatially linear time-periodic potential, by means of numerical simulations. We also provide an explicit two-level model that accurately captures the microscopic evolution of the driven system, with the full time-dependent evolution operator obtained using a Floquet-based approach. The analysis is carried out using as a reference a recently realized experimental platform consisting of arrays of double-well potentials based on Beat-Note Superlattices, to which the proposed control scheme is directly applicable.