Optimal control of quantum superpositions in a bosonic Josephson junction

Abstract

We show how to optimally control the creation of quantum superpositions in a bosonic Josephson junction within the two-site Bose-Hubbard-model framework. Both geometric and purely numerical optimal-control approaches are used, the former providing a generalization of the proposal of Micheli et al. [Phys. Rev. A 67, 013607 (2003)]. While this method is shown not to lead to significant improvements in terms of time of formation and fidelity of the superposition, a numerical optimal-control approach appears more promising, as it allows creation of an almost perfect superposition, within a time short compared to other existing protocols. We analyze the robustness of the optimal solution against atom-number variations. Finally, we discuss the extent to which these optimal solutions could be implemented with state-of-the-art technology.