Optimal control of quantum superpositions in a bosonic Josephson junction

TL;DR

This paper compares geometric and numerical optimal control methods for creating quantum superpositions in a bosonic Josephson junction, finding that numerical approaches yield near-perfect superpositions efficiently and are more robust.

Contribution

It introduces a numerical optimal control method for generating quantum superpositions in a bosonic Josephson junction, outperforming geometric approaches in fidelity and robustness.

Findings

Numerical optimal control achieves near-perfect superpositions.

The method is robust against atom number variations.

Superpositions can be created faster than existing protocols.

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 to create 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 to which extent these optimal solutions could be implemented with the state of art technology.