Optimal control of Bose-Einstein condensates in three dimensions

TL;DR

This paper develops an efficient optimal control framework for manipulating Bose-Einstein condensates in three dimensions, overcoming computational challenges of high-dimensional quantum systems and enabling realistic experimental applications.

Contribution

It introduces a computationally feasible OCT method for the 3D Gross-Pitaevskii equation, extending control techniques beyond 1D approximations with rigorous mathematical support.

Findings

Successful 3D control of Bose-Einstein condensates

Minimization of elementary excitations using multiple controls

Applicability to real experimental setups

Abstract

Ultracold gases promise many applications in quantum metrology, simulation and computation. In this context, optimal control theory (OCT) provides a versatile framework for the efficient preparation of complex quantum states. However, due to the high computational cost, OCT of ultracold gases has so far mostly been applied to one-dimensional (1D) problems. Here, we realize computationally efficient OCT of the Gross-Pitaevskii equation (GPE) to manipulate Bose-Einstein condensates in all three spatial dimensions. We study various realistic experimental applications where 1D simulations can only be applied approximately or not at all. Moreover, we provide a stringent mathematical footing for our scheme and carefully study the creation of elementary excitations and their minimization using multiple control parameters. The results are directly applicable to recent experiments and might thus be of immediate use in the ongoing effort to employ the properties of the quantum world for technological applications.