# Optimal control of the self-bound dipolar droplet formation process

## TL;DR

This paper demonstrates how optimal control algorithms can significantly accelerate the formation of dipolar Bose-Einstein condensate droplets, using advanced numerical methods to improve efficiency and feasibility.

## Contribution

It introduces a multilevel B-spline based optimal control approach for dipolar droplet formation, reducing computational effort and incorporating box constraints effectively.

## Key findings

- Optimal control dramatically accelerates droplet formation.
- Multilevel B-spline method reduces cost function evaluations.
- Efficient evaluation of dipolar interactions maintains spectral convergence.

## Abstract

Dipolar Bose-Einstein condensates have recently attracted much attention in the world of quantum many body experiments. While the theoretical principles behind these experiments are typically supported by numerical simulations, the application of optimal control algorithms could potentially open up entirely new possibilities. As a proof of concept, we demonstrate that the formation process of a single dipolar droplet state could be dramatically accelerated using advanced concepts of optimal control. More specifically, our optimization is based on a multilevel B-spline method reducing the number of required cost function evaluations and hence significantly reducing the numerical effort. Moreover, our strategy allows to consider box constraints on the control inputs in a concise and efficient way. To further improve the overall efficiency, we show how to evaluate the dipolar interaction potential in the generalized Gross-Pitaevskii equation without sacrificing the spectral convergence rate of the underlying time-splitting spectral method.