Optimal nonlinear coherent mode transitions in Bose-Einstein Condensates utilizing spatio-temporal controls

TL;DR

This paper demonstrates optimal control of Bose-Einstein condensates using modulated linear and nonlinear terms in the Gross-Pitaevskii equation to efficiently transition between quantum states with high success rates.

Contribution

It introduces a method for controlling BEC mode transitions by simultaneously modulating linear and nonlinear controls in the GPE, revealing the potential of nonlinear control mechanisms.

Findings

Over 99% success rate in mode-to-mode transitions

Primarily direct transitions between initial and target modes

Nonlinear control alone can effectively induce state transitions

Abstract

Bose-Einstein condensates (BECs) offer the potential to examine quantum behavior at large length and time scales, as well as forming promising candidates for quantum technology applications. Thus, the manipulation of BECs using control fields is a topic of prime interest. We consider BECs in the mean field model of the Gross-Pitaevskii equation (GPE), which contains linear and nonlinear features, both of which are subject to control. In this work we report successful optimal control simulations of a one dimensional GPE by modulating the linear and nonlinear terms to stimulate transitions into excited coherent modes. The linear and nonlinear controls are allowed to freely vary over space and time to seek their optimal forms. The determination of the excited coherent modes targeted for optimization is numerically performed through an adaptive imaginary time propagation method. Numerical simulations are performed for optimal control of mode-to-mode transitions between the ground coherent mode and excited modes of a BEC trapped in a harmonic well. The results show greater than 99% success for nearly all trials utilizing reasonable initial guesses for the controls, and analysis of the optimal controls reveals primarily direct transitions between initial and target modes. The success of using solely the nonlinearity term as a control opens up further research toward exploring novel control mechanisms inaccessible to linear Schr\"odinger-type systems.