Optimal nonlinear coherent mode transitions in Bose-Einstein condensates utilizing spatiotemporal controls
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PhysRevA.93.053612.pdf
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2.01 MB
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Author(s)
Hocker, David
Rabitz, Herschel
Yan, Julia Yun Chien
Date Issued
May 2016
Journal
Physical Review A
Publisher
American Physical Society
Citation
Hocker, David; Yan, Julia and Rabitz, Herschel. "Optimal nonlinear coherent mode transitions in Bose-Einstein condensates utilizing spatiotemporal controls." Physical Review A 93, 053612 (May 2016): 1-11 © 2016 American Physical Society
Version
Final published version
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 modulation of 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 the 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 Schrödinger-type systems.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.93.053612
