Optimal nonlinear coherent mode transitions in Bose-Einstein condensates utilizing spatiotemporal controls

David Hocker, Julia Yan, and Herschel Rabitz
Phys. Rev. A 93, 053612 – Published 18 May 2016
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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.

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  • Received 28 March 2016

DOI:https://doi.org/10.1103/PhysRevA.93.053612

©2016 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

David Hocker1, Julia Yan1,2, and Herschel Rabitz1,*

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
  • 2Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *hrabitz@princeton.edu

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Issue

Vol. 93, Iss. 5 — May 2016

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