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Reduction-based strategy for optimal control of Bose-Einstein condensates.

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Summary

Preparing specific quantum states in Bose-Einstein condensates (BEC) is crucial. This study introduces a hybrid control method to efficiently prepare BEC states, significantly reducing unwanted excitations in the Gross-Pitaevskii equation model.

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Area of Science:

  • Quantum physics
  • Atomic, molecular, and optical physics

Background:

  • Bose-Einstein condensates (BEC) are essential quantum states for various applications.
  • Preparing BECs in specific complex states is challenging and often leads to unwanted excitations.
  • The time-dependent Gross-Pitaevskii equation (GPE) models BEC dynamics but poses computational challenges in multiple dimensions.

Purpose of the Study:

  • To develop an efficient optimal control method for preparing complex BEC states.
  • To reduce the computational complexity of controlling BECs described by the GPE.
  • To minimize unwanted excitations during state preparation.

Main Methods:

  • Dimensionality reduction of the GPE using a Galerkin expansion to a Hamiltonian ordinary differential equation system.
  • A two-stage hybrid control strategy combining a chopped random basis approximation with differential evolution algorithm.
  • Refinement of the control solution using a variant of gradient descent.

Main Results:

  • Successfully reduced the high-dimensional GPE to a low-dimensional system.
  • The hybrid control strategy effectively approximated the optimal control.
  • Significantly reduced excitations in both the reduced model and the full GPE system.

Conclusions:

  • The proposed hybrid control method offers an efficient approach for preparing complex BEC states.
  • This method significantly mitigates excitations, improving the fidelity of state preparation.
  • The strategy provides a computationally tractable framework for optimal control of BECs.