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Shortcut to synchronization in classical and quantum systems.

François Impens1, David Guéry-Odelin2

  • 1Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, 21941-972, Brazil. impens@if.ufrj.br.

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Researchers developed a novel non-sinusoidal driving method to accelerate synchronization in nonlinear quantum systems. This approach enhances control and explores the quantum speed limit in nonlinear dynamics.

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Area of Science:

  • Nonlinear physics
  • Quantum mechanics
  • Quantum control

Background:

  • Synchronization is a key phenomenon in nonlinear systems, typically observed after long durations under sinusoidal excitation.
  • Classical systems achieve synchronization, but direct transposition to quantum systems is challenging due to differences in phase space representation.

Purpose of the Study:

  • To design a transiently non-sinusoidal driving method for faster synchronization in nonlinear systems.
  • To adapt this method for nonlinear quantum systems, considering finite-size quantum distributions in phase space.
  • To investigate the implications for fast quantum control and the quantum speed limit.

Main Methods:

  • Utilized an inverse engineering approach on the Van der Pol oscillator for classical systems.
  • Developed an iterative procedure to adapt the method for quantum systems with finite-size phase space distributions.
  • Employed trace distance to quantify the proximity of the resulting density matrix to the synchronized state.

Main Results:

  • Successfully designed a transiently non-sinusoidal driving for faster synchronization.
  • Demonstrated an effective adaptation of the inverse engineering method for nonlinear quantum systems.
  • Achieved a density matrix close to the synchronized state, validated by trace distance.

Conclusions:

  • The proposed method enables rapid control of nonlinear quantum systems.
  • This work provides insights into achieving faster synchronization in quantum regimes.
  • The findings raise important questions about the quantum speed limit in the context of nonlinear dynamics.