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Characterizing coherent structures in Bose-Einstein condensates through dynamic-mode decomposition.

Christopher W Curtis1,2, R Carretero-González1,2, Matteo Polimeno1

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Dynamic Mode Decomposition (DMD) reveals hidden vortices in turbulent Bose-Einstein condensates. This model-independent method characterizes flow regimes without phase information, aiding complex flow analysis.

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Area of Science:

  • Quantum Physics
  • Fluid Dynamics
  • Nonlinear Dynamics

Background:

  • Bose-Einstein condensates (BECs) exhibit complex dynamics, including turbulence, often modeled by the Gross-Pitaevskii equation.
  • Understanding turbulent flows in BECs is crucial for fundamental physics and potential applications.
  • Characterizing these flows typically requires phase information, which is not always experimentally accessible.

Purpose of the Study:

  • To apply Dynamic Mode Decomposition (DMD) to analyze weakly turbulent 2D Bose-Einstein condensates.
  • To characterize different turbulent regimes (weak-wave, high- and low-frequency saturation) without using phase information.
  • To demonstrate the capability of DMD in extracting coherent structures like vortices from complex flow data.

Main Methods:

  • Simulations of 2D Bose-Einstein condensates using the Gross-Pitaevskii equation with stochastic forcing.
  • Incorporation of hypoviscosity and hyperviscosity terms to balance energy spectrum.
  • Application of Dynamic Mode Decomposition (DMD) to identify dominant flow structures and energy-carrying modes.

Main Results:

  • Successfully characterized three distinct turbulent regimes by analyzing DMD modes.
  • Demonstrated seamless extraction of vortices from the condensate using DMD mode projection, without phase information.
  • Identified DMD as a powerful tool for analyzing complex flows in BECs.

Conclusions:

  • Dynamic Mode Decomposition (DMD) provides a robust, model-independent method for analyzing turbulent Bose-Einstein condensates.
  • This methodology can characterize flow regimes and extract coherent structures even without direct phase information.
  • The DMD approach is transferable to other complex flow systems and experiments, offering insights into turbulence and hidden structures.