Numerical Simulation of Vortex Nucleation in a Two-Dimensional Bose-Einstein Condensate Ring

Core Concepts

The authors numerically study the dynamics of the Gross-Pitaevskii equation on a two-dimensional ring-shaped domain, highlighting the nucleation of quantum vortices in a particular parameter regime.

Abstract

The authors consider the time-dependent Gross-Pitaevskii equation, which is a fundamental model for describing the dynamics of Bose-Einstein condensates (BECs). They focus on the case of a two-dimensional ring-shaped geometry, motivated by experimental setups.
The key aspects of the work are:

Dimensionless formulation of the Gross-Pitaevskii equation: The authors introduce dimensionless variables to simplify the numerical computations.

Numerical discretization: They employ a Strang splitting time integration scheme and a two-point flux approximation Finite Volume scheme for the spatial discretization, based on a particular admissible triangulation of the domain.

Ground state computation: The authors use a normalized gradient flow method to numerically compute the ground state of the Gross-Pitaevskii equation, which serves as the initial condition for the dynamic simulations.

Vortex detection and tracking: The authors develop numerical algorithms to detect and track the formation of quantum vortices during the dynamics.

Eigenmode decomposition: They also implement a method to decompose the wave function onto the eigenmodes of the linear part of the Gross-Pitaevskii equation, in order to analyze the energy distribution among different modes.

The numerical results corroborate theoretical predictions and demonstrate the nucleation of vortices in a particular parameter regime, providing insights into the complex nonlinear phenomena exhibited by rotating Bose-Einstein condensates.

Stats

The authors do not provide any specific numerical values or statistics in the content. The work focuses on the description of the numerical methods and the presentation of the overall approach.

Quotes

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Key Insights Distilled From

Numerical study of the Gross-Pitaevskii equation on a two-dimensional ring and vortex nucleation

by Quen... at arxiv.org 04-17-2024

https://arxiv.org/pdf/2404.10360.pdf

Deeper Inquiries

How do the numerical results compare to experimental observations of vortex nucleation in Bose-Einstein condensates

The numerical results obtained from the study of vortex nucleation in Bose-Einstein condensates using the Gross-Pitaevskii equation show a close resemblance to experimental observations. The introduction of a rotating sinusoidal perturbation in the model led to the nucleation of quantum vortices in a specific regime throughout the dynamics. This phenomenon aligns with experimental findings in atomic quantum gas experiments, where rotating Bose-Einstein condensates exhibit complex nonlinear behaviors such as vortex nucleation and quantum turbulence. The numerical simulations accurately captured the formation and behavior of vortices in the two-dimensional ring-shaped geometry, reflecting the dynamics observed in experimental setups.

What are the limitations of the Gross-Pitaevskii equation in accurately modeling the dynamics of rotating BECs, and how could the model be extended to capture additional physical effects

The Gross-Pitaevskii equation, while a powerful tool for describing the dynamics of Bose-Einstein condensates, has limitations in accurately modeling the dynamics of rotating BECs. One limitation is the assumption of a stationary trapping potential, which may not fully capture the effects of dynamic external forcing such as rotation or stirring. To extend the model and capture additional physical effects, one could incorporate time-dependent external potentials to simulate more realistic experimental conditions. Additionally, the Gross-Pitaevskii equation does not account for dissipative effects or interactions with the environment, which are crucial in understanding the full dynamics of rotating BECs. Including dissipative terms or coupling the system to a thermal reservoir could provide a more comprehensive model of the system.

Can the insights gained from this study on vortex nucleation be applied to understand the emergence of quantum turbulence in rotating BECs

The insights gained from the study on vortex nucleation in rotating Bose-Einstein condensates can be applied to understand the emergence of quantum turbulence in these systems. Quantum turbulence is characterized by the presence of a large number of quantized vortices interacting with each other, leading to complex flow patterns and energy cascades. By studying the nucleation and behavior of vortices in rotating BECs, researchers can gain valuable insights into the mechanisms underlying quantum turbulence. The numerical algorithms developed for vortex tracking and the decomposition of the wave function into eigenmodes can be utilized to analyze the formation and dynamics of vortices in turbulent regimes, shedding light on the transition to chaotic behavior in rotating Bose-Einstein condensates.