Multi-vortex crystal lattices in Bose-Einstein condensates with a rotating trap.

Area of Science:

• Quantum Mechanics
• Atomic, Molecular & Optical Physics
• Condensed Matter Physics

Background:

• Bose-Einstein condensates (BECs) exhibit complex vortex dynamics under rotation.
• Understanding vortex crystal formation is crucial for controlling BEC states.
• The Gross-Pitaevskii (GP) equation describes BECs but is computationally intensive.

Purpose of the Study:

• To derive a reduced system of ordinary differential equations (ODEs) from the GP equation for vortex dynamics.
• To quantitatively describe stable configurations of multiple co-rotating vortices (vortex crystals).
• To analyze vortex behavior in both isotropic and anisotropic rotating traps.

Main Methods:

• Derivation of a novel reduced ODE system from the GP partial differential equation (PDE).
• Asymptotic reduction for the many-vortex limit.
• Numerical simulations of the GP equation for validation.

Main Results:

• The ODE system accurately predicts quantitative vortex crystal configurations.
• Derived effective vortex crystal density, radius, and maximum vortex number.
• Confirmed stability/instability of vortex pairs in anisotropic traps and analyzed 1D density in strong anisotropy.

Conclusions:

• The reduced ODE model offers an accurate and efficient description of vortex crystals in rotating BECs.
• Analytical predictions are robustly confirmed by full PDE simulations.
• The study provides insights into vortex arrangement and density in both isotropic and anisotropic potentials.