Simulating infinite vortex lattices in superfluids (original) (raw)

Abstract

We present an efficient framework to numerically treat infinite periodic vortex lattices in rotating superfluids described by the Gross-Pitaevskii theory. The commonly used split-step Fourier (SSF) spectral methods are inapplicable to such systems as the standard Fourier transform does not respect the boundary conditions mandated by the magnetic translation group. We present a generalisation of the SSF method which incorporates the correct boundary conditions by employing the so-called magnetic Fourier transform. We test the method and show that it reduces to known results in the lowest-Landau-level regime. While we focus on rotating scalar superfluids for simplicity, the framework can be naturally extended to treat multicomponent systems and systems under more general 'synthetic' gauge fields.

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What methods are employed to simulate infinite vortex lattices in superfluids?add

The study introduces a split-step magnetic Fourier method incorporating twisted boundary conditions, which accurately addresses infinite vortex lattices for superfluid systems.

How does the aspect ratio of computational cells affect vortex lattice configurations?add

Numerical results indicate that aspect ratios commensurate with triangular vortex lattices minimize energy, with R = √3 being optimal across examined configurations.

What numerical challenges are associated with simulating vortex lattices in rotating superfluids?add

Simulations typically require grids sufficiently large to minimize boundary effects and can obscure vortex configurations, necessitating over 100 vortices for accurate representation.

How does the healing length influence vortex lattice stability?add

The healing length, defined as ξ = h^2 / (2mgρ), provides a characteristic scale for vortex cores, affecting stability and density of vortex arrangements.

What configurations arise in multi-component vortex lattices compared to single-component?add

Multi-component systems yield richer vortex lattice structures due to additional interactions, expanding configurations beyond those observed in single-component homogeneous condensates.

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