Simulating Infinite Vortex Lattices in Superfluids

TL;DR

This paper introduces an efficient numerical framework for simulating infinite vortex lattices in rotating superfluids, overcoming boundary condition challenges with a magnetic Fourier transform, applicable to various superfluid systems.

Contribution

A generalized split-step Fourier method using magnetic Fourier transform to accurately simulate infinite vortex lattices in superfluids.

Findings

Method reduces to known results in the lowest-Landau-level regime.

Framework can be extended to multicomponent systems and synthetic gauge fields.

Efficiently handles boundary conditions for infinite periodic vortex lattices.

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.