GPU-accelerated solutions of the nonlinear Schr\"odinger equation for simulating 2D spinor BECs

TL;DR

This paper demonstrates how GPU acceleration significantly reduces computational time for solving the nonlinear Schrödinger equation, specifically applied to simulating 2D spinor Bose-Einstein condensates, enabling high-resolution analysis of complex quantum phenomena.

Contribution

The paper introduces a GPU-based computational method that simplifies and accelerates solving the nonlinear Schrödinger equation for 2D spinor BECs, improving efficiency over traditional CPU methods.

Findings

GPU implementation reduces computation time from power-law to linear scaling.

High-resolution simulations reveal an interaction-dependent phase transition.

The approach enables practical analysis of complex quantum systems.

Abstract

As a first approximation beyond linearity, the nonlinear Schr\"odinger equation (NLSE) reliably describes a broad class of physical systems. Though numerical solutions of this model are well-established, these methods can be computationally complex. In this paper, we showcase a code development approach, demonstrating how computational time can be significantly reduced with readily available graphics processing unit (GPU) hardware and a straightforward code migration using open-source libraries. This process shows how CPU computations with power-law scaling in computation time with grid size can be made linear using GPUs. As a specific case study, we investigate the Gross-Pitaevskii equation, a specific version of the nonlinear Schr\"odinger model, as it describes in two dimensions a trapped, interacting, two-component Bose-Einstein condensate (BEC) subject to a spatially dependent interspin coupling, resulting in an analog to a spin-Hall system. This computational approach lets us probe high-resolution spatial features - revealing an interaction-dependent phase transition - all in a reasonable amount of time. Our computational approach is particularly relevant for research groups looking to easily accelerate straightforward numerical simulation of physical phenomena.