Unified way for computing dynamics of Bose-Einstein condensates and degenerate Fermi gases

TL;DR

This paper introduces a simple, efficient numerical scheme based on a modified Split Operator Method for simulating the dynamics of Bose-Einstein condensates and degenerate Fermi gases, ensuring stability and conservation of physical constraints.

Contribution

It presents a novel extension of the Split Operator Method applicable to both bosonic and fermionic quantum gases, improving speed, stability, and physical constraint preservation.

Findings

The method accurately simulates spinor Bose-Einstein condensates with nonlocal interactions.

It effectively models strongly interacting two-component Fermi gases.

The scheme maintains physical constraints with high fidelity during simulations.

Abstract

In this work we present a very simple and efficient numerical scheme which can be applied to study the dynamics of bosonic systems like, for instance, spinor Bose-Einstein condensates with nonlocal interactions but equally well works for Fermi gases. The method we use is a modification of well known Split Operator Method (SOM). We carefully examine this algorithm in the case of $F=1$ spinor Bose-Einstein condensate without and with dipolar interactions and for strongly interacting two-component Fermi gas. Our extension of the SOM method has many advantages: it is fast, stable, and keeps constant all the physical constraints (constants of motion) at high level.