Exploring Bifurcations in Bose-Einstein Condensates via Phase Field Crystal Models

TL;DR

This paper develops an approximate phase field crystal model for Bose-Einstein condensates near the superfluid-supersolid transition, enabling detailed bifurcation analysis and revealing localized states and effects of nonlinearities.

Contribution

It introduces a novel approximate mapping from the Gross-Pitaevskii equation to a PFC model for BECs near phase transition boundaries.

Findings

Bifurcation structures are mapped and analyzed.

Localized states are demonstrated in the model.

Higher-order nonlinearities alter bifurcation diagrams.

Abstract

To facilitate the analysis of pattern formation and of the related phase transitions in Bose-Einstein condensates (BECs) we present an explicit approximate mapping from the nonlocal Gross-Pitaevskii equation with cubic nonlinearity to a phase field crystal (PFC) model. This approximation is valid close to the superfluid-supersolid phase transition boundary. The simplified PFC model permits the exploration of bifurcations and phase transitions via numerical path continuation employing standard software. While revealing the detailed structure of the bifurcations present in the system, we demonstrate the existence of localized states. Finally, we discuss how higher-order nonlinearities change the structure of the bifurcation diagram representing the transitions found in the system.