Pitchfork bifurcations in blood-cell shaped dipolar Bose-Einstein condensates

TL;DR

This paper introduces a Gaussian wave packet method as an effective alternative to numerical solutions for analyzing blood-cell shaped dipolar Bose-Einstein condensates, revealing bifurcation-driven collapse mechanisms.

Contribution

The study demonstrates that coupled Gaussian wave packets can explore both stable and unstable solutions of the Gross-Pitaevskii equation, providing new insights into collapse phenomena.

Findings

Identification of pitchfork bifurcation leading to instability

Gaussian wave packets effectively model collapse dynamics

Clarification of the collapse mechanism in dipolar condensates

Abstract

We demonstrate that the method of coupled Gaussian wave packets is a full-fledged alternative to direct numerical solutions of the Gross-Pitaevskii equation of condensates with electromagnetically induced attractive 1/r interaction, or with dipole-dipole interaction. Moreover, Gaussian wave packets are superior in that they are capable of producing both stable and unstable stationary solutions, and thus of giving access to yet unexplored regions of the space of solutions of the Gross-Pitaevskii equation. We apply the method to clarify the theoretical nature of the collapse mechanism of blood-cell shaped dipolar condensates: On the route to collapse the condensate passes through a pitchfork bifurcation, where the ground state itself turns unstable, before it finally vanishes in a tangent bifurcation.