Localized States in Dipolar Bose-Einstein Condensates: To be or not to be of second order

TL;DR

This paper investigates localized states in dipolar Bose-Einstein condensates confined in tubular geometries, revealing that phase transitions can involve abrupt density changes rather than smooth ones, with localized states existing in both 1D and 3D.

Contribution

It demonstrates the existence of localized states in dipolar BECs and challenges the assumption that supercritical bifurcations imply second-order phase transitions.

Findings

Localized states can become the ground state in certain parameters.

Supercritical bifurcation does not guarantee a second-order phase transition.

Localized states are present in both 1D and 3D geometries.

Abstract

We report the existence of localized states in dipolar Bose-Einstein condensates confined to a tubular geometry. We first perform a bifurcation analysis to track their emergence in a one-dimensional domain for numerical feasibility and find that localized states can become the ground state in suitable parameter regions. Their existence for parameters featuring a supercritical primary bifurcation shows that the latter is not sufficient to conclude that the phase transition is of second order, hence density modulations can jump rather than emerging gradually. Finally, we show that localized states also exist in a three-dimensional domain.