Supersolid transition of a dipolar Bose-Einstein condensate in an infinite tube

Supersolids are state of matter that combine crystalline order with superfluid flow and have been realised in Bose-Einstein condensates (BECs) of Dysprosium and Erbium. In this talk we will examine the supersolid transition of a dipolar BEC which has been confined to an infinite tube. We use the beyond mean-field description known as the extended Gross Pitaevskii equation (EGPE). The ground states of the EGPE theory are calculated in a unit cell using a range of techniques to obtained accurate solutions.  We show that the supersolid transition can be both first order or second order depending on the average density of the system.