Binary Mixture of Quasi-One-Dimensional Dipolar Bose–Einstein Condensates with Tilted Dipoles

We consider a ${}^{168}$Er–${}^{164}$Dy dipolar mixture, trapped by a cigar-shaped harmonic potential. We derive the quasi-1D interspecies effective potential exhibiting the tilting angles and show that it is a quite natural generalization of a single dipolar gas. By solving the coupled Gross–Pitaevskii equations, we observe a transition from miscible to immiscible mixture as the orientations of the magnetic moments are varied. The atom numbers are also shown to lead to noticeable effects on the characteristics of this transition.