# Miscibility in coupled dipolar and non-dipolar Bose-Einstein condensates

## TL;DR

This study investigates the conditions under which coupled dipolar and non-dipolar Bose-Einstein condensates transition between miscible and immiscible phases, emphasizing the influence of trap geometry and inter-species interactions.

## Contribution

It provides a comprehensive 3D analysis of miscibility in coupled BECs, including specific atomic mixtures and the effects of trap symmetry and interactions.

## Key findings

- Trap symmetry significantly affects miscibility transition.
- A new parameter effectively quantifies the overlap of densities.
- Transition from miscible to immiscible is smoother in harmonic traps.

## Abstract

We perform a full three-dimensional study on miscible-immiscible conditions for coupled dipolar and non-dipolar Bose-Einstein condensates (BEC), confined within anisotropic traps. Without loosing general miscibility aspects that can occur for two-component mixtures, our main focus was on the atomic erbium-dysprosium ($^{168}$Er-$^{164}$Dy) and dysprosium-dysprosium ($^{164}$Dy-$^{162}$Dy) mixtures. Our analysis for pure-dipolar BEC was limited to coupled systems confined in pancake-type traps, after considering a study on the stability regime of such systems. In case of non-dipolar systems with repulsive contact intneeractions we are able to extend the miscibility analysis to coupled systems with cigar-type symmetries. For a coupled condensate with repulsive inter- and intra-species two-body interactions, confined by an external harmonic trap, the transition from a miscible to an immiscible phase is verified to be much softer than in the case the system is confined by a symmetric hard-wall potential. Our results, presented by density plots, are pointing out the main role of the trap symmetry and inter-species interaction for the miscibility. A relevant parameter to measure the overlap between the two densities was defined and found appropriate to quantify the miscibility of a coupled system.