# The mixing-demixing phase diagram of ultracold heteronuclear mixtures in a ring trimer

## TL;DR

This paper maps the complete phase diagram of mixing and demixing in ultracold heteronuclear mixtures confined in a ring trimer, combining Bose-Hubbard and Gross-Pitaevskii models to guide experimental realizations.

## Contribution

It provides a comprehensive analysis of the mixing-demixing transitions in heteronuclear mixtures using both quantum and mean-field models, extending to realistic experimental conditions.

## Key findings

- The phase diagram depends only on two effective parameters.
- The mean-field analysis confirms a rich variety of transition scenarios.
- Proposes an experimental setup with Na and K bosonic mixtures.

## Abstract

We derive the complete mixing-demixing phase-diagram relevant to a bosonic binary mixture confined in a ring trimer and modeled within the Bose-Hubbard picture. The mixing properties of the two quantum fluids, which are shown to be strongly affected by the fragmented character of the confining potential, are evaluated by means of a specific indicator imported from Statistical Thermodynamics and are shown to depend only on two effective parameters incorporating the asymmetry between the heteronuclear species. To closely match realistic experimental conditions, our study is extended also beyond the pointlike approximation of potential wells by describing the systems in terms of two coupled Gross-Pitaevskii equations. The resulting mean-field analysis confirms the rich scenario of mixing-demixing transitions of the mixture and also constitutes an effective springboard towards a viable experimental realization. We additionally propose an experimental realization based on a realistic optical-tweezers system and on mixtures of bosonic $^{23}\mathrm{Na}$ and $^{39}\mathrm{K}$, thanks to the large tunability of their intra- and inter-species scattering lengths.