the intra-species and inter-species interactions strengths, which are easily adjustable by Feshbach or confinement induced resonances [@Feshbach2010; @CIR1998; @CIR2000; @CIR2003; @CIR2010].

However, it has been shown that this separation criterion, while valid in homogeneous systems, should be applied with care in inhomogeneous geometries. There, system parameters such as trap frequency, particle numbers or mass ratio, have also an impact on the miscible-immiscible phase boundary [@brokenRuleTrapKevrekidis2009; @brokenRuleTrapHu2012; @brokenRuleTrapProukakis2016; @brokenRuleMassBoronat2018; @brokenRuleImbalanceZhang2020]. From the intuitive point of view the trap pressure favors miscibility, since it costs energy to extend in space. Thus, it requires stronger inter-component repulsion for the species to separate. However, there are still open questions regarding the impact of different length scales, the characterization of boundaries between the immiscible phases and what type of separation will occur once the critical coupling is reached.

Another relevant topic affecting the critical coupling strength for a transition as well as the resulting type of phase are the inter-species correlations, which generate entanglement between the components and lead to bunching of particles of the same species. Although a mean-field treatment is often justified in experimental setups, a very thorough numerical analysis of 1D few-body systems has revealed that an asymmetric immiscible phase is one 