author:
- Maxim Pyzh
- Peter Schmelcher
title: 'Phase separation of a Bose-Bose mixture: impact of the trap and particle number imbalance'
---

Introduction {#sec:intro}
============

Binary mixtures of ultra-cold gases have been extensively studied over the past years. They represent a unique platform for the investigation of complex interacting many-body quantum systems in a well controlled environment. In particular, it is experimentally possible to shape the geometry of the trap [@TailoredTraps2000], to reduce the dimensionality of the relevant motion [@1Dgases2008; @1Dgases2011], to tune the inter-particle interactions [@Feshbach2010; @CIR1998; @CIR2000; @CIR2003; @CIR2010] and prepare samples of only a few atoms [@fewbody2012; @fewbody2019]. Numerous experiments have been conducted with different hyperfine states [@Myatt1997; @Hall1998; @Ketterle1999; @Inguscio2000; @Aspect2001; @Hall2007; @Hirano2010; @Becker2008; @Engels2011; @Oberthaler2015; @Hirano2016collision; @Hirano2016quench; @dropletsCabrera2018; @dropletsInguscio2018], different elements [@Inguscio2002; @Weidemuller2002; @Inguscio2008; @Ospelkaus2008; @Cornish2011; @Nagerl2011; @Grimm2013; @Nagerl2014; @Cornish2014; @Arlt2015; @Wang2015a; @Proukakis2018; @Wang2015b; @Minardi2010] or different isotopes [@Papp2008; @Takahashi2011] to reveal how the interplay between two condensates impacts their stationary properties and non-equilibrium dynamics. Highlights of these explorations include among others the phase separation between the components and symmetry-breaking phenomena [@Hall1998; @Papp2008; @Hirano2010; @Wang2015b; @Proukakis2018], the observation of Efimov physics [@Minardi2010] and creation of deeply bound dipolar molecules [@Ospelkaus2008; @Nagerl2014; @Cornish2014], as well 