Miscibility of Dual-Species Bose-Einstein Condensates

<sec>The miscibility of quantum liquids is an interesting topic in many-body physics, which has been intensively investigated <sup>3</sup>He-<sup>4</sup>He superfluids and the mixtures ultracold atoms. In context dual species Bose-Einstein condensates, mean-field description well established, according to which, condition density independent determined only by ratio inter- intra-species interaction strength. Recently, Nadion Petrov proposed that [<i>Phys. Rev. Lett.</i> <b>126</b> 115301], vicinity mixing-demixing threshold, fluctuations play important role affect equilibrium stability, as a result, partially miscible state emerges. This new phase matter opens up perspective explore beyond effect atomic gases.</sec><sec>In this work, based on equation with inclusion Lee-Huang-Yang correction, we investigate ground diagram repulsive binary Bose interacting regime suffering weak instability. Through thermodynamic balance conditions, boundaries between immiscible state, homogenous are determined. For equal-mass case, these transitions take place under interactions asymmetric form. terms parameters, explicitly derive analytical expressions boundaries, appropriate describe sufficiently dilute gases. At critical point, where terminates, susceptibility tensor response exhibits divergent behavior. unequal-mass beyond-mean-field cannot be written compact form, thus determination more involved. By expanding energy linear concentration minority species, analytically obtain threshold for transition. We also propose discriminant function, from configuration can identified, given mass Applications theoretical results experimental systems, such sodium, potassium, rubidium gases, presented.</sec>