| The miscibility of quantum fluids has been an important topic in many-body physics.In traditional condensed matter systems,the miscibility of ~3He-~4He superfluids has received extensive theoretical and experimental attention.In recent years,the rapid development of cold atomic physics has provided an ideal platform for exploring novel many-body effects in quantum mixtures.Using a variety of techniques,experiments have realized various boson-boson mixture gases,boson-fermion mixture gases,and fermion-fermion mixture gases with different elements or isotopes.Many important properties,including miscibility,have been studied extensively in these systems.Chapter 1 of this article reviews the progress of theoretical and experimental research on the miscibility of binary Bose-Einstein condensates(BECs).According to mean-field theory,the miscibility of binary bosonic condensates is determined by the competition between intra-and inter-component interactions.Experimentally,the system transitions from a miscible to an immiscible state by changing the atomic scattering length using Feshbach resonance technology.Recent studies have shown that quantum fluctuations affect the stability of the system,leading to the appearance of partially miscible states.Chapter 2 of this article investigates the miscibility of equal-mass binary BECs.Starting from a state equation containing the Lee-Huang-Yang correction,the ground-state phase diagram of binary BECs in the weakly unstable region of mean-field theory is given,providing a more comprehensive description of the density range of partially miscible phases.Using phase equilibrium conditions,the phase boundaries between immiscible,partially miscible,and fully miscible states are determined for equal-mass mixtures.Analytical expressions for the phase boundaries,nodal lines,quantum critical points are presented in the quasi-homogeneous leading-order approximation,and the partially miscible state terminates,the susceptibility tensor of the density response exhibits a divergent behavior,which is valid for sufficiently dilute atomic densities.Chapter 3 of this article investigates the miscibility of unequal-mass binary BECs.When there is a mass imbalance between the two components,the LHY energy becomes more complex,and the state equation does not have a simple analytical form.The ground-state phase diagram of the system can only be numerically solved by determining the phase equilibrium conditions.In this chapter,we use the Bose-polaron picture to obtain the state equation at low concentrations and derive the threshold density for the appearance of partially miscible states.An analytical method for determining the configuration of partially miscible states is proposed,and common configurations of partially mixed Bose mixtures are summarized,providing clear theoretical guidance for the experimental observation of cold atomic mixtures such as sodium,potassium and rubidium.Chapter 4 of this article summarizes the current research and discusses areas that can continue to be studied in the future. |
