Title: Strongly interacting Bose-Fermi mixture: mediated interaction, phase diagram and sound propagation Show Chinese title

Title: 强相互作用的玻色费米混合物：媒介相互作用、相图和声波传播

Abstract: Motivated by recent surprising experimental findings, we develop a strong-coupling theory for Bose-Fermi mixtures capable of treating resonant inter-species interactions while satisfying the compressibility sum rule. We show that the mixture can be stable at large interaction strengths close to resonance, in agreement with the experiment but at odds with the widely used perturbation theory. We also calculate the sound velocity of the Bose gas in the $^{133}$Cs-$^6$Li mixture, again finding good agreement with the experimental observations both at weak and strong interactions. A central ingredient of our theory is the generalization of a fermion mediated interaction to strong Bose-Fermi scatterings and to finite frequencies. This further leads to a predicted hybridization of the sound modes of the Bose and Fermi gases, which can be directly observed using Bragg spectroscopy. Show Chinese abstract

Abstract: 受最近令人惊讶的实验发现的启发，我们开发了一种强耦合理论，用于玻色-费米混合物，能够处理共振的物种间相互作用，同时满足压缩性求和规则。 我们表明，在接近共振的大相互作用强度下，混合物可以保持稳定，这与实验结果一致，但与广泛使用的微扰理论相矛盾。 我们还计算了$^{133}$Cs-$^6$Li 混合物中玻色气体的声音速度，再次发现无论在弱相互作用还是强相互作用下，都与实验观测结果有良好的一致性。 我们理论的核心要素是将费米子介导的相互作用推广到强玻色-费米散射以及有限频率的情况。 这进一步导致了玻色气体和费米气体声模的预测杂化，可以通过布拉格光谱学直接观察到。