We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with a tunable Bose-Fermi pairing interaction $-U_{\mathrm{BF}}<0$ associated with a heteronuclear Feshbach resonance, as well as a weak repulsive Bose-Bose interaction $U_{\mathrm{BB}}\ge 0$. Including strong heteropairing fluctuations associated with the former interaction within the self-consistent $T$-matrix approximation, as well as the latter within the mean-field level, we calculate the compressibility matrix, to assess the stability of this system against density fluctuations. In the weak- and the intermediate-coupling regimes with respect to $-U_{\mathrm{BF}}$, we show that an effective attractive interaction between bosons mediated by density fluctuations in the Fermi component makes the system unstable below a certain temperature $T_{\mathrm{clp}}$ (leading to density collapse). When $U_{\mathrm{BB}}=0, T_{\mathrm{clp}}$ is always higher than the Bose-Einstein condensation (BEC) temperature $T_{\mathrm{c}}$. When $U_{\mathrm{BB}}>0$, the density collapse is suppressed, and the BEC transition becomes possible. It is also suppressed by the formation of tightly bound Bose-Fermi molecules when the heteropairing interaction $-U_{\mathrm{BF}}$ is strong; however, since the system may be viewed as a molecular Fermi gas in this case, the BEC transition does not also occur. Since quantum gases involving Bose atoms are known to be sensitive to interparticle correlations, our results would be useful for the study of many-body properties of a Bose-Fermi mixture in a stable manner, without facing the unwanted density collapse.

中文翻译：

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强相互作用玻色-费米混合物中的热力学稳定性、可压缩性矩阵和介导相互作用的影响

我们从理论上研究了常态 Bose-Fermi 混合物的热力学稳定性，具有可调的 Bose-Fermi 配对相互作用 $-{你}_{\mathrm{高炉}}<0$ 与异核 Feshbach 共振以及弱排斥 Bose-Bose 相互作用相关 ${你}_{\mathrm{BB}}\ge 0$. 包括与自洽内的前一种相互作用相关的强烈杂对波动$吨$-matrix 近似，以及后者在平均场水平内，我们计算可压缩性矩阵，以评估该系统对密度波动的稳定性。在弱耦合和中间耦合机制中$-{你}_{\mathrm{高炉}}$，我们表明费米分量中的密度波动介导的玻色子之间的有效吸引力相互作用使系统在一定温度以下不稳定 ${吨}_{\mathrm{剪辑}}$（导致密度崩溃）。什么时候${你}_{\mathrm{BB}}=0, {吨}_{\mathrm{剪辑}}$ 始终高于玻色-爱因斯坦凝聚 (BEC) 温度 ${吨}_{\mathrm{C}}$. 什么时候${你}_{\mathrm{BB}}>0$，密度崩溃被抑制，BEC转变成为可能。当杂配对相互作用时，它也被紧密结合的 Bose-Fermi 分子的形成所抑制$-{你}_{\mathrm{高炉}}$强; 然而，由于在这种情况下系统可以被视为分子费米气体，因此也不会发生 BEC 跃迁。由于已知涉及玻色原子的量子气体对粒子间相关性很敏感，因此我们的结果将有助于以稳定的方式研究玻色-费米混合物的多体特性，而不会面临不需要的密度崩溃。