We study the properties of the Bose-Fermi mixture from the perspective of reaching a state of a self-bound quantum droplet. The variational analysis shows that the system exhibits bistability. For weak repulsion between bosons, one of the equilibrium states, smaller in size, spherically symmetric, and with negative energy, corresponds to quantum droplet, the other with always positive energy represents the elongated droplet-like state immersed in the sea of a fermionic cloud. For stronger repulsion between bosons the bifurcation is seized and only the former state is left. Now it represents an elongated object which, for strong enough boson-fermion attraction, gets negative energy. It becomes an excited Bose-Fermi droplet when the trap is released, what is demonstrated by solving the quantum hydrodynamics equations for the Bose-Fermi system. To depict our ideas we consider the $^{133}$Cs-$^6$Li mixture under ideal conditions, i.e. we assume no losses.

中文翻译：

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玻色-费米混合物的双稳定性

我们从达到自束缚量子液滴状态的角度研究玻色-费米混合物的性质。变分分析表明系统表现出双稳态。对于玻色子之间的弱斥力，平衡态之一，尺寸较小，球对称，负能量，对应于量子液滴，另一个总是正能量，代表浸入费米子云海中的细长液滴状状态. 对于玻色子之间更强的排斥力，分岔被抓住，只剩下前一个状态。现在它代表一个细长的物体，对于足够强的玻色子-费米子吸引力，它会获得负能量。当陷阱被释放时，它变成激发的 Bose-Fermi 液滴，这可以通过求解 Bose-Fermi 系统的量子流体动力学方程来证明。