We unravel the ground-state properties and the nonequilibrium quantum dynamics of two bosonic impurities immersed in a one-dimensional fermionic environment by applying a quench of the impurity-medium interaction strength. In the ground state, the impurities and the Fermi sea are phase separated for strong impurity-medium repulsions while they experience a localization tendency around the trap center for large attractions. We demonstrate the presence of attractive induced interactions mediated by the host for impurity-medium couplings of either sign and analyze the competition between induced and direct interactions. A quench to repulsive interactions triggers a breathing motion in both components, with an interaction dependent frequency and amplitude for the impurities, and a dynamical phase separation between the impurities and their surrounding for strong repulsions. For attractive postquench couplings a beating pattern owing its existence to the dominant role of induced interactions takes place with both components showing a localization trend around the trap center. In both quench scenarios, attractive induced correlations are manifested between noninteracting impurities and are found to dominate the direct ones only for quenches to attractive couplings.

中文翻译：

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浸没在费米海中的玻色子的诱导相互作用和猝灭动力学

通过应用杂质-介质相互作用强度的猝灭，我们揭示了浸没在一维费米离子环境中的两种玻色子杂质的基态性质和非平衡量子动力​​学。在基态下，杂质和费米海相分离，以产生强的杂质-介质排斥力，同时它们在捕集阱中心附近经历局部化趋势，形成较大的吸引力。我们证明了存在的由主机介导的任意杂质-介质偶联的诱人诱导相互作用的存在，并分析了诱导相互作用和直接相互作用之间的竞争。排斥反应的猝灭会触发两个组件的呼吸运动，杂质的相互作用频率和幅度取决于相互作用，以及杂质与周围环境之间的动态相分离，以实现强排斥。对于诱人的猝灭后耦合，由于其存在是诱导相互作用的主要作用，因此会发生跳动模式，两个组件都显示出陷阱中心附近的定位趋势。在这两种淬灭情况下，非相互作用杂质之间均表现出有吸引力的诱导相关性，并且发现它们仅对淬灭至有吸引力的偶联起主导作用。