Induced interactions and quench dynamics of bosonic impurities immersed in a Fermi sea

TL;DR

This paper investigates the ground state properties and non-equilibrium dynamics of two bosonic impurities in a one-dimensional fermionic environment, revealing phase separation, induced interactions, and complex breathing and beating behaviors following interaction quenches.

Contribution

It provides a detailed analysis of induced interactions and quench dynamics in a bosonic-fermionic mixture, highlighting the role of induced correlations and their dominance over direct interactions.

Findings

Phase separation occurs for strong repulsions and localization for large attractions.

Induced interactions mediated by the Fermi sea are attractive for both signs of impurity-medium coupling.

Quenches induce breathing motions and dynamical phase separation, with beating patterns emerging for attractive couplings.

Abstract

We unravel the ground state properties and the non-equilibrium quantum dynamics of two bosonic impurities immersed in an 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. Following 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 post-quench 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 non-interacting impurities and are found to dominate the direct ones only for quenches to attractive couplings.