Correlated Dynamics Of Fermionic Impurities Induced By The Counterflow Of An Ensemble Of Fermions

We Investigate The Nonequilibrium Quantum Dynamics Of One And Two Heavy Fermionic Impurities Being Harmonically Trapped And Repulsively Interacting With A Finite Ensemble Of Majority Fermions. A Quench Of The Potential Of The Majority Species From A Double-Well To A Harmonic Trap Is Applied, Enforcing Its Counterflow, Which In Turn Perturbs The Impurities. For Weak Repulsions, It Is Shown That The Mixture Undergoes A Periodic Mixing And Demixing Dynamics, While Stronger Interactions Lead To A More Pronounced Dynamical Spatial Separation. In The Presence Of Correlations, The Impurity Exhibits An Expansion Dynamics Which Is Absent In The Hartree-Fock Case, Resulting In An Enhanced Degree Of Miscibility. We Generalize Our Results To Different Impurity Masses And Demonstrate That The Expansion Amplitude Of The Impurity Reduces For A Larger Mass. Furthermore, We Showcase That The Majority Species Is Strongly Correlated And A Phase Separation Occurs On The Two-Body Level. Most Importantly, Signatures Of Attractive Impurity-Impurity Induced Interactions Mediated By The Majority Species Are Identified In The Time Evolution Of The Two-Body Correlations Of The Impurities, A Result That Is Supported By Inspecting Their Spatial Size.