by averaging over a sample of single-shot images.'
author:
- 'J. Erdmann'
- 'S. I. Mistakidis'
- 'P. Schmelcher'
bibliography:
- 'bibliography.bib'
title: |
    Phase Separation Dynamics Induced by an Interaction Quench\
    of a Correlated Fermi-Fermi Mixture in a Double Well
---

Introduction
============

Ultracold Fermi gases offer an excellent testbed for simulating and exploring exotic quantum phases of matter [@giorgini2008theory; @chevy2010ultra; @bloch2008many]. Recent experimental advances constitute a valuable resource for disclosing the intricate complexity of condensed matter systems. Indeed several key quantities can be adjusted in the laboratory including the interparticle interaction strength via Feshbach resonances [@inouye1998observation; @chin2010feshbach], the particle number [@serwane2011deterministic; @zurn2012fermionization; @wenz2013few] and the external potential landscape [@bloch2008many; @greiner2002quantum]. Besides single species also mixtures of fermions can nowadays be experimentally prepared with neutral fermionic atoms e.g. in different hyperfine states such as $\prescript{40}{}{K}$ [@wu2012ultracold; @wille2008exploring], $\prescript{6}{}{Li}$ [@wille2008exploring; @moerdijk1995resonances] and $\prescript{87}{}{Sr}$ [@takamoto2006improved].

In this context, impressive features have been revealed evincing for instance superfluidity [@chen2005bcs; @chin2006evidence], quantum magnetism [@sowinski2018ground; @hung2011exotic; @yannouleas2016ultracold; @koutentakis2018probing], insulating phases [@lisandrini2017topological; @nataf2016chiral; @zhou2016mott], phase separation [@shin2006observation; @partridge2006pairing; @shin2008phase], fermi polarons [@massignan2014polarons; @scazza2017repulsive; @schmidt2018universal; @mistakidis2018repulsive] and Josephson junctions [@macri2013tunneling; @valtolina2015josephson; @spuntarelli2007josephson; @erdmann2018correlated]. A major focus has been the phase diagram of Fermi-Fermi (FF) mixtures ranging 