interest. The nonequilibrium dynamics induced by an interspecies interaction quench for particle imbalanced and balanced species within a double-well is analyzed in Secs. \[sec:particle\_imbalanced\] and \[sec:particle\_balanced\] respectively. We summarize our findings and provide an outlook in Section \[sec:conclusion\]. In Appendix \[single\_shots\_details\] we provide a brief discussion regarding our numerical implementation of the single-shot procedure. Finally, in Appendix \[sec:numerics\] we present further details of our numerical simulations and demonstrate the convergence of the results discussed in the main text.

Theoretical Framework {#sec:theory}
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Setup {#sec:setup}
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We consider a FF mixture consisting of $N_A$ and $N_B$ spin polarized fermions with equal masses $M_A=M_B\equiv M$ for the $A$ and $B$ species respectively. Such a mass balanced fermionic mixture can be experimentally realized by two different hyperfine states e.g. of $\prescript{40}{}{K}$ or $\prescript{6}{}{Li}$ [@wang2000ground; @dieckmann2002decay]. These internal states could refer, for instance, to the $\ket{F=9/2,m_F-9/2}$ and $\ket{F=9/2,m_F=-7/2}$ of $\prescript{40}{}{K}$ [@zwierlein2006fermionic]. The mixture is confined in an one-dimensional double-well external potential [@bloch2005ultracold] which is composed by a harmonic oscillator with frequency $\omega$ and a centered Gaussian with height $V_0$ and width $w$. The resulting MB Hamiltonian reads $$\begin{aligned}
\mathcal{H}&=\sum\limits_{\sigma=A,B} \sum\limits_{i=1}^{N_\sigma}\left[  -\frac{\hbar^2}{2M}\left( \frac{d}{d x_i^\sigma}\right)^2
+\frac{1}{2}M\omega_\sigma^2(x_i^\sigma)^2 \right. \nonumber\\
&+ \left.\frac{V_0}{w \sqrt{2\pi}} e^{-\frac{(x_i^\sigma)^2 }{2w^2}}\right]\nonumber \\  &+ \sum\limits_{i=1}^{N_A} 