quench imported interaction energy into the system [@fang2014quench]. Below, we first analyze the dynamics of a particle imbalanced mixture with $N_A=3$ ($N_A=5$) and $N_B=1$ fermions respectively, and subsequently examine the corresponding particle balanced case with $N_A=N_B=2$ and $N_A=N_B=5$.

Many-Body Approach {#sec:wfn}
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To solve the underlying MB Schr[ö]{}dinger equation that governs the quech-induced dynamics of the FF mixture we utilize ML-MCTDHX [@ML-MCTDHX]. It is based on an expansion of the MB wavefunction with respect to a time-dependent and variationally optimized MB basis. Such a treatment enables us to take into account both the inter- and intraspecies correlations inherent in the system. In order to include the inter- and intraspecies correlations, we first introduce $M$ distinct species functions, $\Psi^{\sigma}_k (\vec x^{\sigma};t)$. Here, $\vec x^{\sigma}=\left( x^{\sigma}_1, \dots, x^{\sigma}_{N_{\sigma}} \right)$ refer to the spatial $\sigma=A,B$ species coordinates of each component consisting of $N_{\sigma}$ fermions. Then the MB wavefunction, $\Psi_{MB}$, is expressed as a truncated Schmidt decomposition [@horodecki2009quantum] of rank $D$ $$\Psi_{MB}(\vec x^A,\vec x^B;t) = \sum_{k=1}^D \sqrt{ \lambda_k(t) }~ \Psi^A_k (\vec x^A;t) \Psi^B_k (\vec x^B;t).    
\label{Eq:WF}$$ In this expression $D\le \min(\dim(\mathcal{H}^A),\dim(\mathcal{H}^B))$ and $\mathcal{H}^{\sigma}$ is the Hilbert space of the $\sigma$-species (see also the discussion below). The Schmidt coefficients $\lambda_k(t)$ in decreasing order are denoted 