contraction of the cloud, see e.g. Figs. \[abb:den3-1\] (a) and (g) at $t\approx40$. In sharp contrast to the above behavior, $\Lambda(t)$ shows small fluctuations around 0.9 within the MB approach during the entire evolution. The aforementioned evolution of $\Lambda(t)$ reflects the miscible character of the dynamics on the single-particle level. The same overall phenomenology in terms of $\Lambda(t)$ holds equally, in both approaches, for other postquench interaction strengths, see e.g. Figs. \[abb:den3-1\] (g) and (h) for $g_{AB}=4.0$. We further remark that for postquench interaction strengths $g_{AB}>2.0$ the overlap function features a similar dynamics, while for quenches to $g_{AB}<2.0$ the mixture remains miscible in both the HF and the MB approach (results not shown here for brevity).

![One-body correlation function $g_\sigma^{(1)}(x,x^\prime;t)$ shown for different time instants (see legends) during the interaction quench dynamics of a FF mixture for ($a_1$)-($a_4$) the $A$-species and ($b_1$)-($b_4$) the $B$-species. ($c_1$)-($c_4$) Snapshots of the two-body intraspecies correlation function $g_{AA}^{(2)}(x,x^\prime;t)$ and ($d_1$)-($d_4$) the interspecies two-body correlation function $g_{AB}^{(2)}(x,x^\prime;t)$. In all cases, the FF mixture consists of $N_A=3$, $N_B=1$ particles and it is initialized in the weakly interacting ground state, $g_{AB}=0.1$, of the double-well. To induce the dynamics we perform an interaction quench from $g_{AB}=0.1$ to $g_{AB}=4.0$. []{data-label="abb:coh3-1"}](Fig3.eps){width="49.00000%"}

