Correlation Dynamics {#cor_par_imb}
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To unveil the underlying correlation mechanisms [@sanner2012correlations; @pekker2011competition] that lead to the intrawell fragmentation during the MB quench dynamics, we investigate the one-body $g_{\sigma}^{(1)}(x,x^\prime,t)$ \[Eq. (\[one\_body\_cor\])\] and the two-body $g_{\sigma\sigma'}^{(2)}(x,x',t)$ \[Eq. (\[two\_body\_cor\])\] intra- and interspecies correlation functions during evolution, see Fig. \[abb:coh3-1\]. As it is expected the intraspecies two-body correlation function for the $B$-species is zero, since this species contains only a single particle. Below we examine $g_{\sigma}^{(1)}(x,x^\prime,t)$ and $g_{\sigma\sigma'}^{(2)}(x,x',t)$ following an interaction quench of the FF mixture from $g_{AB}=0.1$ to $g_{AB}=4.0$.

Figures \[abb:coh3-1\] (a~1~)-(a~4~) and (b~1~)-(b~4~) show $g_{A}^{(1)}(x,x^\prime,t)$ and $g_{B}^{(1)}(x,x^\prime;t)$ respectively for selected time instants of the MB evolution. Overall, we observe that throughout the evolution the off-diagonal elements of $g_{\sigma}^{(1)}(x,x^\prime,t)$ are supressed. Indeed on the one-body level, each filament of both species is fully coherent with itself \[see e.g. $g_A^{(1)}(x=-2.5,x^\prime=-2.5;t=24)\approx1$ in Fig. \[abb:coh3-1\] (a~1~)\] and mainly incoherent with any of the other filaments \[see e.g. $g_A^{(1)}(x=-2.5,x^\prime=2.5;t=24)\approx0$ in Fig. \[abb:coh3-1\] (a~1~)\]. We note that this behavior of $g_{\sigma}^{(1)}(x,x^\prime,t)$ is more pronounced for the $A$-species, while in the $B$-species two distinct filaments appear to be partially incoherent \[e.g. $g_B^{(1)}(x=-2.5,x^\prime=2.5;t=76)\approx0.3$ in Fig. \[abb:coh3-1\] (b~3~)\], as shown in Figs. \[abb:coh3-1\] (b~1~)-(b~4~). This structure of $g_{\sigma}^{(1)}(x,x^\prime,t)$ indicates the occurrence 