providing the possibility for an $A$ and a $B$-species fermion to be located at different filaments. We remark, that similar correlation structures have also been observed for the $N_A=5$, $N_B=1$ case (not shown here for brevity).

An important conclusion that can be extracted from the above analysis is that on the MB level phase separation between the species can be inferred only on the two-body level and not by simply observing the corresponding single-particle densities. Recall that the single-particle density evolution does not exhibit any phase separation within the MB approach, see Figs. \[abb:den3-1\] (c), (d), which is in sharp contrast to the HF approximation where the fermionic components are evidently immiscible, see Figs. \[abb:den3-1\] (a), (b). Combining also the results of $g_{\sigma}^{(1)}(x,x^\prime,t)$ and $g_{\sigma\sigma'}^{(1)}(x,x^\prime,t)$, it becomes apparent that all $N_A+N_B$ fermions reside in distinct filaments. Therefore regarding the spatially resolved distribution of the system, a superposition state consisting of all permutations of possible fermionic configurations concerning the four filaments formed, i.e $(B-A-A-A)$, $(A-B-A-A)$, $(A-A-B-A)$ and $(A-A-A-B)$, is permitted. This latter behavior suggests the tendency towards an anti-ferromagnetic like state of the few-body system [@koutentakis2018probing; @murmann2015antiferromagnetic].

![Single-shot images of each species, at distinct time instants of the interaction quench dynamics 