of the two possible configurations of an entangled many-body state, the other one being the mirror image. The one body densities of this so-called composite fermionization phase [@phasesZollner2008; @phasesHao2008; @phasesPolls2014; @phasesZinner2015; @phasesPyzh2018] preserve parity symmetry of the underlying trapping potential and have a high spatial overlap, which is uncharacteristic for an immiscible phase. Nevertheless, the components are indeed separated, which is encoded in the inter-species two-body density matrix. In experiments, the single-shots do not represent one-body densities but are projections on one of the two mutually exclusive configurations. An averaging procedure would reveal a parity preserving density, unless the Hamiltonian itself violates that symmetry, such as not coinciding trap centers of the one-body potentials. Apart from composite fermionization, there is a whole class of so called spin-chain phases with an even higher degree of entanglement [@spinchain2014; @spinchain2015; @spinchain2016]. When all interactions in the system become nearly-resonant, many states become quasi-degenerate and particles, being bosons, gain fermionic features like the Pauli exclusion principle.

Considering the above, our work addresses three different points. First, we characterize the phase diagram in a three-dimensional parameter space spanned by the ratio of the harmonic trap lengths, the inter-species coupling strength and the particle number ratio. 