Atomic boson-fermion mixtures in one-dimensional box potentials: Few-body and mean-field many-body analyses

We study binary atomic boson-fermion mixtures confined in one dimensional box potentials by few-body theory with contact interactions and mean-field many-body density-density interactions. A variety of correlations structures arise as the inter- intra- species are tuned. Both results show that miscible phase three-chunk separation directly observable density profiles. Meanwhile, two-chunk can be inferred from present diagrams selected types to where different survive. The analysis demonstrates two-body correlation functions reveal information relevant calculations or experiments. From profiles phase-separation regime, we extract healing lengths each explain scaling behavior an energy-competition argument.