Atomic boson-fermion mixtures in 1D 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 theory with density-density interactions. A variety of correlations and structures arise as the inter- and intra- species interactions are tuned. Both few-body and many-body results show that miscible phase and three-chunk phase separation are directly observable in the density profiles. Meanwhile, two-chunk phase separation can be inferred from the few-body correlations and many-body density profiles. We present phase diagrams of selected types of atomic mixtures to show where different structures survive. The few-body analysis demonstrates that two-body correlation functions can reveal information relevant to the results from many-body calculations or experiments. From the many-body density profiles in the phase-separation regime, we extract the healing lengths of each species and explain the scaling behavior by an energy-competition argument.