Miscibility of binary Bose-Einstein condensates with $p$-wave interaction

We investigate the ground-state phase diagram of a binary mixture of Bose-Einstein condensates (BECs) with competing interspecies $s$- and $p$-wave interactions. Exploiting a pseudopotential model for the $l=1$ partial wave, we derive an extended Gross-Pitaevskii (GP) equation for the BEC mixture that incorporates both $s$- and $p$-wave interactions. Based on it, we study the miscible-immiscible transition of a binary BEC mixture in the presence of interspecies $p$-wave interaction, by combining numerical solution of the GP equation and Gaussian variational analysis. Our paper uncovers a dual effect—to either enhance or reduce miscibility—of positive interspecies $p$-wave interaction, which can be precisely controlled by adjusting relevant experimental parameters. By completely characterizing the miscibility phase diagram, we establish a promising avenue towards experimental control of the miscibility of binary BEC mixtures via high partial-wave interactions.