Collective modes of two-species Bose-Einstein condensates in a Josephson junction barrier

Abstract: The ultracold atoms are an ideal platform to implement atomtronics and Josephson junctions analogous to superconducting circuits. The collective modes of a Bose gas split by a potential barrier have been known. However, the role of barriers in the interspecies correlation of ultracold atomic mixtures has not been examined. Here, we examine the low-lying collective modes of (an)harmonically trapped quasi-one-dimensional Bose-Einstein condensates in a Josephson barrier by employing the variational approach and the Hartree-Fock-Bogoliubov formalism. We first reveal the increase in barrier strength of mode softening due to anharmonicity in a single-species condensate. The Josephson barrier drives the softening of in-phase and out-of-phase dipole modes of two-species Bose-Einstein condensates, and consequently leads to two additional Goldstone modes in the miscible phase, in agreement with the variational approach. Furthermore, the sandwich immiscible state results in an additional Goldstone mode due to the barrier, in contrast to the spatial symmetry-broken side-by-side profile. Our results unveil the distinct collective response of the Josephson barrier in binary mixtures owing to interspecies atomic correlations.