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

Ultracold atoms are an ideal platform for the implementation of atomtronic and Josephson junctions analogous to superconducting circuits. The collective modes of Bose gas split by a potential barrier are known. However, the role of barriers in the collective excitation spectra of ultracold atomic mixtures has not yet 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 Bogoliubov theory. We first show that the anharmonicity of the external potential leads to an increase in the critical barrier strength of mode softening 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 zero-energy 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 spatially 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.