Quasiparticle spectra of mixtures of dipolar and non-dipolar condensates at zero and finite temperatures

We examine the low-lying collective quasiparticle modes of a mixture of flattened infinite-pancake Bose-Einstein condensates having dipolar and non-dipolar atomic species. The dipolar atomic species have permanent magnetic dipolar moments. We employ Hartree-Fock-Bogoliubov theory to investigate the distinct axial collective spectra at zero and finite temperatures corresponding to phase separation phenomena stemming from the dipole-dipole interaction of dipolar atomic species. When the dipolar interaction is tuned to be repulsive, the number of zero-energy axial modes decreases, reflecting the system's tendency towards mixing. For a large number of atoms per unit area, we show that the attractive (repulsive) dipolar interaction strengths lead to ground states with non-dipolar (dipolar) atomic species at the periphery, and this leads to a discontinuity in quasiparticle mode evolution. We finally reveal that miscibility driven by thermal fluctuations at finite temperatures exhibits dipole mode hardening of axial excitations, confirmed by the loss of long-range phase coherence through the correlation function. The mode mixing in the dispersion relations ascertains a dipolar strength-dependent mis-
cibility transition and the low-lying quasiparticle mode evolution.