Recent experiments confirmed that fluctuations beyond the mean-field approximation can lead to self-bound liquid droplets of ultra-dilute binary Bose mixtures. We proceed beyond the beyondmean-field approximation, and study liquid Bose mixtures using the variational hypernetted-chain Euler Lagrange method, which accounts for correlations non-perturbatively. Focusing on the case of a mixture of uniform density, as realized inside large saturated droplets, we study the conditions for stability against evaporation of one of the components (both chemical potentials need to be negative) and against liquid-gas phase separation (spinodal instability), the latter being accompanied by a vanishing speed of sound. Dilute Bose mixtures are stable only in a narrow range near an optimal ratio ρ1/ρ2 and near the total energy minimum. Deviations from a universal dependence on the s-wave scattering lengths are significant despite the low density.

A spin‐sensitive linear response theory is presented that includes correlations beyond the well‐known random phase approximation. Especially for very dilute systems, such correlations play an important role. The response functions obtained give insight into both charge and longitudinal magnetic excitations. In addition to the spin‐plasmon, we propose a new regime where no magnetic excitation is possible, namely the magnetic anti‐resonance. Both effects lie in experimentally accessible ranges.

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