Emergence of magnetic excitations in one-dimensional quantum mixtures under confinement

We obtain an exact solution for the spectral function for one-dimensional Bose-Bose and Fermi-Fermi mixtures with strong repulsive interactions, valid in arbitrary confining potentials and at all frequency scales. For the case of harmonic confinement, we show that, on top of the ladder structure of the density excitations imposed by the external confinement, spin excitations emerge as sideband peaks, with dispersion related to the one of ferromagnetic or antiferromagnetic spin chains and a width fundamentally larger for fermionic mixtures than for bosonic ones, as determined by the different symmetry of spin-excited states. The observation of spin excitation branches can provide a univocal probe of interaction-induced magnetism in ultracold atoms.