Title: Spectral properties and breathing dynamics of a few-body Bose-Bose mixture in a 1D harmonic trap,
Abstract: We investigate a few-body mixture of two bosonic components, each consisting
of two particles confined in a quasi one-dimensional harmonic trap. By means of
exact diagonalization with a correlated basis approach we obtain the low-energy
spectrum and eigenstates for the whole range of repulsive intra- and
inter-component interaction strengths. We analyse the eigenvalues as a function
of the inter-component coupling, covering hereby all the limiting regimes, and
characterize the behaviour in-between these regimes by exploiting the
symmetries of the Hamiltonian. Provided with this knowledge we study the
breathing dynamics in the linear-response regime by slightly quenching the trap
frequency symmetrically for both components. Depending on the choice of
interactions strengths, we identify 1 to 3 monopole modes besides the breathing
mode of the center of mass coordinate. For the uncoupled mixture each monopole
mode corresponds to the breathing oscillation of a specific relative
coordinate. Increasing the inter-component coupling first leads to multi-mode
oscillations in each relative coordinate, which turn into single-mode
oscillations of the same frequency in the composite-fermionization regime.