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.

arXiv comment15 pages, 5 figures, replacement of figure 3 a-c

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• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Correlation Effects in the Quench-Induced Phase Separation Dynamics of a Two-Species Ultracold Quantum Gas
• Entanglement-assisted tunneling dynamics of impurities in a double well immersed in a bath of lattice trapped bosons
• Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential
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• Phase separation of a Bose-Bose mixture: impact of the trap and particle number imbalance
• State engineering of impurities in a lattice by coupling to a Bose gas
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• Fermionic properties of two interacting bosons in a two-dimensional harmonic trap
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