Spectral properties and breathing dynamics of a few-body Bose-Bose mixture in a 1D harmonic trap

TL;DR

This paper explores the spectral properties and breathing dynamics of a two-component Bose mixture in a 1D harmonic trap, revealing how interactions influence collective excitations and mode behavior across different regimes.

Contribution

It provides an exact diagonalization analysis of a two-boson mixture's spectrum and dynamics, covering all interaction regimes and identifying multiple breathing modes.

Findings

Multiple monopole modes depend on interaction strengths.

Increasing inter-component coupling leads to multi-mode oscillations.

In the composite-fermionization regime, oscillations become single-mode.

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.