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 centre 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.
Highlights
The physics of ultra-cold atoms has gained a great boost of interest since the first experimental realization of an atomic Bose-Einstein condensate [1, 2], where research topics such as collective modes [3,4,5], binary mixtures [6, 7] and lower-dimensional geometries [8,9,10] were in the focus right from the start
In this work we have explored a few-body problem of a Bose-Bose mixture with two atoms in each component confined in a quasi-1D HO trapping potential by exact diagonalization
By applying a coordinate transformation to a suitable frame we have constructed a rapidly converging basis consisting of HO and PCF eigenfunctions
Summary
The physics of ultra-cold atoms has gained a great boost of interest since the first experimental realization of an atomic Bose-Einstein condensate [1, 2], where research topics such as collective modes [3,4,5], binary mixtures [6, 7] and lower-dimensional geometries [8,9,10] were in the focus right from the start. A profound investigation of the ground state phases of a few-body Bose-Bose mixture [37, 38] showed striking differences to the MF calculations: for coinciding trap centres, a new phase with bimodal symmetric density structure, called composite fermionization (CF ), is observed while SB is absent for any finite inter-component coupling. While the breathing spectrum of a single component was recently investigated comprehensively in [43,44,45,46,47,48], reporting a transition from a two mode beating of the center of mass ΩCM and relative motion Ωrel frequencies for few atoms to a single mode breathing for many particles, the breathing mode properties of few-body Bose-Bose mixtures are not characterized so far For this reason, we analyse the number of breathing frequencies and the kind of motion to which they correspond in dependence on the intra- and intercomponent interaction for the binary mixture at hand. I,j=1 where gα ≈ (2a3αDω⊥)/(ωaho) with a3αD the 3D s-wave scattering length and α ∈ {A, B, AB} are effective (offresonant) interaction strengths
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