Abstract
We present the complete phase diagram for one-dimensional binary mixtures of bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with direct numerical diagonalization for a small number of atoms, which permits us to quantify quantum many-body correlations. The quantum Monte Carlo method is used to calculate energies and density profiles for larger system sizes. We study the system properties for a wide range of interaction parameters. For the extreme values of these parameters, different correlation limits can be identified, where the correlations are either weak or strong. We investigate in detail how the correlations evolve between the limits. For balanced mixtures in the number of atoms in each species, the transition between the different limits involves sophisticated changes in the one- and two-body correlations. Particularly, we quantify the entanglement between the two components by means of the von Neumann entropy. We show that the limits equally exist when the number of atoms is increased for balanced mixtures. Also, the changes in the correlations along the transitions among these limits are qualitatively similar. We also show that, for imbalanced mixtures, the same limits with similar transitions exist. Finally, for strongly imbalanced systems, only two limits survive, i.e., a miscible limit and a phase-separated one, resembling those expected with a mean-field approach.
Highlights
The fascinating physics of interpenetrating superfluids has recently become a topic of great interest due to the experimental realization of multi-component, atomic Bose–Einstein condensates [1,2,3,4,5]
In the weakly interacting regime, these mixtures are well described by coupled mean-field Gross–Pitaevskii equations (GPEs), and within this framework, processes that lead to phase separation are well described [6,7,8,9,10,11,12,13,14]
Since increasing the coupling constant will drive the system from the weakly to the strongly correlated regime, the coherence is a good quantity for identifying different regions in the phase diagram
Summary
The fascinating physics of interpenetrating superfluids has recently become a topic of great interest due to the experimental realization of multi-component, atomic Bose–Einstein condensates [1,2,3,4,5]. We use direct numerical diagonalization to study the ground-state properties of a mixture of ultracold bosons confined in a 1D trap over a wide range of correlations regimes, determined by the scattering properties between the atoms. These are supplemented by DMC calculations to confirm trends for systems with larger particle numbers. The quantum correlations between both components are characterized by means of the von Neumann entropy This allows us to show that close to the crossover between the composite fermionization and phase separation, the ground state exhibits strong correlations between the two bosonic components.
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