Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures

TL;DR

This paper maps the phase diagram of one-dimensional ultracold bosonic mixtures, analyzing quantum correlations and entanglement across various interaction regimes for different atom number balances using exact and Monte Carlo methods.

Contribution

It provides a comprehensive phase diagram with detailed correlation analysis for 1D bosonic mixtures, including entanglement quantification and the effects of atom number imbalance.

Findings

Identification of correlation limits at extreme interaction values

Quantification of entanglement via von Neumann entropy

Existence of similar correlation transitions in imbalanced mixtures

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 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 correlation 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.