Quantum correlations and spatial localization in one-dimensional ultracold bosonic 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 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 Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. limit and a phase-separated one, resembling those expected with a mean-field approach.

Strongly interacting quantum gases in one-dimensional traps

“…Finally, it is also possible to generalize our work to Bose-Fermi mixtures [49,50], which can be compared with recent few-body studies of such mixtures [51][52][53][54]. We will consider these generalizations in future work.…”

Quantum correlations and degeneracy of identical bosons in a two-dimensional harmonic trap

“…There are many works studying fermionization in 1D, for instance, in optical lattices [8], in few-atom mixtures [9][10][11], for attractive interactions [12] and for few dipolar bosons [13]. In other cases, the focus are quantum correlations [14,15], its effects in mixtures of distinguishable and identical particles [16] and analytic ansatz to capture the physics in all interaction regimes [17].…”

Distinguishability, degeneracy, and correlations in three harmonically trapped bosons in one dimension

“…By playing with both the intra-and interspecies interactions one can explore different physical phenomena, like phase separation on small atom mixtures [29][30][31][32][33]. Other relevant phenomena are the presence of a composite fermionized gas [34][35][36], quantum magnetism [37][38][39], or a crossover between composite fermionization and phase separation [40,41]. Also, these small number bosonic mixtures allow for the study of dynamical phenomena, like the tunneling of one species through the barrier formed by the other species [42,43] or the dynamical emergence of orthogonality catastrophe [44].…”

“…We use a many-mode exact diagonalization method, as the one discussed in Refs. [40,41], to obtain the whole spectra for different values of the interactions together with the corresponding wave functions. We propose analytical Ansätze for the wave function of different states with straightforward physical interpretations in each limit.…”