We study a one dimensional gas of repulsively interacting ultracold bosons trapped in a double-well potential as the atom-atom interactions are tuned from zero to infinity. We concentrate on the properties of the excited states which evolve from the
so-called NOON states to the NOON Tonks-Girardeau states. The relation between the latter and the Bose-Fermi mapping limit is explored. We state under which conditions NOON Tonks-Girardeau states, which are not predicted by the Bose-Fermi mapping, will appear in the spectrum.
We study a system of two bosons of one species and a third boson of a second species in a one-dimensional parabolic trap at zero temperature. We assume contact repulsive inter- and intra-species interactions. By means of an exact diagonalization meth
od we calculate the ground and excited states for the whole range of interactions. We use discrete group theory to classify the eigenstates according to the symmetry of the interaction potential. We also propose and validate analytical ansatzs gaining physical insight over the numerically obtained wavefunctions. We show that, for both approaches, it is crucial to take into account that the distinguishability of the third atom implies the absence of any restriction over the wavefunction when interchanging this boson with any of the other two. We find that there are degeneracies in the spectra in some limiting regimes, that is, when the inter-species and/or the intra-species interactions tend to infinity. This is in contrast with the three-identical boson system, where no degeneracy occurs in these limits. We show that, when tuning both types of interactions through a protocol that keeps them equal while they are increased towards infinity, the systemss ground state resembles that of three indistinguishable bosons. Contrarily, the systemss ground state is different from that of three-identical bosons when both types of interactions are increased towards infinity through protocols that do not restrict them to be equal. We study the coherence and correlations of the system as the interactions are tuned through different protocols, which permit to built up different correlations in the system and lead to different spatial distributions of the three atoms.
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 quan
tum 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.
