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

Abstract

We study a system of two bosons of one species and a third atom of a second species in a one-dimensional parabolic trap at zero temperature. We assume contact repulsive inter-and intraspecies interactions. By means of an exact diagonalization method 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 Ansätze gaining physical insight over the numerically obtained wave functions. 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 wave function 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 interspecies and/or the intraspecies 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 systems's ground state resembles that of three indistinguishable bosons. Contrarily, the systems's 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 us to build up different correlations in the system and lead to different spatial distributions of the three atoms.

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.…”

Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

“…In the other limit, the wave function is numerically found with exact diagonalization [59], it may be analytically obtained for three or four particles when similar species of particles do not interact with each other [64,65,66,67], or in the most general case the wave function is exactly given up to 30 particles in the strongly interacting limit [68]. Here we show that this variational method works extremely well and use it to estimate energies as function of the interaction strength g where numerical or analytical results are not available.…”

Spectral properties and breathing dynamics of a few-body Bose–Bose mixture in a 1D harmonic trap

“…In this work we solve the time-independent problem of the simplest Bose-Bose mixture confined in a quasi-1D HO trap with two particles in each component, covering the whole parameter space of repulsive intra-and inter-species interactions, thereby complementing the analysis of some previous studies [39][40][41]. To accomplish this, an exact diagonalization method based on a correlated basis is introduced.…”