Few-body correlations in two-dimensional Bose and Fermi ultracold mixtures

TL;DR

This paper investigates few-body correlations in two-dimensional ultracold Bose and Fermi mixtures, revealing how trap states, scattering lengths, and thermal effects influence atom-dimer, trap, and trimer states, with analytical and numerical insights.

Contribution

It provides a comprehensive analysis of few-body correlations in 2D mixtures, including analytical predictions and the effects of thermal fluctuations, advancing understanding of few- to many-body crossover.

Findings

Two- and three-body correlations are enhanced in trimer states.

Contacts exhibit an upper bound for atom-dimer and trap states, but not for trimers.

Contacts oscillate with scattering length tuning due to avoided crossings.

Abstract

Few-body correlations emerging in two-dimensional harmonically trapped mixtures, are comprehensively investigated. The presence of the trap leads to the formation of atom-dimer and trap states, in addition to trimers. The Tan's contacts of these eigenstates are studied for varying interspecies scattering lengths and mass ratio, while corresponding analytical insights are provided within the adiabatic hyperspherical formalism. The two- and three-body correlations of trimer states are substantially enhanced compared to the other eigenstates. The two-body contact of the atom-dimer and trap states features an upper bound regardless of the statistics, treated semi-classically and having an analytical prediction in the limit of large scattering lengths. Such an upper bound is absent in the three-body contact. Interestingly, by tuning the interspecies scattering length the contacts oscillate as the atom-dimer and trap states change character through the existent avoided-crossings in the energy spectra. For thermal gases, a gradual suppression of the involved two- and three-body correlations is evinced manifesting the impact of thermal effects. Moreover, spatial configurations of the distinct eigenstates ranging from localized structures to angular anisotropic patterns are captured. Our results provide valuable insights into the inherent correlation mechanisms of few-body mixtures which can be implemented in recent ultracold atom experiments and will be especially useful for probing the crossover from few- to many-atom systems.