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

Few-body correlations emerging in two-dimensional harmonically trapped mixtures, consisting either of two identical bosons or fermions and another distinguishable particle, for arbitrary mass ratios are investigated. In particular, the properties of the relevant two- and three-body contacts are discussed for varying interspecies interaction and corresponding analytical insights are provided within the hyperspherical formalism. It is exemplified that the presence of the trap leads to the formation of additional atom-dimer and trap states. Remarkably, the two-body contact of the atom-dimer and trap states features an analytically predicted upper bound depending solely on the two-dimensional scattering length. Such a correlation bound is absent in the three-body contact. Interestingly, by tuning the scattering length the contacts oscillate as the atom-dimer and trap states change character, a behavior captured in the energy spectra of the system. For thermal gases the oscillation amplitude decreases with increasing temperature, resulting in turn to the suppression of the involved two- and three-body correlations.