Few-body correlations for Bose and Fermi mixtures in two dimensions

10 December 2021

Photo: AG Schmelcher

Two-body contact between one fermion (F) and another atom (X) of an FFX system in the case of a light-light-heavy (LLH), equal mass (EM) and heavy-hevy-light (HHL) setting. The blue dashed lines signify the enhanced two-body contact of the trimer states, whereas the gray solid lines denote the two-body contact of the atom-dimer and trap states, featuring an oscillatory pattern due to the avoided crossings present in the spectra.

Few-body ultracold systems serve as building blocks in understanding the fundamental processes occurring in ultracold gases. In particular, it was recently shown that a few parameters called Tan contacts, defined through the asymptotic expansion of the momentum distribution of an interacting gas, define its thermodynamic properties as well as its spectroscopic features via a set of universal relations. These relations are universal in the sense that they hold regardless of the quantum statistics of the gas or the interaction strength or even the particle number. The Tan contacts have a microscopic character originating from two- and three-body collisions, and thus few-body models are essential in unveiling the behaviour of these parameters. Another aspect, shown recently, connects the contact parameters with the onset of few-body correlations and the dynamical formation of few-body bound states.

In this work, the two- and three-body correlations are investigated for binary setups of three-body systems trapped in two dimensions, consisting of bosons and fermions via these Tan contacts. In particular the few-body correlations display a distinct behavior depending on the type of eigenstates we focus on. Correlations for trimer states, that is three-body bound states, are substantially enhanced. The other eigenstates, atom-dimer and trap states, that is a dimer interacting with a third atom and three interacting particles respectively, feature an oscillatory dependence of the Tan contacts. This is explained through the avoided crossings present in the energy spectra of the three-body systems, affecting only these two types of states. This behavior holds for bosonic and fermionic mixtures alike. This oscillatory pattern however is damped when a temperature is introduced for the three-body system and the magnitude of the few-body correlations is also greatly diminished. Our work achieved a classification of the few-body correlations from a microscopic perspective at different regimes of interaction for binary three-body mixtures in two dimensions. This paves the way for the investigation of the dynamical formation of few-body bound states, and therefore the creation of gases with a significant population of atom-dimer and trimer states, which is currently pursued in ultracold atom experiments.

Publication

G. Bougas, S. I. Mistakidis, P. Giannakeas and P. Schmelcher

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

New Journal of Physics 23, 093022 (2021)