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

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.

Losses, Many‐Body Correlations, and Universality in Ultracold Molecules

“…[ 79–81 ] As of now, contacts have been well accepted as the most fundamental quantities that govern quantum gases and other related dilute systems. [ 82–121 ] Implementing contacts in ultracold molecules, we are able to unfold exact relations between the loss rate and other quantities, including but not limited to the momentum distribution and the density‐density correlation function, which are valid at any temperatures, any interaction strength, and any particle numbers. On the one hand, these universal relations show that universality exists in chemical reactions and other two‐body losses in a simple form despite the fact that the quantum many‐body environment could be very complicated.…”

Dynamical excitation processes and correlations of three-body two-dimensional mixtures

“…Owing to the decoupling of the center of mass, the hyperspherical coordinates representation is employed and the relative position of the atoms is described by a set of three hyperangles (which collectively are denoted by Ω) and the hyperradius R that controls the overall size of the system. Hence, by employing the hyperspherical coordinates the relative three-body Hamiltonian [39] reads:…”

“…Here, U ν (R) represents the ν-th adiabatic potential curve including the trap, whereas the P νν ′ (R) and Q νν ′ (R) terms denote the non-adiabatic coupling matrix elements. More specifically, the adiabatic potential curves and the non-adiabatic coupling matrix elements are given by the following expressions [39,41,60],…”

“…There the corresponding trimer wave functions have a small amplitude at short distances suppressing three-body recombination processes [34,35] as compared to 3D systems. Additionally, theoretical studies in 2D three-body systems [36][37][38][39][40][41][42] have addressed their time-independent attributes in terms of their eigenspectrum as well as their corresponding few-body correlations via Tan contacts [39,[43][44][45]. In particular, it was shown that mass-imbalanced mixtures support a multitude of trimer states with amplified two-and three-body correlations compared to the mass-balanced case [39,43].…”

“…The above mentioned features occur for both LLH and HHL settings regardless the exchange symmetry of the particles. However, the enhancements in the few-body contacts become narrower in the HHL case, as compared to the LLH one, due to the existence of sharp avoided-crossings in the respective energy spectrum [39]. This work proceeds as follows: In Sec.…”