A general T-matrix approach applied to two-body and three-body problems in cold atomic gases

TL;DR

This paper introduces a systematic T-matrix method for solving few-body problems with contact interactions in ultracold gases, enabling precise calculations of scattering and resonance phenomena in various configurations.

Contribution

It develops a unified, renormalized T-matrix framework for two- and three-body problems, providing clear physical insights and high-precision results in complex scattering scenarios.

Findings

Accurate determination of resonance positions and widths in mixed-dimensional systems.

Identification of exotic scattering behaviors in three-fermion systems.

A versatile approach applicable to diverse few-body problems in ultracold gases.

Abstract

We propose a systematic T-matrix approach to solve few-body problems with s-wave contact interactions in ultracold atomic gases. The problem is generally reduced to a matrix equation expanded by a set of orthogonal molecular states, describing external center-of-mass motions of pairs of interacting particles; while each matrix element is guaranteed to be finite by a proper renormalization for internal relative motions. This approach is able to incorporate various scattering problems and the calculations of related physical quantities in a single framework, and also provides a physically transparent way to understand the mechanism of resonance scattering. For applications, we study two-body effective scattering in 2D-3D mixed dimensions, where the resonance position and width are determined with high precision from only a few number of matrix elements. We also study three fermions in a (rotating) harmonic trap, where exotic scattering properties in terms of mass ratios and angular momenta are uniquely identified in the framework of T-matrix.