Strongly interacting few-fermion systems in a trap

TL;DR

This paper introduces a rigged Hilbert space-based theoretical framework for modeling strongly interacting few-fermion systems in traps, enabling exact solutions that include bound, resonant, and scattering states, with applications to ultracold atom experiments.

Contribution

The authors develop a novel rigged Hilbert space approach for solving the few-body problem, including bound and scattering states, and provide detailed numerical analysis for tunneling decay in fermionic systems.

Findings

Decay rate of two distinguishable fermions varies with interaction strength

Method achieves numerical convergence for complex few-body systems

Provides detailed technical and numerical insights into the approach

Abstract

Few- and many-fermion systems on the verge of stability, and consisting of strongly interacting particles, appear in many areas of physics. The theoretical modeling of such systems is a very difficult problem. In this work we present a theoretical framework that is based on the rigged Hilbert space formulation. The few-body problem is solved by exact diagonalization using a basis in which bound, resonant, and non-resonant scattering states are included on an equal footing. Current experiments with ultracold atoms offer a fascinating opportunity to study universal properties of few-body systems with a high degree of control over parameters such as the external trap geometry, the number of particles, and even the interaction strength. In particular, particles can be allowed to tunnel out of the trap by applying a magnetic-field gradient that effectively lowers the potential barrier. The result is a tunable open quantum system that allows detailed studies of the tunneling mechanism. In this Contribution we introduce our method and present results for the decay rate of two distinguishable fermions in a one-dimensional trap as a function of the interaction strength. We also study the numerical convergence. Many of these results have been previously published (R. Lundmark, C. Forss\'en, and J. Rotureau, arXiv: 1412.7175). However, in this Contribution we present several technical and numerical details of our approach for the first time.