Tunneling Theory for Tunable Open Quantum Systems of Ultracold Atoms in One-Dimensional Traps

TL;DR

This paper develops a theoretical framework for understanding tunneling dynamics in tunable open quantum systems of ultracold atoms in one-dimensional traps, highlighting the roles of sequential and correlated pair tunneling.

Contribution

It introduces a rigged Hilbert space approach that includes bound, resonant, and scattering states for accurate tunneling analysis in ultracold atom systems.

Findings

Sequential tunneling dominates in repulsive and weakly attractive regimes.

Correlated pair tunneling appears in strongly attractive interactions.

The framework captures threshold phenomena accurately.

Abstract

The creation of tunable open quantum systems is becoming feasible in current experiments with ultracold atoms in low-dimensional traps. In particular, the high degree of experimental control over these systems allows detailed studies of tunneling dynamics, e.g., as a function of the trapping geometry and the interparticle interaction strength. In order to address this exciting opportunity we present a theoretical framework for two-body tunneling based on the rigged Hilbert space formulation. In this approach, bound, resonant and scattering states are included on an equal footing, and we argue that the coupling of all these components is vital for a correct description of the relevant threshold phenomena. In particular, we study the tunneling mechanism for two-body systems in one-dimensional traps and different interaction regimes. We find a strong dominance of sequential tunneling of single particles for repulsive and weakly attractive systems, while there is a signature of correlated pair tunneling in the calculated many-particle flux for strongly attractive interparticle interaction.