Multiscale quantum-defect theory for two interacting atoms in a symmetric harmonic trap

TL;DR

This paper develops a multiscale quantum-defect theory combining van der Waals interactions and harmonic trapping to comprehensively describe two atoms in a symmetric trap, revealing new insights into their bound and excited states.

Contribution

It introduces a unified quantum-defect framework that integrates short-range and long-range atomic interactions in a harmonic trap, advancing understanding of atomic states.

Findings

Strong p-wave pairing can produce lower energy states than s-wave pairing.

The theory describes bound molecular states and highly excited trap states.

It provides a systematic approach for analyzing two-atom systems in traps.

Abstract

We present a multiscale quantum-defect theory (QDT) for two identical atoms in a symmetric harmonic trap that combines the quantum-defect theory for the van der Waals interaction [B. Gao, Phys. Rev. A \textbf{64}, 010701(R) (2001)] at short distances with a quantum-defect theory for the harmonic trapping potential at large distances. The theory provides a systematic understanding of two atoms in a trap, from deeply bound molecular states and states of different partial waves, to highly excited trap states. It shows, e.g., that a strong $p$ wave pairing can lead to a lower energy state around the threshold than a $s$ wave pairing.