Universal relations between atomic dipolar relaxation and van der Waals interaction

TL;DR

This paper demonstrates that dipolar relaxation in ultracold atoms exhibits universal behavior governed by van der Waals interactions, enabling potential control of relaxation processes through scattering length tuning.

Contribution

It introduces a quantum defect theory approach that extends the understanding of dipolar relaxation beyond perturbative limits, revealing universal relations involving $C_6$ and scattering lengths.

Findings

Dipolar relaxation lineshapes are largely universal across different atomic states.

The universality depends on the van der Waals coefficient $C_6$ and scattering lengths.

Potential for controlling relaxation processes by tuning scattering lengths.

Abstract

Dipolar relaxation happens when one or both colliding atoms flip their spins exothermically inside a magnetic ($B$) field. This work reports precise measurements of dipolar relaxation in a Bose-Einstein condensate of ground state $^{87}$Rb atoms together with in-depth theoretical investigations. Previous perturbative treatments fail to explain our observations except at very small $B$-fields. By employing quantum defect theory based on analytic solutions of asymptotic van der Waals interaction $-C_6/R^6$ ($R$ being interatomic spacing), we significantly expand the applicable range of perturbative treatment. We find the $B$-dependent dipolar relaxation lineshapes are largely universal, determined by the coefficient $C_6$ and the associated $s$-wave scattering lengths $a_{\rm sc}$ of the states before and after spin flips. This universality, which applies generally to other atomic species as well, implicates potential controls of dipolar relaxation and related cold chemical reactions by tuning $a_{\rm sc}$.