Multipole Analysis of Radio-Frequency Reactions in Ultra-Cold Atoms

TL;DR

This paper uses multipole expansion to analyze photo-induced reactions in ultra-cold bosonic gases, revealing how monopole and quadrupole contributions influence reaction rates and their dependence on photon wave number.

Contribution

It introduces a multipole analysis framework for ultra-cold atom reactions, highlighting the roles of monopole and quadrupole terms in frozen-spin processes and their temperature and scattering length dependence.

Findings

Reaction rate in frozen-spin processes depends on monopole and quadrupole terms.

Reaction rate acquires an extra $k^4$ factor compared to spin-flip reactions.

The importance of multipole modes varies with temperature and scattering length.

Abstract

Using the multipole expansion we analyze photo induced reactions in an ultra-cold atomic gas composed of identical neutral bosons. While the Frank-Condon factor dominates the photo induced spin-flip reactions, we have found that for frozen-spin process where the atomic spins are conserved the reaction rate is governed by the monopole $r^2$ and the quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number $k$ acquires an extra $k^4$ factor in comparison to the spin-flip process. Comparing the relative strength of the $r^2$ and quadrupole modes in dimer photoassociation we predict that the mutual importance of these two modes changes with temperature and scattering length.