Infrared Dynamics of Cold Atoms on Hot Graphene Membranes

TL;DR

This paper investigates how low-energy atoms interact with suspended graphene at finite temperature, revealing infrared divergences and providing a non-perturbative solution to predict atom damping and sticking rates influenced by sample size.

Contribution

It introduces a two-channel model generalizing the independent boson model, enabling exact resummation of divergences and precise predictions of atom sticking rates on graphene.

Findings

Infrared divergences cause significant effects in atom-graphene interactions.

Resummation of divergences enhances the predicted sticking rate.

Sample size influences the atom's damping rate and sticking probability.

Abstract

We study the infrared dynamics of low-energy atoms interacting with a sample of suspended graphene at finite temperature. The dynamics exhibits severe infrared divergences order by order in perturbation theory as a result of the singular nature of low-energy flexural phonon emission. Our model can be viewed as a two-channel generalization of the independent boson model with asymmetric atom-phonon coupling. This allows us to take advantage of the exact non-perturbative solution of the independent boson model in the stronger channel while treating the weaker one perturbatively. In the low-energy limit, the exact solution can be viewed as a resummation (exponentiation) of the most divergent diagrams in the perturbative expansion. As a result of this procedure, we obtain the atom's Green function which we use to calculate the atom damping rate, a quantity equal to the quantum sticking rate. A characteristic feature of our results is that the Green's function retains a weak, infrared cutoff dependence that reflects the reduced dimensionality of the problem. As a consequence, we predict a measurable dependence of the sticking rate on graphene sample size. We provide detailed predictions for the sticking rate of atomic hydrogen as a function of temperature and sample size. The resummation yields an enhanced sticking rate relative to the conventional Fermi golden rule result (equivalent to the one-loop atom self-energy), as higher-order processes increase damping at finite temperature.