Diagrammatic Approach to Cold Atom-Surface Interactions

We study the sticking rate of cold atoms on elastic membrane by exploring the self-energy Σ of the cold atom. We use the Feynman-Dyson perturbation theory to calculate the free atom self-energy to 1-loop. We find non-zero finite sticking rate Γ that agrees with the Golden rule result in ultra-low energy regime. However, with the 1-loop self-energy insertion, we find a suppressed sticking rate Γ at ultra-low energies. The self-energy Σ(E) of the atom is also calculated analytically to second-order in the atom-membrane interaction. We explicitly show that while the first-order contribution to the self-energy is well-behaved, the second-order contribution is divergent in the limit of infinite membrane size, and we classify the various divergent contributions. These results are discussed in the context of the “quantum sticking” and scattering of cold atoms from membranelike 2D materials such as graphene, boron nitride and the monolayer transition metal dichalcogenides.