Faddeev-Kulish Asymptotic States in Cold Atom Quantum Physisorption on 2D Materials

Theories with long-range interactions like QED or perturbative gravity exhibit severe infrared divergences in their scattering rates due to the emission of infinitely many soft quanta. Remarkably, a low-energy condensed matter analogue of this infamous infrared problem in QED is realized in a hybrid system of cold atoms coupled to a vibrating elastic membrane. We focus on the atom-phonon coupling of the vibrating membrane and provide procedures to address the infrared divergences. Our methods include non-perturbative techniques that can be broadly categorized into two schemes: (1) inclusion of emission of infinitely many soft-phonons and (2) dressing of asymptotic states which is similar in essence to the Faddeev-Kulish treatment of the infrared divergences in QED. We provide results for both the schemes in the spirit of the well-known exact solution of the independent boson model and discuss the validity of the results corresponding to the different scales of the infrared. In particular, we present the results of our resummation procedures for the physisorption rate of cold atomic hydrogen as function of membrane sizes and temperature.