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Quantum electrodynamics (QED) provides a highly accurate description ofphenomena involving the interaction of atoms with light. We argue that thequantum theory describing the interaction of cold atoms with a vibratingmembrane--quantum acoustodynamics (QAD)--shares many issues and features withQED. Specifically, the adsorption of an atom on a vibrating membrane can beviewed as the counterpart to QED radiative electron capture. A calculation ofthe adsorption rate to lowest-order in the atom-phonon coupling is finite;however, higher-order contributions suffer from an infrared problem mimickingthe case of radiative capture in QED. Terms in the perturbation series for theadsorption rate diverge as a result of massless particles in the model(flexural phonons of the membrane in QAD and photons in QED). We treat thisinfrared problem in QAD explicitly to obtain finite results by regularizingwith a low-frequency cutoff that corresponds to the inverse size of themembrane. Using a coherent state basis for the soft phonon final state, we thensum the dominant contributions to derive a new formula for the multiphononadsorption rate of atoms on the membrane that gives results that are finite,nonperturbative in the atom-phonon coupling, and consistent with the KLNtheorem. For micromembranes, we predict a reduction with increasing membranesize for the low-energy adsorption rate. We discuss the relevance of this tothe adsorption of a cold gas of atomic hydrogen on suspended graphene.

Infrared Problem in Quantum Acoustodynamics