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Infrared Dynamics of Cold Atoms on Hot Graphene Membranes

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 Added by Valeri Kotov
 Publication date 2016
  fields Physics
and research's language is English




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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 atoms 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 Greens 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.

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A continuum model for low-energy physisorption on a membrane under tension is proposed and studied with variational mean-field theory. A discontinuous change in the energy-dependent sticking coefficient is predicted under certain conditions. This singularity is a result of the bosonic orthogonality catastrophe of the vibrational states of the membrane. The energy-dependent sticking coefficient is predicted to have exponential scaling in 1/E above the singularity. The application of this model to the quantum sticking of cold hydrogen to suspended graphene is discussed. The model predicts that a beam of atomic hydrogen can be completely reflected by suspended graphene at ultralow energies.
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