Thermal Casimir-Polder interaction of different atoms with graphene

TL;DR

This paper investigates how temperature and the energy gap in graphene influence the Casimir-Polder interaction with various atoms, comparing models to predict measurable differences in quantum reflection experiments.

Contribution

It provides a detailed analysis of thermal corrections to Casimir-Polder forces on atoms near graphene, highlighting the importance of the Dirac model and the energy gap parameter.

Findings

Thermal correction size depends on the gap in graphene quasiparticles.

Dirac and hydrodynamic models predict significantly different free energies below 2μm separation.

Predictions can be experimentally distinguished through quantum reflection measurements.

Abstract

The thermal correction to the energy of Casimir-Polder interaction of atoms with a suspended graphene membrane described by the Dirac model is investigated. We show that a major impact on the thermal correction is made by the size of the gap in the energy spectrum of graphene quasiparticles. Specifically, if the temperature is much smaller than the gap parameter (alternatively, larger or of the order of the gap parameter), the thermal correction is shown to be relatively small (alternatively, large). We have calculated the free energy of the thermal Casimir-Polder interaction of atoms of He, Na, Rb, and Cs with graphene described by both the hydrodynamic and Dirac models. It is shown that in exact computations using the Dirac model, one should use the polarization operator at nonzero temperature. The computational results for the Casimir-Polder free energy obtained in the framework of hydrodynamic model of graphene are several times larger than in the Dirac model within the separation region below 2$\mu$m. We conclude that the theoretical predictions following from the two models can be reliably discriminated in experiments on quantum reflection of different atoms on graphene.