Nonperturbative theory of atom-surface interaction: Corrections at short separations

Abstract

The nonperturbative expressions for the free energy and force of interaction between a ground-state atom and a real-material surface at any temperature are presented. The transition to the Matsubara representation is performed, whereupon the comparison is made with the commonly used perturbative results based on the standard Lifshitz theory. It is shown that the Lifshitz formulas for the free energy and force of an atom-surface interaction follow from the nonperturbative ones in the lowest order of the small parameter. Numerical computations of the free energy and force for the atoms of He${}^{\ast }$ and Na interacting with a surface of an Au plate have been performed using the frequency-dependent dielectric permittivity of Au and highly accurate dynamic atomic polarizabilities in the framework of both the nonperturbative and perturbative theories. According to our results, the maximum deviations between the two theories are reached at the shortest atom-surface separations of about 1nm. Simple analytic expressions for the atom-surface free energy are derived in the classical limit and for an ideal-metal plane. In the lowest order of the small parameter, they are foundX// in agreement with the perturbative ones following from the standard Lifshitz theory. Possible applications of the obtained results in the theory of van der Waals adsorption are discussed.

13 pages, 4 figures; accepted for publication in J. Phys.: Condens. Matter

References in corpus (13)

• Measurement of the Temperature Dependence of the Casimir-Polder Force
• Novel constraints on light elementary particles and extra-dimensional physics from the Casimir effect
• Effect of the Casimir-Polder force on the collective oscillations of a trapped Bose-Einstein condensate
• Demonstration of the Casimir force between ferromagnetic surfaces of a Ni-coated sphere and a Ni-coated plate
• Casimir-Polder interaction between an atom and a cavity wall under the influence of real conditions
• Advance and prospects in constraining the Yukawa-type corrections to Newtonian gravity from the Casimir effect
• Lifshitz theory of atom-wall interaction with applications to quantum reflection
• Impact of graphene coating on the atom-plate interaction
• Casimir entropy for magnetodielectrics
• Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy
• How to confirm and exclude different models of material properties in the Casimir effect
• Vacuum Casimir energy densities and field divergences at boundaries
• Casimir and Casimir-Polder forces with dissipation from first principles

Cited by in corpus (4)

• Casimir and Casimir-Polder Forces in Graphene Systems: Quantum Field Theoretical Description and Thermodynamics
• Casimir-Polder Interaction of an Atom with a Cavity Wall Made of Phase-Change Material out of Thermal Equilibrium
• Nonequilibrium Casimir-Polder Force between Nanoparticles and Graphene-Coated Silica Plate: Combined Effect of the Chemical Potential and Mass Gap
• Casimir-Polder Force on Atoms or Nanoparticles from the Gapped and Doped Graphene: Asymptotic Behavior at Large Separations