We derive the Casimir-Polder force and Casimir torque expressions for an anisotropic molecule close to a conducting plane with a tensorial conductivity. We apply our general expressions to the case of a carbon dioxide CO$_2$ molecule close to a plane with pure Hall conductivity and to graphene. We show that the equilibrium position of this linear molecule is with its main axis perpendicular to the surface. We hence conjecture a possible way to exploit the Casimir torque to mechanically improve the performance of CO$_2$ separation membranes useful for an efficient atmospheric CO$_2$ reduction.
The Casimir and Casimir-Polder interactions are investigated in a stack of equally spaced graphene layers. The optical response of the individual graphene is taken into account using gauge invariant components of the polarization tensor extended to the whole complex frequency plane. The planar symmetry for the electromagnetic boundary conditions is further used to obtain explicit forms for the Casimir energy stored in the stack and the Casimir-Polder energy between an atom above the stack. Our calculations show that these fluctuation induced interactions experience strong thermal effects due t…
We consider the low-temperature expansion of the Casimir-Polder free energy for an atom and graphene by using the Poisson representation of the free energy. We extend our previous analysis on the different relations between chemical potential $μ$ and mass gap parameter $m$. The key role plays the dependence of graphene conductivities on the $μ$ and $m$. For simplicity, we made the manifest calculations for zero values of the Fermi velocity. For $μ>m$ the thermal correction $\sim T^2$ and for $μ< m$ we confirm the recent result of Klimchitskaya and Mostepanenko, that the thermal correction $\si…
We present a formalism based on first principles of quantum electrodynamics at nonzero temperature which permits to calculate the Casimir-Polder interaction between an atom and a graphene sheet with arbitrary mass gap and chemical potential, including graphene-coated substrates. The free energy and force of the Casimir-Polder interaction are expressed via the polarization tensor of graphene in (2+1)-dimensional space-time in the framework of the Dirac model. The obtained expressions are used to investigate the influence of the chemical potential of graphene on the Casimir-Polder interaction. C…
The low temperature expansion of the free energy of atom/plane system is considered for general symmetric form of tensor conductivity of the plane. It is shown that the first correction is proportional to second order of the temperature $\sim T^2$ and comes from TM mode. The agreement of the expansion and exact expressions for different models of conductivity is numerically demonstrated.
The mutual electromagnetic correlations between two spatially separated systems gives rise to Casimir and Casimir-Polder effect. The corresponding forces, which are generally attractive for most vacuum-separated metallic or dielectric geometries, are due to the contribution to the ground-state energy of the coupled system. We investigate here the Casimir-Polder free energy corresponding to interactions of a magnetically and electrically polarizable micro-particle with a magneto-dielectric sheet. Our semi-phenomenological study shows that such an interaction is reversibly tunable in strength an…
We find the low-temperature behavior of the Casimir-Polder free energy and entropy for an atom interacting with real graphene sheet possessing nonzero energy gap and chemical potential. Employing the formalism of the polarization tensor, it is shown that the Casimir-Polder entropy goes to zero by the power law with vanishing temperature, i.e., the Nernst heat theorem is satisfied. This result is discussed in connection with the problems connected with account of free charge carriers in the Lifshitz theory.
We consider the resonant Casimir-Polder interaction of an excited alkali-type atom which has a single (electric dipole) transition with a Chern insulator. The Chern insulator has a nonzero, time reversal symmetry breaking Hall conductance, leading to an additional contribution to the resonant Casimir-Polder interaction which depends on the coupling between the Hall conductance and the circular polarization state of the atomic transition. We find that the resonant Casimir-Polder shift can be significantly enhanced for de-excitation frequencies near values associated with the van Hove singularit…
The Casimir-Polder interaction between an atom and a multilayered system composed of infinitely thin planes is considered using the zeta-function regularization approach with summation of the zero-point energies. As a prototype material, each plane is represented by a graphene sheet whose optical response is described by a constant conductivity or Drude-Lorentz model conductivity. Asymptotic expressions for various separations are derived and compared to numerical calculations. We distinguish between large atom/plane limit, where retardation effects are prominent, and small atom/plane limit, w…
We derive upper and lower bounds on the Casimir--Polder force between an anisotropic dipolar body and a macroscopic body separated by vacuum via algebraic properties of Maxwell's equations. These bounds require only a coarse characterization of the system---the material composition of the macroscopic object, the polarizability of the dipole, and any convenient partition between the two objects---to encompass all structuring possibilities. We find that the attractive Casimir--Polder force between a polarizable dipole and a uniform planar semi-infinite bulk medium always comes within 10% of the …
We propose a scheme to actively cool the fundamental flexural (out-of-plane) mode of a graphene sheet via vacuum forces. Our setup consists in a cold atom cloud placed close to a graphene sheet at distances of a few micrometers. The atoms couple to the graphene membrane via Casimir-Polder forces. By deriving a self-consistent set of equations governing the dynamics of the atomic gas and the flexural modes of the graphene, we show to be possible to cool graphene from room temperatures by actively (laser) cooling an atomic gas. By choosing the right set of experimental parameter we are able to c…
Metamaterials are fascinating tools that can structure not only surface plasmons and electromagnetic waves but also electromagnetic vacuum fluctuations. The possibility of shaping the quantum vacuum is a powerful concept that ultimately allows engineering the interaction between macroscopic surfaces and quantum emitters such as atoms, molecules or quantum dots. The long-range atom-surface interaction, known as Casimir-Polder interaction, is of fundamental importance in quantum electrodynamics but also attracts a significant interest for platforms that interface atoms with nanophotonic devices.…
