Abstract:
The Casimir-Polder interaction between an atom and a metal wall is investigated under the influence of real conditions including the dynamic polarizability of the atom, finite conductivity of the wall metal and nonzero temperature of the system. Both analytical and numerical results for the free energy and force are obtained over a wide range of the atom-wall distances. Numerical computations are performed for an Au wall and metastable He${}^{\ast}$, Na and Cs atoms. For the He${}^{\ast}$ atom we demonstrate, as an illustration, that at short separations of about the Au plasma wavelength at room temperature the free energy deviates up to 35% and the force up to 57% from the classical Casimir-Polder result. Accordingly, such large deviations should be taken into account in precision experiments on atom-wall interactions. The combined account of different corrections to the Casimir-Polder interaction leads to the conclusion that at short separations the corrections due to the dynamic polarizability of an atom play a more important role than -- and suppress -- the corrections due to the nonideality of the metal wall. By the comparison of the exact atomic polarizabilities with those in the framework of the single oscillator model, it is shown that the obtained asymptotic expressions enable calculation of the free energy and force for the atom-wall interaction under real conditions with a precision of one percent.

Abstract:
The Casimir-Polder and van der Waals interactions between an atom and a flat cavity wall are investigated under the influence of real conditions including the dynamic polarizability of the atom, actual conductivity of the wall material and nonzero temperature of the wall. The cases of different atoms near metal and dielectric walls are considered. It is shown that to obtain accurate results for the atom-wall interaction at short separations, one should use the complete tabulated optical data for the complex refractive index of the wall material and the accurate dynamic polarizability of an atom. At relatively large separations in the case of a metal wall, one may use the plasma model dielectric function to describe the dielectric properties of wall material. The obtained results are important for the theoretical interpretation of experiments on quantum reflection and Bose-Einstein condensation.

Abstract:
The Casimir-Polder interaction potential is evaluated for a polarizable microparticle and a conducting wall in the geometry of a cosmic string perpendicular to the wall. The general case of the anisotropic polarizability tensor for the microparticle is considered. The corresponding force is a function of the wall-microparticle and cosmic string-microparticle distances. Depending on the orientation of the polarizability tensor principal axes the force can be either attractive or repulsive. The asymptotic behavior of the Casimir-Polder potential is investigated at large and small separations compared to the wavelength of the dominant atomic transitions. We show that the conical defect may be used to control the strength and the sign of the Casimir-Polder force.

Abstract:
The time-dependent Casimir-Polder force arising during the time evolution of an initially bare two-level atom, interacting with the radiation field and placed near a perfectly conducting wall, is considered. Initially the electromagnetic field is supposed to be in the vacuum state and the atom in its ground state. The analytical expression of the force as a function of time and atom-wall distance, is evaluated from the the time-dependent atom-field interaction energy. Physical features and limits of validity of the results are discussed in detail.

Abstract:
Using the general expressions for level shifts obtained from the master equation for a small system interacting with a large one considered as a reservoir, we calculate the dispersive potentials between an atom and a wall in the dipole approximation. We analyze in detail the particular case of a two-level atom in the presence of a perfectly conducting wall. We study the van der Waals as well as the resonant interactions. All distance regimes as well as the high and low temperature regimes are considered. We show that the Casimir-Polder interaction can not be considered as a direct result of the vacuum fluctuations only. Concerning the interaction between the atom and the wall at high temperature, which show that a saturation of the potential for all distances occurs. This saturated potential coincides exactly with that obtained in the London-van der Waals limit.

Abstract:
The calculations of the elementary atom (the Coulomb bound state of elementary particles) interaction with the atom of matter, which are performed in the Born approximation, are reviewed. We first discuss the nonrelativistic approach and then its relativistic generalization. The cross section of the elementary atom excitation and ionization as well as the total cross section are considered. A specific selection rule, which applies for the atom formed as positronium by particle-antiparticle pair, is analyzed.

Abstract:
We consider the time evolution of the electric and magnetic field operators for a two-level atom, interacting with the electromagnetic field, placed near an infinite perfectly conducting wall. We solve iteratively the Heisenberg equations for the field operators and obtain the electric and magnetic energy density operators around the atom (valid for any initial state). Then we explicitly evaluate them for an initial state with the atom in its bare ground state and the field in the vacuum state. We show that the results can be physically interpreted as the superposition of the fields propagating directly from the atom and the fields reflected on the wall. Relativistic causality in the field propagation is discussed. Finally we apply these results to the calculation of the dynamical Casimir-Polder interaction energy in the far zone between two atoms when a boundary condition such as a conducting wall is present. Magnetic contributions to the interatomic Casimir-Polder interaction in the presence of the wall are also considered. We show that, in the limit of large times, the known results of the stationary case are recovered.

Abstract:
The Lifshitz-type formulas describing the free energy and the force of the van der Waals interaction between an atom (molecule) and a single-wall carbon nanotube are obtained. The single-wall nanotube is considered as a cylindrical sheet carrying a two-dimensional free electron gas with appropriate boundary conditions on the electromagnetic field. The obtained formulas are used to calculate the van der Waals free energy and force between a hydrogen atom (molecule) and single-wall carbon nanotubes of different radia. Comparison studies of the van der Waals interaction of hydrogen atoms with single- and multi-wall carbon nanotubes show that depending on atom-nanotube separation distance the idealization of graphite dielectric permittivity is already applicable to nanotubes with only two or three walls.

Abstract:
We have used the results of micromagnetic simulations to investigate the effects of nanowire geometry and domain wall magnetization structure on the characteristic parameters of magnetic atom traps formed by domain walls in planar ferromagnetic nanowires. It is found that when traps are formed in the near-field of a domain wall both nanowire geometry and wall structure have a substantial effect on trap frequency and adiabaticity. We also show that in certain regimes a trap's depth depends only on the amplitude of an externally applied rotating magnetic field, thus allowing it to be tuned independently of the trap's other critical parameters.

Abstract:
We investigate the interaction of ultracold antihydrogen with a conducting surface. Our discussion focuses on the physical regime where the phenomenon of quantum reflection manifests. We calculate the reflection probability as function of incident atom energy. We find that, for ground state $\bar{H}$ atoms (with $T< 10^{-5}$ K), the probability of reflection is $R \simeq 1-k b$, where $k$ is the momentum of the atom and $b = 2174.0$ a.u. is a constant determined solely by the van der Waals-Casimir tail of the atom-wall interaction. We show that quantum reflection, which suppresses the direct contact of ultra-cold atoms with the surface, allows for the possibility of confinement and storage of cold antihydrogen atoms. We calculate the life-time of confinement as a function of antihydrogen energy. We develop a theory of $\bar{H}$ in a wave-guide and propose its application to fundamental measurements. In particular, for measurement of retardation corrections in the long-range component of the antiatom - wall potential. We demonstrate, for $\bar{H}$ falling in the gravitational field of Earth onto a conducting surface, the existence of quantized $\bar{H}$ states. We calculate that the lifetime of ultracold $\bar{H}$ in its lowest gravitational state and obtain $\tau=(Mg b/2\hbar)^{-1}\simeq 0.1$ s, where $Mg$ is a gravitational force acting on the antiatom. We propose that measurement of this lifetime may provide a new test for the gravitational properties of antimatter.