Polder Forces Research Articles

Multiple scattering Casimir force calculations: Layered and corrugated materials, wedges, and Casimir–Polder forces

Various applications of the multiple scattering techniques to calculating the Casimir energy are described. These include the interaction between dilute bodies of various sizes and shapes, temperature dependence, interactions with multilayered and corrugated bodies, and new examples of exactly solvable separable bodies.

Casimir force on amplifying bodies

Based on a unified approach to macroscopic QED that allows for the inclusion of amplification in a limited space and frequency range, we study the Casimir force as a Lorentz force on an arbitrary partially amplifying system of linearly locally responding (isotropic) magnetoelectric bodies. We demonstrate that the force on a weakly polarisable/magnetisable amplifying object in the presence of a purely absorbing environment can be expressed as a sum over the Casimir--Polder forces on the excited atoms inside the body. As an example, the resonant force between a plate consisting of a dilute gas of excited atoms and a perfect mirror is calculated.

Nanowire atomchip traps for sub-micron atom–surface distances

We present an analysis of magnetic traps for ultracold atoms based on current-carrying wires with sub-micron dimensions. We analyze the physical limitations of these conducting wires as well as how such miniaturized magnetic traps are affected by the nearby surface due to tunneling to the surface, surface thermal noise, electron scattering within the wire and the Casimir–Polder force. We show that wires with cross sections as small as a few tens of nanometers should enable robust operating conditions for coherent atom optics (e.g. tunneling barriers for interferometry). In particular, trap sizes of the order of the de Broglie wavelength become accessible, based solely on static magnetic fields, thereby bringing the atomchip a step closer to fulfilling its promise of a compact device for complex and accurate quantum optics with ultracold atoms.

Multi-layer atom chips for atom tunneling experiments near the chip surface

This paper describes the design and fabrication of an atom chip to be used in ultra-high-vacuum cells for cold-atom tunneling experiments. A fabrication process was developed to pattern micrometer- and nanometer-scale copper wires onto a single chip. The wires, with fabricated widths down to 200 nm, can sustain current densities of more than 7.5 × 10 7 A/cm 2. Partially suspended wires, developed in order to reduce the Casimir–Polder force between atoms and surface, were also fabricated and tested. Extensive measurements for variable wire width show that the sustainable currents are sufficiently large to allow chip-based atom tunneling experiments. Such chips may allow the realization of an atom transistor.

Atom–wall dispersive forces: a microscopic approach

We present a study of atom–wall interactions in non-relativistic quantum electrodynamics by functional integral methods. The Feynman–Kac path integral representation is generalized when the particle interacts with a radiation field, providing an additional effective potential that contains all the interactions induced by the field. We show how one can retrieve the standard van der Waals, Casimir–Polder and classical Lifshiftz forces in this formalism for an atom in its ground state. Moreover, when electrostatic interactions are screened in the medium, we find low-temperature corrections that are not included in the Lifshitz theory of fluctuating forces and are opposite to them.

Resonant Casimir–Polder forces in planar meta-materials

We study the resonant Casimir–Polder potential of an excited atom near a half-space containing magneto-electric meta-material of various kinds on the basis of macroscopic quantum electrodynamics. Analytical results are obtained in the nonretarded and retarded distance regimes and numerical examples are given. We compare our findings with the potential of an excited atom near a left-handed superlens.

Nonequilibrium thermal Casimir–Polder forces

We study the nonequilibrium Casimir–Polder force on an atom prepared in an incoherent superposition of internal energy eigenstates, which is placed in a magnetoelectric environment of nonuniform temperature. After solving the coupled atom–field dynamics within the framework of macroscopic quantum electrodynamics, we derive a general expression for the thermal Casimir–Polder force.

DISPERSION FORCES AND DUALITY

We formulate a symmetry principle on the basis of the duality of electric and magnetic fields and apply it to dispersion forces. Within the context of macroscopic quantum electrodynamics, we rigorously establish duality invariance for the free electromagnetic field in the presence of causal magnetoelectrics. Dispersion forces are given in terms of the Green tensor for the electromagnetic field and the atomic response functions. After discussing the behavior of the Green tensor under a duality transformation, we are able to show that Casimir forces on bodies in free space as well as local-field corrected Casimir–Polder and van der Waals forces are duality invariant.

No quantum friction between uniformly moving plates

The Casimir forces between two plates moving parallel to each other at arbitrary constant speed are found by calculating the vacuum electromagnetic stress tensor. The perpendicular force between the plates is modified by the motion but there is no lateral force on the plates. Electromagnetic vacuum fluctuations do not therefore give rise to ‘quantum friction’ in this case, contrary to previous assertions. The result shows that the Casimir–Polder force on a particle moving at constant speed parallel to a plate also has no lateral component.

3D MULTICELL DESIGNS FOR REGISTERING OF BOSE–EINSTEIN CONDENSATE CLOUDS

In this letter, the results on the development and simulation of new three-dimensional nanotraps for cold dressed atoms are considered. The traps are the multi-cell structures built by crossed non-touching carbon or metallic nanotubes. The trapping effect is tuned by the DC and RF currents to confine the strong- or low-potential seeking atoms far enough from the areas of strong Casimir–Polder and spin-flip forces. It is supposed that the developed and simulated multi-cell structures are pertinent for catching the Bose–Einstein condensates to demonstrate the Josephson effect, and to enable the study of the entanglement of confined clouds in three-dimensional nano-cells.

Macroscopic quantum electrodynamics - Concepts and applications

Macroscopic quantum electrodynamics - Concepts and applicationsIn this article, we review the principles of macroscopic quantum electrodynamics and discuss a variety of applications of this theory to medium-assisted atom-field coupling and dispersion forces. The theory generalises the standard mode expansion of the electromagnetic fields in free space to allow for the presence of absorbing bodies. We show that macroscopic quantum electrodynamics provides the link between isolated atomic systems and magnetoelectric bodies, and serves as an important tool for the understanding of surface-assisted atomic relaxation effects and the intimately connected position-dependent energy shifts which give rise to Casimir—Polder and van der Waals forces.

Bloch oscillators in a slowly perturbed external field

A quantum particle in a periodical lattice under the effect of an external homogeneous field shows a periodical motion, usually a named Bloch oscillator, for long times. When we introduce a weak and slowly varying inhomogeneous field then the dynamics of the quantum particle still exhibits a periodical motion but with a different period and a different width of the interval of oscillation. In this paper we obtain a formula for the dominant terms of the perturbed period and width, then we apply our result to the study of the effect of Casimir–Polder forces to a vertical Bose–Einstein condensate trapped in an optical lattice.

Lateral Casimir–Polder force with corrugated surfaces

We derive the lateral Casimir–Polder force on a ground-state atom on top of a corrugated surface, up to first order in the corrugation amplitude. Our calculation is based on the scattering approach, which takes into account nonspecular reflections and polarization mixing for electromagnetic quantum fluctuations impinging on real materials. We compare our first order exact result with two commonly used approximation methods. We show that the proximity force approximation (large corrugation wavelengths) overestimates the lateral force, while the pairwise summation approach underestimates it due to the non-additivity of dispersion forces. We argue that a frequency shift measurement for the dipolar lateral oscillations of cold atoms could provide a striking demonstration of non-trivial geometrical effects on the quantum vacuum.

Casimir–Polder forces, boundary conditions and fluctuations

We review different aspects of atom–atom and atom–wall Casimir–Polder forces. We first discuss the role of a boundary condition on the interatomic Casimir–Polder potential between two ground-state atoms, and give a physically transparent interpretation of the results in terms of vacuum fluctuations and image atomic dipoles. We then discuss the known atom–wall Casimir–Polder force for ground- and excited-state atoms, using a different method which is also suited to extension to time-dependent situations. Finally, we consider the fluctuation of the Casimir–Polder force between a ground-state atom and a conducting wall, and discuss possible observation of this force fluctuation.

Nonlocal field correlations and dynamical Casimir–Polder forces between one excited- and two ground-state atoms

The problem of nonlocality in the dynamical three-body Casimir–Polder interaction between an initially excited and two ground-state atoms is considered. It is shown that the nonlocal spatial correlations of the field emitted by the excited atom during the initial part of its spontaneous decay may become manifest in the three-body interaction. The observability of this new phenomenon is discussed.

Unified approach to dispersion forces within macroscopic QED

We outline our Lorentz-force approach to the description of dispersion forces (see also C. Raabe and D.-G. Welsch, Phys. Rev. A 71:013814, 2005; Phys. Rev. A 73:063822, 2006). It is based on the ground-state Lorentz force density that acts on the charge and current densities attributed to the polarization and magnetization in linearly, locally, and causally responding media. Application of the theory to dielectric systems yields very general formulas for the Casimir force on dielectric bodies or parts of them. It is shown that well-known expressions for the Casimir–Polder force on a single atom and for the van der Waals force between atoms are also contained in our formula. The theory may thus be viewed as providing a unified basis for the calculation of dispersion forces from a macroscopic point of view.

Long-distance behaviour of the surface–atom Casimir–Polder forces out of thermal equilibrium

Long-distance behaviour of the Casimir-Polder-Lifshitz force between an atom and the surface of a substrate is investigated. When the temperatures of the substrate and the environment are different, the new decay law 1/z 3 of the force at large distances is discovered, which is slower than at thermal equilibrium. The force is of a quantum nature and attractive or repulsive depending on whether the temperature of the substrate is higher or lower than that of the environment. A transparent derivation of this law is presented. It is based on a picture of evanescent waves, created in vacuum by the black-body radiation impinging on the surface near the angle of total reflection. Some new experimental possibilities of the measurement of the forces are discussed: oscillations of a Bose-Einstein condensate near the surface, Bloch oscillations of fermions in an optical lattice and phase evolution of a BEC in a double-well trap.

Casimir–Polder forces from density matrix formalism

We use the density matrix formalism in order to calculate the energy level shifts, in second order on interaction, of an atom in the presence of a perfectly conducting wall in the dipole approximation. The thermal corrections are also examined when $\hbar \omega_0/k_B T = k_0 \lambda_T \gg 1$, where ${$\omega_0=k_0 c$}$ is the dominant transition frequency of the atom and $\lambda_T$ is the thermal length. When the distance $z$ between the atom and the wall is larger than $\lambda_T$ we find the well known result obtained from Lifshitz's formula, whose leading term is proportional to temperature and is independent of $c$, $\hbar$ and $k_0$. In the short distance limit, when $z\ll\lambda_T$, only very small corrections to the leading vacuum term occur. We also show, for all distance regimes, that the main thermal corrections are independent of $k_0$ (dispersion is not important) and dependent of $c$, which means that there is not a non-retarded regime for the thermal contributions.

Born expansion of the Casimir–Polder interaction of a ground-state atom with dielectric bodies

Within leading-order perturbation theory, the Casimir–Polder potential of a ground-state atom placed within an arbitrary arrangement of dispersing and absorbing linear bodies can be expressed in terms of the polarizability of the atom and the scattering Green tensor of the body-assisted electromagnetic field. Based on a Born series of the Green tensor, a systematic expansion of the Casimir–Polder potential in powers of the electric susceptibilities of the bodies is presented. The Born expansion is used to show how and under which conditions the Casimir–Polder force can be related to microscopic many-atom van der Waals forces, for which general expressions are presented. As an application, the Casimir–Polder potentials of an atom near a dielectric ring and an inhomogeneous dielectric half space are studied and explicit expressions are presented that are valid up to second order in the susceptibility.

Matter-screened Casimir force and Casimir–Polder force in planar structures

Using a recently developed theory of the Casimir force (Raabe C and Welsch D-G 2005 Phys. Rev. A 71 013814), we calculate the force that acts on a plate in front of a planar wall and the force that acts on the plate in the case where the plate is part of matter that fills the space in front of the wall. We show that in the limit of a dielectric plate whose permittivity is close to unity, the force obtained in the former case reduces to the ordinary, i.e., unscreened Casimir-Polder force acting on isolated atoms. In the latter case, the theory yields the Casimir-Polder force that is screened by the surrounding matter.