The Casimir effect in the sphere-plane geometry

We present calculations of the Casimir interaction between a sphere and a plane, using a multipolar expansion of the scattering formula. This configuration enables us to study the nontrivial dependence of the Casimir force on the geometry, and its correlations with the effects of imperfect reflection and temperature. The accuracy of the Proximity Force Approximation (PFA) is assessed, and is shown to be affected by imperfect reflexion. Our analytical and numerical results at ambient temperature show a rich variety of interplays between the effects of curvature, temperature, finite conductivity, and dissipation.Comment: Proceedings of the 10th International Conference "Quantum Field Theory Under the Influence of External Conditions" (Benasque, Spain, 2011); 10 pages and 6 figure

The Scattering Approach to the Casimir Force

We present the scattering approach which is nowadays the best tool for describing the Casimir force in realistic experimental configurations. After reminders on the simple geometries of 1d space and specular scatterers in 3d space, we discuss the case of stationary arbitrarily shaped mirrors in electromagnetic vacuum. We then review specific calculations based on the scattering approach, dealing for example with the forces or torques between nanostructured surfaces and with the force between a plane and a sphere. In these various cases, we account for the material dependence of the forces, and show that the geometry dependence goes beyond the trivial {\it Proximity Force Approximation} often used for discussing experiments.Comment: Proceedings of the QFEXT'09 conference (Oklahoma, 2009

Thermal Casimir Effect in the Plane-Sphere Geometry

The thermal Casimir force between two metallic plates is known to depend on the description of material properties. For large separations the dissipative Drude model leads to a force a factor of 2 smaller than the lossless plasma model. Here we show that the plane-sphere geometry, in which current experiment are performed, decreases this ratio to a factor of 3/2, as revealed by exact numerical and large distance analytical calculations. For perfect reflectors, we find a repulsive contribution of thermal photons to the force and negative entropy values at intermediate distances.Comment: 4 pages, 3 figure

Casimir interaction between plane and spherical metallic surfaces

We give an exact series expansion of the Casimir force between plane and spherical metallic surfaces in the non trivial situation where the sphere radius $R$, the plane-sphere distance $L$ and the plasma wavelength $\lambda_\P$ have arbitrary relative values. We then present numerical evaluation of this expansion for not too small values of $L/R$. For metallic nanospheres where $R, L$ and $\lambda_\P$ have comparable values, we interpret our results in terms of a correlation between the effects of geometry beyond the proximity force approximation (PFA) and of finite reflectivity due to material properties. We also discuss the interest of our results for the current Casimir experiments performed with spheres of large radius $R\gg L$.Comment: 4 pages, new presentation (highlighting the novelty of the results) and added references. To appear in Physical Review Letter

Classical Casimir interaction in the plane-sphere geometry

We study the Casimir interaction in the plane-sphere geometry in the classical limit of high temperatures. In this limit, the finite conductivity of the metallic plates needs to be taken into account. For the Drude model, the classical Casimir interaction is nevertheless found to be independent of the conductivity so that it can be described by a single universal function depending only on the aspect ratio $x=L/R$ where $L$ is the interplate distance and $R$ the sphere radius. This universal function differs from the one found for perfect reflectors and is in principle amenable to experimental tests. The asymptotic approach of the exact result to the Proximity Force Approximation appears to be well fitted by polynomial expansions in $\ln x$.Comment: Updated version with minor modifications and addition of a referenc

Chiral discrimination in optical trapping and manipulation

When circularly polarized light interacts with chiral molecules or nanoscale particles powerful symmetry principles determine the possibility of achieving chiral discrimination, and the detailed form of electrodynamic mechanisms dictate the types of interaction that can be involved. The optical trapping of molecules and nanoscale particles can be described in terms of a forward-Rayleigh scattering mechanism, with trapping forces being dependent on the positioning within the commonly non-uniform intensity beam profile. In such a scheme, nanoparticles are commonly attracted to local potential energy minima, ordinarily towards the centre of the beam. For achiral particles the pertinent material response property usually entails an electronic polarizability involving transition electric dipole moments. However, in the case of chiral molecules, additional effects arise through the engagement of magnetic counterpart transition dipoles. It emerges that, when circularly polarized light is used for the trapping, a discriminatory response can be identified between left- and right-handed polarizations. Developing a quantum framework to accurately describe this phenomenon, with a tensor formulation to correctly represent the relevant molecular properties, the theory leads to exact analytical expressions for the associated energy landscape contributions. Specific results are identified for liquids and solutions, both for isotropic media and also where partial alignment arises due to a static electric field. The paper concludes with a pragmatic analysis of the scope for achieving enantiomer separation by such methods

Casimir interaction between a dielectric nanosphere and a metallic plane

We study the Casimir interaction between a dielectric nanosphere and a metallic plane, using the multiple scattering theory. Exact results are obtained with the dielectric described by a Sellmeier model and the metal by a Drude model. Asymptotic forms are discussed for small spheres, large or small distances. The well-known Casimir-Polder formula is recovered at the limit of vanishingly small spheres, while an expression better behaved at small distances is found for any finite value of the radius. The exact results are of particular interest for the study of quantum states of nanospheres in the vicinity of surfaces.Comment: 6 pages, 5 figure

Strong Casimir force reduction through metallic surface nanostructuring

The Casimir force between bodies in vacuum can be understood as arising from their interaction with an infinite number of fluctuating electromagnetic quantum vacuum modes, resulting in a complex dependence on the shape and material of the interacting objects. Becoming dominant at small separations, the force plays a significant role in nanomechanics and object manipulation at the nanoscale, leading to a considerable interest in identifying structures where the Casimir interaction behaves significantly different from the well-known attractive force between parallel plates. Here we experimentally demonstrate that by nanostructuring one of the interacting metal surfaces at scales below the plasma wavelength, an unexpected regime in the Casimir force can be observed. Replacing a flat surface with a deep metallic lamellar grating with sub-100 nm features strongly suppresses the Casimir force and for large inter-surfaces separations reduces it beyond what would be expected by any existing theoretical prediction.Comment: 11 pages, 8 figure