Experimental investigation of the Casimir force beyond the proximity-force approximation

Casimir-Induced Instabilities at Metallic Surfaces and Interfaces

Surface distortion splits surface plasmons asymmetrically in energy with a net lowering of zero-point energy. We contrast this with the symmetrical distortion of electronic energy levels. We use conformal mapping to demonstrate this splitting and find that surface corrugation always leads to a decrease in the zero-point energy of a metallic surface, but the decrease is not strong enough to drive a surface reconstruction on its own. A second metallic surface in proximity to the first gives a more significant lowering of energy, sufficient to drive the instability of a mercury thin film. This mechanism provides a fundamental length scale limit to planar nanostructures.

Measurement of the Casimir Force between Two Spheres

Complex interaction geometries offer a unique opportunity to modify the strength and sign of the Casimir force. However, measurements have traditionally been limited to sphere-plate or plate-plate configurations. Prior attempts to extend measurements to different geometries relied on either nanofabrication techniques that are limited to only a few materials or slight modifications of the sphere-plate geometry due to alignment difficulties of more intricate configurations. Here, we overcome this obstacle to present measurements of the Casimir force between two gold spheres using an atomic force microscope. Force measurements are alternated with topographical scans in the x-y plane to maintain alignment of the two spheres to within approximately 400 nm (∼1% of the sphere radii). Our experimental results are consistent with Lifshitz's theory using the proximity force approximation (PFA), and corrections to the PFA are bounded using nine sphere-sphere and three sphere-plate measurements with spheres of varying radii.

Plasma versus Drude Modeling of the Casimir Force: Beyond the Proximity Force Approximation

We calculate the Casimir force and its gradient between a spherical and a planar gold surface. Significant numerical improvements allow us to extend the range of accessible parameters into the experimental regime. We compare our numerically exact results with those obtained within the proximity force approximation (PFA) employed in the analysis of all Casimir force experiments reported in the literature so far. Special attention is paid to the difference between the Drude model and the dissipationless plasma model at zero frequency. It is found that the correction to PFA is too small to explain the discrepancy between the experimental data and the PFA result based on the Drude model. However, it turns out that for the plasma model, the corrections to PFA lie well outside the experimental bound obtained by probing the variation of the force gradient with the sphere radius [D. E. Krause et al., Phys. Rev. Lett. 98, 050403 (2007)PRLTAO0031-900710.1103/PhysRevLett.98.050403]. The corresponding corrections based on the Drude model are significantly smaller but still in violation of the experimental bound for small distances between plane and sphere.

Casimir switch: steering optical transparency with vacuum forces

The Casimir force, originating from vacuum zero-point energy, is one of the most intriguing purely quantum effects. It has attracted renewed interests in current field of nanomechanics, due to the rapid size decrease of on-chip devices. Here we study the optomechanically-induced transparency (OMIT) with a tunable Casimir force. We find that the optical output rate can be significantly altered by the vacuum force, even terminated and then restored, indicating a highly-controlled optical switch. Our result addresses the possibility of designing exotic optical nano-devices by harnessing the power of vacuum.

Theory of Casimir Forces without the Proximity-Force Approximation

We analyze both the attractive and repulsive Casimir-Lifshitz forces recently reported in experimental investigations. By using a kinetic approach, we obtain the Casimir forces from the power absorbed by the materials. We consider collective material excitations through a set of relaxation times distributed in frequency according to a log-normal function. A generalized expression for these forces for arbitrary values of temperature is obtained. We compare our results with experimental measurements and conclude that the model goes beyond the proximity-force approximation.

Giant vacuum forces via transmission lines

Quantum electromagnetic fluctuations induce forces between neutral particles, known as the van der Waals and Casimir interactions. These fundamental forces, mediated by virtual photons from the vacuum, play an important role in basic physics and chemistry and in emerging technologies involving, e.g., microelectromechanical systems or quantum information processing. Here we show that these interactions can be enhanced by many orders of magnitude upon changing the character of the mediating vacuum modes. By considering two polarizable particles in the vicinity of any standard electric transmission line, along which photons can propagate in one dimension, we find a much stronger and longer-range interaction than in free space. This enhancement may have profound implications on many-particle and bulk systems and impact the quantum technologies mentioned above. The predicted giant vacuum force is estimated to be measurable in a coplanar waveguide line.

Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids

Virtual phonons of a quantum liquid scatter off impurities and mediate a long-range interaction, analogous to the Casimir effect. In one dimension the effect is universal and the induced interaction decays as 1/r3, much slower than the van der Waals interaction ∼1/r6, where r is the impurity separation. The sign of the effect is characterized by the product of impurity-phonon scattering amplitudes, which take a universal form and have been seen to vanish for several integrable impurity models. Thus, if the impurity parameters can be independently tuned to lie on opposite sides of such integrable points, one can observe an attractive interaction turned into a repulsive one.

Scattering approach for fluctuation-induced interactions at fluid interfaces

We develop the scattering formalism to calculate the interaction between colloidal particles trapped at a fluid interface. Since, in addition to the interface, the colloids may also fluctuate in this system, we implement the fluctuation of the boundaries into the scattering formalism and investigate how the interaction between colloids is modified by their fluctuations. This general method can be applied to any number of colloids with various geometries at an interface. We apply the formalism derived in this work to a system of spherical colloids at the interface between two fluid phases. For two spherical colloids, this method very effectively reproduces the previous known results. For three particles we find analytical expressions for the large separation asymptotic energies and numerically calculate the Casimir interaction at all separations. Our results show an interesting three-body effect for fixed and fluctuating colloids. While the three-body effect strengthens the attractive interaction between fluctuating colloids, it diminishes the attractive force between colloids fixed at an interface.

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 experiments 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.

Efficient computation of Casimir interactions between arbitrary 3D objects

We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles nonspheroidal, nonaxisymmetric objects, and objects with sharp corners. Using our new technique, we obtain the first predictions of Casimir interactions in a number of experimentally relevant geometries, including crossed cylinders and tetrahedral nanoparticles.

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 nontrivial 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 and of finite reflectivity due to material properties. We also discuss the interest of our results for the current Casimir experiments which are performed with spheres of large radius R>>L.