We consider the Casimir interaction between (nonmagnetic) dielectric bodies or conductors. Our main result is a proof that the Casimir force between two bodies related by reflection is always attractive, independent of the exact form of the bodies or dielectric properties. Apart from being a fundamental property of fields, the theorem and its corollaries also rule out a class of suggestions to obtain repulsive forces, such as the two hemisphere repulsion suggestion and its relatives. DOI: 10.1103/PhysRevLett.97.160401 PACS numbers: 12.20.ÿm, 03.65.ÿw, 03.70.+k The Casimir effect has been a fundamental issue in quantum physics since its prediction [1]. The effect has become increasingly approachable in recent years with the achievement of precise experimental measurements of the effect [2 -5], probing the detailed dependence of the force on the properties of the materials, and measuring new variants such as corrugation effects. The theory and experiment have good agreement for simple geometries.In spite of the vast body of work on the subject (for a review, see [6] ), some properties of the force are yet under controversy. Because of the computational complexity of the problem, the main body of work on the effect is a collection of explicit calculations for simple geometries. In this Letter we resolve one of these controversies and supply general statements about Casimir forces, applicable to a broad class of geometries.The interest in repulsive Casimir and van der Waals forces has grown substantially recently due to possible practical importance in nanoscience, where such forces may play a role as a solution to stiction problems. It is known that repulsive forces are possible between molecules immersed in a medium whose properties are intermediate between the properties of two polarizable molecules [7]. Conditions for repulsion between paramagnetic materials and dielectrics without recourse for an intermediate medium were given in [8]. However, the prospect of realizing materials with nontrivial permeability on a large enough frequency range is unclear [9].It is common knowledge, based on the Casimir-Polder interaction, that small dielectric bodies interacting at large distance attract [10]. Based on summation of two-body forces one may speculate that any two dielectrics would attract at all distances. In this Letter we show that at least for the case of a symmetric configuration of two dielectrics or conductors this prediction holds independently of their distance and shape for models which can be described by a local dielectric function. Of course, in any real material as distances become small enough, i.e., compared with interatomic distances, Casimir treatment of the problem is not adequate anymore.We first emphasize that the two-body picture is not enough to prove this. Calculations of the interaction between macroscopic bodies by summation of pair interactions are only justified within second order perturbation theory. Indeed, in [8] it was demonstrated how summing two-body forces may give wrong predic...

Photonic cluster states are a resource for quantum computation based solely on single-photon measurements. We use semiconductor quantum dots to deterministically generate long strings of polarization-entangled photons in a cluster state by periodic timed excitation of a precessing matter qubit. In each period, an entangled photon is added to the cluster state formed by the matter qubit and the previously emitted photons. In our prototype device, the qubit is the confined dark exciton, and it produces strings of hundreds of photons in which the entanglement persists over five sequential photons. The measured process map characterizing the device has a fidelity of 0.81 with that of an ideal device. Further feasible improvements of this device may reduce the resources needed for optical quantum information processing.

We explore the scattering approach to Casimir forces. Our main tool is the description of Casimir energy in terms of transition operators. The approach is valid for scalar fields as well as for electromagnetic fields. We provide several equivalent derivations of the formula presented by Kenneth and Klich ͓Phys. Rev. Lett. 97, 160401 ͑2006͔͒. We study the convergence properties of the formula and how to utilize it together with scattering data to compute the force. Next, we discuss the form of the formula in special cases such as the simplified form obtained when a single object is placed next to a mirror. We illustrate the approach by describing the force between scatterers in one dimension and three dimensions, where we obtain the interaction energy between two spherical bodies at all distances. We also consider the cases of scalar Casimir effect between spherical bodies with different radii as well as different dielectric functions.

We discuss repulsive Casimir forces between dielectric materials with nontrivial magnetic susceptibility. It is shown that considerations based on the naive pairwise summation of van der Waals and Casimir-Polder forces may not only give an incorrect estimate of the magnitude of the total Casimir force but even the wrong sign of the force when materials with high dielectric and magnetic responses are involved. Indeed repulsive Casimir forces may be found in a large range of parameters, and we suggest that the effect may be realized in known materials. The phenomenon of repulsive Casimir forces may be of importance both for experimental study and for nanomachinery applications.

The swimming of a pair of spherical bladders that change their volumes and mutual distance is efficient at low Reynolds numbers and is superior to other models of artificial swimmers. The change of shape resembles the wriggling motion known as metaboly of certain protozoa.