Casimir energy for two and three superconducting coupled cavities: Numerical calculations

Abstract

In this paper we study the behavior of the Casimir energy of a "multi-cavity" across the transition from the metallic to the superconducting phase of the constituting plates. Our analysis is carried out in the framework of the ARCHIMEDES experiment, aiming at measuring the interaction of the electromagnetic vacuum energy with a gravitational field. For this purpose it is foreseen to modulate the Casimir energy of a layered structure composing a multi-cavity coupled system by inducing a transition from the metallic to the superconducting phase. This implies a thorough study of the behavior of the cavity, where normal metallic layers are alternated with superconducting layers, across the transition. Our study finds that, because of the coupling between the cavities, mainly mediated by the transverse magnetic modes of the radiation field, the variation of energy across the transition can be very large. PACS numbers: 12.20.Ds, 74.78.Fk

Progress in a Vacuum Weight Search Experiment

“…Type II layered superconductors, such as the Yttrium Barium Copper Oxide (YBCO) or the Bismuth Strontium Calcium Copper Oxide (BiSCCO), are formed by planes that undergo a superconductive transition separated by nanometric layers that remain dielectric. As first noticed by Kempf, they are naturally rigid Casimir cavities, so that in these samples not only the absolute energy variation could be compatible with a weight measurement, but also the relative contribution of Casimir energy is expected to be high [32][33][34]. On this basis,we recently started an experiment, called Archimedes, to measure the weight variation of a type II superconductive sample undergoing a superconductive transition in order to evaluate the force exerted by the gravitational field on a Casimir cavity.…”

“…The percentage of condensation energy that is due to the Casimir energy is still under evaluation. In the most optimistic case, it is almost the totality [32]; further theoretical and experimental studies are not in disagreement with Kempf's order of magnitude estimation of the effect [33,34]. It is important to note that all calculations to estimate the vacuum fluctuations contribution to the superconductor condensation energy have been performed until now within a macroscopic approximation.…”

Weighing the vacuum with the Archimedes experiment

“…The superconductor will be actually a layered type II superconductor, like YBCO or BiSCCO: indeed a type II superconductor is formed by planes that perform the transition to superconductivity alternate to layers that remain dielectric. Thus a layered superconductor is a natural stack of partially-reflecting, coupled Casimir cavities, whose condensation energy is expected to be influenced by vacuum fluctuation [7,8,9]. The percentage of condensation energy that is due to Casimir energy is still under evaluation and in the optimistic case is almost the totality [8].…”

“…Further, considering the present small force detectors we also provided an experimental scheme to measure the Archimedes force of vacuum: the cavity is actually a multi-layer cavity obtained using a layered superconductor of type II, like YBCO or BSCOO. In these kind of superconductors the superconducting planes are separated by dielectric planes, thus forming a natural multi-layer Casimir cavity [8,9]. Thus the actual measure will be the weight of the condensation energy of a layered-superconductor.…”

Archimedes experiment: weighing the vacuum

“…The proposed experimental scheme to measure the Archimedes force of the vacuum was provided considering the present small force detectors and the available superconductors materials of type II, like YBCO or BSCOO. This kind of materials can be considered as natural cascade of Casimir cavities, being structured as multilayer of superconducting planes separated by dielectric planes [7,8]. By measuring the weight of the condensation energy of the layered-superconductor, we will able to measure the weigh of the vacuum fluctuations.…”