Repulsive Casimir and Casimir-Polder Forces (1202.6415v2)

Abstract: Casimir and Casimir-Polder repulsion have been known for more than 50 years. The general "Lifshitz" configuration of parallel semi-infinite dielectric slabs permits repulsion if they are separated by a dielectric fluid that has a value of permittivity that is intermediate between those of the dielectric slabs. This was indirectly confirmed in the 1970s, and more directly by Capasso's group recently. It has also been known for many years that electrically and magnetically polarizable bodies can experience a repulsive quantum vacuum force. More amenable to practical application are situations where repulsion could be achieved between ordinary conducting and dielectric bodies in vacuum. The status of the field of Casimir repulsion with emphasis on recent developments will be surveyed. Here, stress will be placed on analytic developments, especially of Casimir-Polder (CP) interactions between anisotropically polarizable atoms, and CP interactions between anisotropic atoms and bodies that also exhibit anisotropy, either because of anisotropic constituents, or because of geometry. Repulsion occurs for wedge-shaped and cylindrical conductors, provided the geometry is sufficiently asymmetric, that is, either the wedge is sufficiently sharp or the atom is sufficiently far from the cylinder.

• The paper provides an analytical framework surveying Casimir repulsion, focusing on how Lifshitz theory predicts repulsive forces under specific dielectric configurations.
• It examines Boyer's finding of positive quantum self-energy for a perfect conducting spherical shell, representing a scenario yielding repulsive quantum forces.
• The study details conditions for Casimir-Polder repulsion, particularly in anisotropic systems, highlighting the influence of material anisotropy and geometry on achieving repulsive interactions.

Overview of "Repulsive Casimir and Casimir-Polder Forces"

The paper "Repulsive Casimir and Casimir-Polder Forces," authored by Milton et al., is a comprehensive exploration of the phenomenon of repulsive forces in the context of Casimir and Casimir-Polder interactions. Traditionally considered to be attractive, these forces are fundamental outcomes of quantum fluctuations between objects and have significant implications in quantum field theory and nanotechnology. The paper explores the conditions under which these forces become repulsive and discusses the mathematical formalisms and physical configurations that lead to such outcomes.

Context and Motivation

Van der Waals forces and their extensions into Casimir and Casimir-Polder (CP) regimes are typically attractive; however, the authors highlight that under specific circumstances, these forces can be repulsive. This repulsion is particularly intriguing as it could lead to practical applications in micro and nanoscale systems where stiction poses a challenge. The theoretical possibility of such repulsion was originally proposed in the 1970s, with recent experimental validations accentuating the relevance of this research area.

Key Contributions

1. Analytical Framework for Casimir Repulsion: The authors provide a theoretical survey of Casimir repulsion, primarily focusing on systems where this phenomenon can occur. The lifshitz theory plays a crucial role here, predicting repulsion between dielectric slabs separated by a medium with intermediate permittivity. This theoretical backdrop is critical for comprehending observed repulsive behavior in recent experiments.
2. Boyer's Repulsion Phenomenon: This aspect examines Boyer's surprising result that a perfectly conducting spherical shell has a positive quantum self-energy. This is one of the few situations where quantum field theoretic calculations yield repulsive forces.
3. Casimir-Polder Repulsion in Anisotropic Systems: A significant portion of the analysis is dedicated to CP repulsion between anisotropically polarizable atoms and geometrically or dielectrically anisotropic surfaces. The authors detail the conditions necessary for repulsion, such as specific geometric configurations and polarizability tensors.
4. Geometrical Influence on Repulsive Forces: The paper includes the examination of various geometries, such as wedge-shaped and cylindrical conductors. For instance, it is shown that anisotropic CP forces can yield repulsive forces if an atom exhibits sufficient anisotropy in its polarizability and if the geometry is suitably configured.

Numerical and Experimental Insights

The paper also draws attention to numerical simulations and theoretical predictions supporting the possibility of repulsion, emphasizing experimental insights that have indirectly or directly confirmed these forces under specific configurations. Efforts are highlighted to observe repulsion experimentally by employing innovative materials and configurations, such as metamaterials or Rydberg atoms.

Implications and Future Directions

This work has profound implications, both theoretically and practically. From a theoretical standpoint, it enriches the understanding of quantum field interactions in confined configurations, providing insights that challenge conventional notions of quantum mechanical forces. Practically, the property of achieving repulsion at micro and nanoscales could revolutionize the design of nanomechanical devices, potentially reducing issues related to stiction and allowing for novel engineering applications.

Going forward, the synthesis of metamaterials or novel atomic configurations might allow for tunable attractive and repulsive forces, paving the way for new experiments and devices. Future research could explore more complex dielectric and magnetic configurations, seeking to generalize and experimentally validate the conditions for repulsion in diverse material properties and geometries.

In conclusion, this paper integrates a rich theoretical framework with experimental observations and potential applications, marking a significant advancement in understanding and utilizing Casimir and Casimir-Polder forces. The insights presented could catalyze further research into tailoring quantum forces for innovative technological applications.