Dynamic toroidizability as ubiquitous property of atoms and molecules in optical electric fields

The continuous search for metamaterials with special properties, suitable for new technological applications, is presently being driven by a preceding theoretical development, which took place after the introduction of new physical entities, anapole and a family of toroidal multipoles, having a border in common with those considered in the more familiar electric and magnetic multipole expansions. The related concept of toroidization, i.e., toroidal moment per unit volume, has been advocated in analogy to electric polarization and magnetization operated by electromagnetic fields and should be considered on the same footing regarding its relevance and practicality for understanding certain properties, e.g., ferrotoroidicity in condensed matter physics, and for rationalizing the behavior of charge-current distributions that neither radiate nor interact with external fields in classical and quantum electrodynamics. Toroidizability, i.e., the ability of sustaining toroidal moments, can also be defined by an analogy with electric polarizability and magnetizability. The present study shows that such a property is general and characterizes atoms and molecules and that the optical electric field of a light beam induces an oscillating anapole moment, i.e., the superposition of toroidal moment with an electric dipole moment. However, values of anapole polarizabilities induced by monochromatic light, estimated by time-dependent perturbation theory for rare gas atoms and a few molecules, are quite small and possibly hard to detect experimentally.