Toroidal optical transitions in hydrogen-like atoms

It is commonly believed that electromagnetic spectra of atoms and molecules can be fully described by interactions involving electric and magnetic multipoles. However, it has recently become clear that interactions between light and matter also involve toroidal multipoles-toroidal absorption lines have been observed in electromagnetic metamaterials. Here, we show that a previously unexplored type of spectroscopy of the hitherto largely neglected toroidal dipolar interaction becomes feasible if, apart from the classical r × r × p toroidal dipole density term responsible for the toroidal transitions in metamaterials, the spin-dependent r × σ term (which only occurs in relativistic quantum mechanics) is taken into account. Toroidal dipole operators are odd under parity and time-reversal symmetries; toroidal dipole transitions can therefore be distinguished from electric multipole and magnetic dipole transitions.Ministry of Education (MOE)Published versionThis work was supported by the U.K. Engineering and Physical Sciences Research Council (EP/M009122/1), the Singapore Ministry of Education (MOE2016-T3-1-006 and MOE-T2EP50120-0005), European Research Council (FLEET-786851), and the Defense Advanced Research Projects Agency (DARPA) under the Nascent Light Matter Interactions program. N.Z. acknowledges support from Hagler Institute for Advances Study, Texas A&M University