From left: Professor Nikolay Zheludev, Professor Ilya Kuprov and Associate Professor David Wilkowski presented theoretical calculations showing that atoms can also emit light through a new process called a toroidal transition.
Visible light, and other forms of electromagnetic radiation, are produced by oscillations of electrons in atoms. These oscillations cause the atoms to act as tiny electromagnetic antennas, emitting different colors and patterns of light. Since the 20th century, physicists have achieved a detailed and highly accurate understanding of this process, which underlies numerous technologies from sodium lamps to modern LED displays.
Recently, a new twist to this old story has been discovered by physicists from Nanyang Technological University, Singapore (NTU Singapore) and the University of Southampton in the UK. In a new paper published in Science Advances in November 2022, Associate Professor Ilya Kuprov, Associate Professor David Wilkowski, and Professor Nikolay Zheludev presented theoretical calculations showing that atoms can also emit light through a new process called a toroidal transition. This mechanism, which involves electrons moving along paths arranged in a torus or “donut”, may allow scientists to develop new optical technologies such as light sources and sensors.
Dances with electrons
In electromagnetic theory, light is emitted by configurations of oscillating charges (such as electrons) called “multipoles”. There are several kinds of multipoles, the simplest being the electric dipole, which consists of charges jiggling back-and-forth along a line, as shown in the left panel of the figure below.
Schematic of an electric dipole (left), magnetic dipole (center), and toroidal dipole (right). Each kind of multipole can lead to the emission of light, but radiation from atoms due to toroidal multipoles has never been observed. Figure excerpted from Kuprov, Wilkowski, and Zheludev (2022).
Another kind of multipole, called the magnetic dipole, is formed by charges moving in a loop, as shown in the middle panel of the figure. Other kinds of electric and magnetic multipoles, such as “quadrupoles” or “octupoles”, consist of more intricate motions of charges. Each kind of multipole radiates light in a specific pattern; for example, an electric dipole emits light mostly in the directions perpendicular to the line of motion.
However, electric and magnetic multipoles are not the only possibilities. In 1958, the Soviet physicist Yakov Zel’dovich discovered a separate family of multipoles called toroidal multipoles. For example, the right panel of the figure shows a “toroidal dipole”, which consists of charges moving in a collection of loops forming a donut-like shape.
Since toroidal multipoles are distinct from electric and magnetic multipoles, they could serve as another way for atoms to emit light. However, in the decades after Zel’dovich’s theoretical discovery, experimentalists failed to turn up any evidence for light emission via toroidal multipoles. Toroidal multipoles thus seemed to be consigned to be theoretical curiosities of no practical relevance.
In 2010, experimental evidence for toroidal dipoles was finally obtained by a research team led by Professor Nikolay Zheludev, now a faculty member at both NTU Singapore and the University of Southampton. Instead of using real atoms, the researchers used an electromagnetic metamaterial – an artificial medium formed by an array of metal wires specially arranged to enhance the effects of toroidal dipoles. Subsequently, researchers have developed other metamaterials that also support toroidal multipoles, including nanometre scale metamaterials fabricated using semiconductor patterning techniques.
Shedding new light on toroidal multipoles
In the new theoretical work, Kuprov, Wilkowski, and Zheludev undertook a fresh examination of toroidal multipoles in atoms, starting from the fundamental quantum mechanics of electrons in atoms. In quantum theory, light is created when an electron undergoes a transition from a higher-energy state to a lower-energy state. The energy lost by the electron is turned into a photon, or particle of light, which is emitted from the atom.
Not every transition between two quantum states can actually give rise to light emission. Physicists have worked out an intricate set of “selection rules” that govern which pairs of quantum states can undergo transitions that lead to the emission of light. It turns out that allowed transitions can be associated with electromagnetic multipoles. Most commonly, these are electric or magnetic dipoles, but it is also possible for transitions to correspond to other kinds of multipoles, including toroidal multipoles.
Kuprov, Wilkowski, and Zheludev discovered that toroidal transitions obey a different set of selection rules than those based on electric and magnetic dipole transitions. This means, for example, that an atom can emit light via a toroidal transition between two quantum states that could not normally be allowed. If the specific wavelength and radiation pattern for this transition is detected, that would serve as irrefutable evidence for the existence of toroidal transitions in atoms.
Their theoretical analysis also revealed that Einstein’s laws of special relativity plays an important role in the experimental detection of toroidal multipole transitions. Relativity modifies the selection rules, making possible special toroidal transitions in which the electron’s spin, or internal angular momentum, switches direction. As such spin-flipping processes are disallowed for any kind of electric multipole transition, it would be easy to prove that the emitted light stems from a toroidal transition.
Moving forward, Kuprov, Wilkowski, and Zheludev hope to perform spectroscopic experiments to make the first observations of toroidal transitions in atoms. To do this, it is first necessary to choose the atoms in which the experimental signatures of toroidal transitions will be strongest, and easiest to distinguish from electric and magnetic multipole transitions. As a first step, the team is looking into using alkali metal atoms, such as lithium, immersed into a strong static magnetic field. This experiment is currently being set up at the Centre for Disruptive Photonic Technologies, a photonics research centre in NTU Singapore.
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