Destruction of exceptional points from different degeneration points observed for the first time

A team of researchers from the University of Warsaw in Poland, the Institute Pascal CNRS in France, the Military University of Technology in Poland and the British University of Southampton have shown that it is possible to control the so-called exception points. For the first time, physicists also observed the destruction of exceptional points from different degeneracy points. You can read about the discovery, which could help the development of modern optical devices, in the latest issue nature communication.

The universe around us consists of elementary particles, most of which have their antiparticles. If a particle and an antiparticle, i.e. matter and antimatter, meet, annihilation occurs. Physicists have long been able to create quasiparticles and quasiantiparticles – elementary excitations: charge, vibration, energy – trapped in matter, most often in crystals or liquids.

“The world of quasiparticles can be very complicated, although, paradoxically, the quasiparticles themselves help simplify the description of quantum phenomena,” explains Jacek Szczytko from the Faculty of Physics at the University of Warsaw.

“Without quasiparticles, it would be difficult to understand how transistors, light-emitting diodes, superconductors and some quantum computers work. Even abstract mathematical concepts can become quasiparticles as long as they can be implemented in physical systems. One of those abstract concepts is extraordinary points.”

Theorists from the Institute Pascal CNRS in France, Guillaume Malpuech and Dmitry Solnyshkov explain.

“The so-called ‘exceptions’ are specific system parameters that lead to the commonality of two different solutions that can only exist in systems with losses, i.e. those in which the oscillations slowly decay over time,” says Malpuech.

“They enable the creation of efficient sensors, single-mode lasers or unidirectional transport. Importantly, every extraordinary point has a non-zero topological charge – a certain mathematical feature that describes the basic geometric properties and allows you to determine which extraordinary point is going to be the ‘antiparticle’ for another extraordinary point.” , adds Solnyshkov.

Scientists from the University of Warsaw and the Military University of Technology, in collaboration with researchers from CNRS and the University of Southampton, have analyzed the liquid crystal-filled optical cavity. Liquid crystals are a special phase of matter in which, despite their liquid form, certain directions are distinguished.

Difference between the previously considered EP annihilation and this work. a Typical XP kill involving only a single Dirac Valley. EPs are generated from a DP when the relative non-Hermiticity is increased χ. Conversely, when the relative non-Hermiticity decreases, they merge and form a DP. b Destruction of EPs described in this work affecting different valleys. Increasing the relative non-Hermiticity turns 2 DPs into 4 EPs. If it is increased further, the EPs will meet and annihilate, leaving the system without a singularity. w here is the wrap count. Recognition: nature communication (2022). DOI: 10.1038/s41467-022-33001-9

It can be scanned, for example, by a light beam that behaves differently from the optical axes of the liquid crystal, depending on the direction of incidence. This property, combined with easy tunability by an external electric field, is the basis for the operation of conventional liquid crystal displays (LCD). Polarized light – that is, a certain direction of oscillation of the electric field of an electromagnetic wave – perfectly “recognizes” the direction of the optical axes, and these are related to the direction of the elongated molecules of the liquid crystal.

“In the research carried out, the liquid crystal layer was placed between two flat mirrors,” explains Wiktor Piecek from the Military University of Technology in Warsaw. “The entire structure creates an optical cavity through which only light of a certain wavelength can pass.”

This condition is met for the so-called cavity resonance modes – i.e. light with a specific color (energy), polarization and direction of propagation. This corresponds to a situation where a photon falling into the resonator can ricochet between the two mirrors multiple times.

The presence of a liquid crystal whose orientation can be changed by the application of a voltage makes it possible to tune the energy of the resonator modes. In addition, the resonance condition changes when the light is incident at an angle, which can lead in particular to different resonator modes overlapping, i.e. having the same energy despite different polarization of the light.

For the specific orientation of the liquid crystal considered in the article, the two different cavity modes should only intersect for the four specific angles of incidence of light when considering an ideal structure with no losses. In fact, the light trapped in the cavity can escape or be scattered by imperfect mirrors.

The average residence time of the photon in the microcavity can be determined using spectroscopic measurements. In addition, a difference in the scattering of light polarized along and perpendicular to the axis of the liquid crystal was observed due to the orientation of the liquid crystal layer. As a result, at the location of each degeneracy point for an idealized lossless resonator, a pair of so-called exceptional points were observed, for which both the energy and the lifetime of the photon in the resonator are equal.

Mateusz Krol, the first author of the publication, describes the experiment: “In the tested system, it was observed that the position of exceptional points can be controlled by changing the voltage applied to the cavity. First of all as an electrical bias.” is reduced, the exceptional points that have arisen from different degeneracy points come closer together and with a correspondingly low voltage they overlap. Since the approaching points have an opposite topological charge, they annihilate at the moment of encounter, i.e. disappear, leaves no exceptional points.”

“This type of topological singularity behavior, that is, the annihilation of exceptional points from different degeneracy points, was observed for the first time. Previous work showed the annihilation of exceptional points, but they appeared and disappeared at the exact same degeneracy points,” adds Ismael Septembre, a Ph.D . Student at the CNRS.

Extraordinary points have been intensively studied in many different areas of physics in recent years. “Our discovery will enable the creation of optical devices whose topological properties can be controlled by voltage,” concludes Barbara Pietka from the Faculty of Physics at the University of Warsaw.