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 has shown that it is possible to control the
so-called exceptional points. For the first time, physicists also observed the
annihilation of exceptional points from different degeneracy points. You can
read about the discovery that may contribute to the creation of modern optical
devices in the latest Nature Communications.
The universe around us is made of elementary
particles, most of which have their antiparticles. When a particle and an
antiparticle, that is, matter and antimatter, meet each other, annihilation
occurs. Physicists have long been able to produce 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 the operation of transistors, light-emitting diodes,
superconductors and some quantum computers. Even abstract mathematical concepts
can become quasiparticles, as long as they can be implemented in physical
systems. One of such abstract concepts are exceptional points."
Theorists from Institute Pascal CNRS in France,
Guillaume Malpuech and Dmitry Solnyshkov explain.
"The so-called 'exceptional points' are
specific system parameters leading to the commonality of two different
solutions that can only exist in systems with losses, i.e. those in which the
oscillations slowly fade over time," says Malpuech.
"They allow the creation of efficient sensors,
single-mode lasers, or unidirectional transport. What is important, each
exceptional point has a non-zero topological charge—a certain mathematical
feature that describes the fundamental geometric properties and allows you to
determine which exceptional point will be the 'antiparticle' for another
exceptional point," adds Solnyshkov.
Scientists from the University of Warsaw and the
Military University of Technology in cooperation with researchers from the CNRS
and the University of Southampton analyzed the optical resonator filled with
liquid crystal. Liquid crystals are a special phase of matter in which certain
directions are distinguished despite its liquid form.
It can be probed, for example, by a light beam,
which behaves differently depending on the direction of incidence in relation
to the optical axes of the liquid crystal. This feature, combined with the easy
tunability by an external electric field, is the basis for the operation of
common liquid crystal displays (LCD). Polarized light—that is, a specific
direction of vibrations of the electric field of an electromagnetic
wave—perfectly "senses" the direction of optical axes, and these are
related to the direction of the elongated molecules of the liquid crystal.
"In the conducted research, the liquid crystal
layer was placed between two flat mirrors," explains Wiktor Piecek from
the Military University of Technology in Warsaw. "The whole structure
creates an optical cavity, through which only light with a specific wavelength
can pass."
This condition is met for the so-called cavity
resonance modes—that is, light with a certain color (energy), polarization and
direction of propagation. This corresponds to a situation where a photon that
falls into the cavity can bounce multiple times between the two mirrors.
The presence of a liquid crystal, the orientation of
which can be changed by applying a voltage, allows the energy of the cavity
modes to be tuned. In addition, the resonance condition changes when the light
is incident at an angle, which in particular can lead different cavity modes to
intersect with each other, i.e. have 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 intersect only
for the four specific incidence angles of light when considering an ideal
structure without any losses. In fact, the light trapped in the cavity can
escape through imperfect mirrors or be scattered.
The average time the photon remains inside the
microcavity can be determined on the basis of spectroscopic measurements.
Moreover, due to the orientation of the liquid crystal layer, a difference was
observed in the scattering of light polarized along and perpendicular to the
axis of the liquid crystal. As a result, at the place of each degeneracy point
for an idealized lossless cavity, a pair of so-called exceptional points were
observed for which both the energy and lifetime of the photon in the cavity are
the same.
Mateusz Krol, who is 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 the electric bias is reduced,
the exceptional points created from different degeneracy points get closer to
each other, and for a suitably low voltage, they overlap. As the approaching
points have an opposite topological charge, they annihilate at the time of the
encounter, so they disappear, leaving no exceptional points."
"This type of topological singularity behavior,
i.e. the annihilation of exceptional points from different degeneracy points,
has been observed for the first time. Earlier work showed the annihilation of
exceptional points, but they appeared and disappeared at exactly the same
degeneracy points," adds Ismael Septembre, a Ph.D. student at the CNRS.
Exceptional points have been intensively studied in
many different areas of physics in recent years. "Our discovery will allow
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.
Reference: Nature Communications
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