A Rebellion Against Boredom
(and Translational Symmetry)
(and Translational Symmetry)
Бунт против скуки
(и трансляционной симметрии)
(и трансляционной симметрии)
The Recipe for a Quasicrystal
Magic — for the Good of Humanity
Assistant Professor,
Deputy Head of Laboratory of Hybrid Photonics. Makes wonders with lights and lasers.
Deputy Head of Laboratory of Hybrid Photonics. Makes wonders with lights and lasers.
Sergey Alyatkin //
Distinguished Professor,
Head of the Laboratory of Hybrid PhotonicsБ Director of the Center for Photonic Science and Engineering
Head of the Laboratory of Hybrid PhotonicsБ Director of the Center for Photonic Science and Engineering
Pavlos Lagoudakis //
Or how to create a quasicrystal with fivefold symmetry
If you look at fresh snow through a microscope — a mandatory morning ritual here at the Institute of Winter Wonders — you will notice a boring pattern. All snowflakes are hexagonal. This is the dictate of crystallography: Nature loves hexagonal lattices and tolerates no liberties.
But on the eve of the holidays, our Hybrid Photonics Group decided to break this immutable law. We created an object that shouldn’t exist in the classical world of solids: a quasicrystal made of “liquid light.” It looks like an “impossible snowflake” with five rays, possessing a unique pattern that is infinite yet never precisely repeats itself.
Welcome to the geometry of miracles.
But on the eve of the holidays, our Hybrid Photonics Group decided to break this immutable law. We created an object that shouldn’t exist in the classical world of solids: a quasicrystal made of “liquid light.” It looks like an “impossible snowflake” with five rays, possessing a unique pattern that is infinite yet never precisely repeats itself.
Welcome to the geometry of miracles.
In ordinary crystals — whether diamond, table salt, or ice — atoms sit in dull, repetitive cells. Shift the lattice by a certain increment, and it overlaps perfectly with itself. This property of periodic structures is called translational symmetry. It is reliable, predictable, and … frankly, a bit banal.
Quasicrystals are the jazz of the material world. They possess long-range order but refuse to repeat themselves precisely. For a long time, such structures were considered impossible — until their discovery in metal alloys was awarded with a Nobel Prize. But our physicists decided to go further. Instead of the heavy atoms, they chose to weave this forbidden pattern from something far more ephemeral: light and quantum matter.
Quasicrystals are the jazz of the material world. They possess long-range order but refuse to repeat themselves precisely. For a long time, such structures were considered impossible — until their discovery in metal alloys was awarded with a Nobel Prize. But our physicists decided to go further. Instead of the heavy atoms, they chose to weave this forbidden pattern from something far more ephemeral: light and quantum matter.
Development
Sketch
As our stencil, we chose the Penrose tiling — a mathematical pattern possessing a fivefold symmetry “forbidden” for crystals. You can tile an infinite plane with this ordered pattern, yet you will never match this intricate mosaic to itself by sliding one such snowflake against another.
Inc
We switched on the laser and by sheer magic of the laws of physics created multiple laser beams focused as a mosaic on the microcavity. The individual “droplets of liquid light” created by laser light in the nodes of the mosaic suddenly “agreed” with each other and started to oscillate in unison, forming a single macroscopic quantum state. In ordinary life, chaos often defeats order, but here phase synchronization took over.
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Magic
To see this mosaic, we used exciton-polaritons. These are the centaurs of the quantum world: half light, half matter. They behave like a fluid that can glow.
To cook up an “impossible snowflake,” you won’t need frost or water, but rather a semiconductor microcavity and a laser.
And there it was: our “impossible snowflake.” If you look at its emission in reciprocal space, you see 10 razor-sharp Bragg peaks — revealing the symmetry forbidden to ordinary crystals.
Why do we need all of this? Of course, we could write here what we write in every grant report: “Quasicrystals hold promise for creating superhard coatings.” And that is strictly true. Coat ice skates with such a material, and they won’t dull for a very long time.
Or we could sound even smarter: “This is an ideal platform for observing Anderson localization and implementing topological photonics.” And that would also be totally true.
But, to be honest, we also did it because it is beautiful. As the study’s lead author, Sergey Alyatkin, noted: “The results turned out to be beautiful in the literal sense of the word.”
The “impossible snowflake” proves that even in a complex, unpredictable system with no simple repetition, perfect harmony is possible. That is, perhaps, the best metaphor for the coming year.
Or we could sound even smarter: “This is an ideal platform for observing Anderson localization and implementing topological photonics.” And that would also be totally true.
But, to be honest, we also did it because it is beautiful. As the study’s lead author, Sergey Alyatkin, noted: “The results turned out to be beautiful in the literal sense of the word.”
The “impossible snowflake” proves that even in a complex, unpredictable system with no simple repetition, perfect harmony is possible. That is, perhaps, the best metaphor for the coming year.
Based on research by Sergey Alyatkin published in Science Advances and work by the laboratory led by Professor Pavlos Lagoudakis at the Center for Photonic Science and Engineering, conducted in collaboration with the University of Iceland, the Institute of Spectroscopy of the Russian Academy of Sciences, and the University of Warsaw.
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