I Time rondeau crystals, experimental observations

[Astronuc]

A relative asked me about the following article: Experimental observation of a time rondeau crystal
https://www.nature.com/articles/s41567-025-03028-y

Abstract​

Conventional phases of matter can be characterized by the symmetries they break, one example being water ice whose crystalline structure breaks the continuous translation symmetry of space. Recently, breaking of time-translation symmetry was observed in non-equilibrium systems, producing so-called time crystals. Here we investigate different kinds of partial temporal ordering, stabilized by non-periodic yet structured drives, which we call the rondeau order. Using carbon-13 nuclear spins in diamond as a quantum simulator, we use microwave driving fields to create tunable short-time disorder in a system exhibiting long-time stroboscopic order. Our spin control architecture allows us to implement a family of driving fields including periodic, aperiodic and structured random drives. We use a high-throughput read-out scheme to continuously observe the spin polarization and its rondeau order, with controllable lifetimes exceeding 4 s. Using degrees of freedom associated with the short-time temporal disorder of rondeau order, we demonstrate the capacity to encode information in the response of observables. Our work broadens the landscape of observed non-equilibrium temporal order, and raises the prospect for the potential applications of driven quantum matter.

I pointed my relative to following article: Scientists Discovered a Time Crystal That Reveals a New Way to Order Time
https://www.yahoo.com/news/articles/scientists-discovered-time-crystal-reveals-180055389.html

Time crystals, first predicted by US theoretical physicist Frank Wilczek in 2012 before being observed for the first time in 2016, bring additional complexity to the patterned atomic matrix that makes up regular solids.

. . .

A time crystal describes particles moving through sequences that aren't dictated by the timing of any external push, breaking the expected flow. The particles oscillate within their lowest energy states with a timing pattern that repeats; that pattern can also be perfectly superimposed, like the spatial arrangement of atoms in a crystal.

A time quasicrystal is one in which the oscillations of the atoms are structured, but do not repeat, like a Penrose tiling – a pattern in dimensional space that never quite repeats, yet still follows a set of rules.

According to Moon and his colleagues, a time rondeau crystal is yet another version, exhibiting both order and disorder, repeating and not repeating, like the musical form known as a rondeau.

This area is outside of my regular experience. I'm interested in radiation effects in polycrystalline material, i.e., grain boundaries as well as vacancies, which "are lattice sites where an atom should sit, but nothing is there," and interstitials. Ions, electrons, neutrons and gammas cause atomic displacements assuming sufficient energy, and overtime, a solid crystal will accumulate a populations of vacancies and interstitials, which tend to saturate at a given fluence (particles per unit area) or cumulative displacements.

Does anyone at PF work in this area of time crystals or time rondeau crystals?