Researchers have made a significant breakthrough in the understanding of temporal order by experimentally observing a new phase of matter known as the time rondeau crystal. This discovery, published in the journal Nature Physics on November 10, 2025, reveals a unique phenomenon where long-range temporal order exists alongside short-time disorder.
The term “rondeau” is inspired by a classical musical form characterized by repeating themes and contrasting variations, much like the behavior exhibited by this new crystal. According to Leo Moon, a Ph.D. student at UC Berkeley and co-author of the study, the research explores the coexistence of order and variation across both art and nature. Moon notes that “repetitive periodic patterns naturally arise in early art forms due to their simplicity, while more advanced music and poetry build intricate variations atop a monotonous background.”
Previous studies have primarily focused on deterministic patterns, such as quasicrystals, but the time rondeau crystal represents the first instance of combining stroboscopic order with controllable random disorder. This makes it a novel addition to the landscape of non-equilibrium phases of matter.
Creating the Time Rondeau Crystal
To create this new phase, researchers utilized carbon-13 nuclear spins within diamond as a quantum simulator. The setup involved randomly positioned nuclear spins interacting through long-range dipole-dipole couplings. The process began with the hyperpolarization of carbon-13 nuclear spins using nitrogen-vacancy (NV) centers—defects in the diamond lattice where a nitrogen atom is adjacent to an empty site.
By illuminating the NV centers with a laser, the researchers were able to achieve a significant boost in the nuclear spin polarization, enhancing it nearly 1,000-fold above its thermal equilibrium value. This strong signal enabled prolonged tracking of the spins. Following this, advanced microwave pulse sequences were applied, integrating protective “spin-locking” pulses with precisely timed polarization-flipping pulses, ultimately leading to the emergence of rondeau order.
“The diamond lattice with carbon-13 nuclear spins is an ideal setting for exploring these exotic temporal phases,” Moon explained, citing the stability and strong interactions of diamond as contributing factors.
The researchers employed a technique known as random multipolar drives (RMD), where structured sequences allowed for systematic control of randomness. At regular intervals, the nuclear spins exhibited deterministic polarization flipping, indicating the periodic behavior typical of time crystals. In contrast, random fluctuations occurred between these regular measurements, exemplifying the hallmark of rondeau order.
Significance of the Findings
The team observed that this rondeau order could maintain itself for over 170 periods, lasting more than four seconds. Analysis through the discrete Fourier transform revealed a continuous frequency distribution, diverging from the sharp peaks typically associated with conventional discrete time crystals. This continuous spectrum serves as strong evidence for the coexistence of temporal order and disorder.
“Rondeau order shows that order and disorder don’t have to be opposites—they can actually coexist in a stable, driven quantum system,” Moon stated. The researchers were able to manipulate the system’s behavior, mapping out an extensive phase diagram of rondeau order stability. They discovered that variations in drive parameters allowed for tuning the lifetime of the order, aligning with predicted scaling laws.
An intriguing aspect of this research is the potential for encoding information within the temporal disorder. By engineering specific sequences of drive pulses, the team encoded the title of their paper, “Experimental observation of a time rondeau crystal. Temporal Disorder in Spatiotemporal Order,” into the dynamics of the nuclear spins, successfully storing over 190 characters.
Moon highlighted the fascinating implications of this finding, stating, “The idea itself is captivating that disorder in a non-periodic drive can actually store information while preserving long-time order.” He drew a parallel to the structural differences between water and ice, where ice exhibits ordered oxygen positions but disordered hydrogen bonds.
Looking to the future, the researchers anticipate that the controllable nature of this disorder could lead to advancements in quantum sensors sensitive to specific frequency ranges. The work not only expands the understanding of non-equilibrium temporal order but also opens avenues for exploring related phenomena in quantum systems.
The team is now investigating alternative material platforms beyond diamond, including pentacene-doped molecular crystals, where hydrogen-1 nuclear spins may provide enhanced sensitivity. “Harnessing the tunable disorder in such systems could pave the way for practical quantum sensors or memory devices,” Moon noted, emphasizing the potential applications of this groundbreaking research.
This study illustrates the remarkable interplay between order and disorder, enriching our comprehension of quantum phenomena and setting the stage for future innovations in quantum technology.
