In a groundbreaking study published in Nature Physics on November 10, 2025, researchers have achieved the first experimental observation of a time rondeau crystal, a novel phase of matter where long-range temporal order coexists with short-term disorder. This discovery marks a significant advancement in the understanding of temporal structures, showcasing a complex interplay between order and randomness.
The time rondeau crystal is named after the classical musical form where a repeating theme alternates with contrasting variations, similar to the patterns found in compositions like Mozart’s Rondo alla Turca. Researchers found that while the system demonstrates perfectly periodic behavior at specific measurement times, it also exhibits controllable random fluctuations in between these intervals.
Leo Moon, a third-year Ph.D. student in Applied Science and Technology at UC Berkeley and co-author of the study, explained, “The motivation for this research stems from how order and variation coexist across art and nature.” He noted that early art forms often display repetitive patterns, while more complex works incorporate intricate variations.
Creating this new phase of matter involved using carbon-13 nuclear spins in diamond, which served as a quantum simulator. The setup consisted of randomly positioned nuclear spins interacting through long-range dipole-dipole couplings at room temperature. By hyperpolarizing the carbon-13 nuclear spins using nitrogen-vacancy (NV) centers—defects in the diamond lattice—the researchers generated a strong signal that could be monitored over extended periods.
To achieve the rondeau order, the team employed a series of sophisticated microwave pulse sequences. These sequences combined protective “spin-locking” pulses with strategically timed polarization-flipping pulses. This innovative method allowed the researchers to create a structured yet partially random driving pattern, pivotal for generating the rondeau order.
Moon emphasized the advantages of using diamond for this research: “The diamond lattice with carbon-13 nuclear spins is an ideal setting for exploring these exotic temporal phases because it naturally combines stability, strong interactions, and easy readout.” The researchers utilized what they termed random multipolar drives (RMD), which are structured sequences where randomness can be systematically controlled.
The team observed that this rondeau order maintained itself for over 170 periods, lasting more than four seconds. Analysis of the dynamics through discrete Fourier transforms revealed evidence for the new phase. Unlike conventional discrete time crystals, which typically show a single peak in their frequency spectrum, the time rondeau crystal displayed a smooth, continuous distribution across all frequencies, confirming 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. This discovery allows researchers to control the system’s behavior, enabling them to map an extensive phase diagram of rondeau order stability.
In a significant development, the researchers also demonstrated the potential for encoding information within the temporal disorder. By engineering specific sequences of drive pulses, they encoded the title of their paper into the micromotion dynamics of the nuclear spins, effectively storing over 190 characters in time rather than space.
“While there isn’t an immediate application yet, the notion that disorder in a non-periodic drive can store information while preserving long-term order is indeed fascinating,” Moon remarked. He drew an analogy to ice, where ordered oxygen positions coexist with disordered hydrogen bonds, suggesting that this local randomness can carry structural information.
The implications of this research extend to the design of quantum sensors that could exploit the tunable disorder within these systems. The study also broadens the landscape of non-equilibrium temporal order beyond conventional time crystals. Using the same experimental platform, the team explored related phenomena with deterministic aperiodic drives, such as the Thue-Morse sequence and Fibonacci sequence, realizing both time aperiodic crystals and time quasicrystals alongside the rondeau order.
Looking forward, Moon indicated that the team is investigating alternative material platforms beyond diamond, including pentacene-doped molecular crystals, which may offer enhanced sensitivity. He noted, “Harnessing the tunable disorder in such systems could pave the way for practical quantum sensors or memory devices that exploit stability in the temporal domain.”
This study represents a significant leap in the understanding of temporal order and its applications in quantum technology, paving the way for future innovations in the field.
