Researchers at the University of California, Berkeley, have made a significant breakthrough in physics by experimentally observing a new phase of matter known as the time rondeau crystal. This novel form exhibits a remarkable combination of long-range temporal order and short-term disorder, as reported in a study published in Nature Physics on November 10, 2025.
The term “rondeau” draws inspiration from a classical musical form characterized by repeating themes interspersed with contrasting variations. The time rondeau crystal mirrors this concept, presenting a predictable periodic behavior at specific measurement times while also allowing for controllable random fluctuations during those intervals.
Leo Moon, a co-author of the study and Ph.D. student in Applied Science and Technology at UC Berkeley, explained, “The motivation for this research stems from how order and variation coexist across art and nature.” Moon elaborated on the analogy, noting that even in familiar substances like ice, ordered structures coexist with randomness.
The research team utilized carbon-13 nuclear spins embedded in diamond as a quantum simulator. This setup featured randomly positioned nuclear spins that interacted through long-range dipole-dipole couplings. The process began by hyperpolarizing the carbon-13 spins using nitrogen-vacancy (NV) centers within the diamond. These NV centers, when illuminated by a laser, become spin-polarized, allowing the polarization to be transferred to surrounding nuclear spins using microwave pulses.
This hyperpolarization process enhanced the nuclear spin polarization nearly 1,000-fold above the thermal equilibrium value, yielding a strong signal that could be observed over extended periods. Subsequently, the researchers applied sophisticated microwave pulse sequences that merged protective “spin-locking” pulses with carefully timed polarization-flipping pulses. This combination created the unique structure of the rondeau order.
Innovative Techniques Lead to New Discoveries
The researchers implemented an advanced control system, utilizing an arbitrary waveform generator capable of executing over 720 different pulses in one run. This was crucial for generating the structured yet non-periodic drives needed to establish rondeau order within the crystal. Moon remarked, “The diamond lattice with carbon-13 nuclear spins is an ideal setting for exploring these exotic temporal phases because it combines stability, strong interactions, and easy readout.”
The team introduced what they termed random multipolar drives (RMD), which allowed for systematic control of randomness within the sequences. During these drive cycles, the nuclear spins exhibited deterministic polarization flips, showcasing periodic behavior typical of time crystals. In contrast, the polarization fluctuated randomly between measurements, exemplifying the coexistence of predictable long-range order and random short-term variations characteristic of rondeau order.
The researchers successfully maintained the rondeau order for over 170 periods, equivalent to more than four seconds. Their analysis revealed that the frequency spectrum of the time rondeau crystal demonstrated a smooth, continuous distribution, diverging from conventional discrete time crystals that display a single sharp peak. This finding served as a “smoking gun” for the coexistence of temporal order and disorder.
Potential Applications and Future Research
The implications of this research extend beyond theoretical exploration. The team demonstrated that information could be encoded within the temporal disorder. By designing specific sequences of drive pulses, they encoded the paper’s title, “Experimental Observation of a Time Rondeau Crystal: Temporal Disorder in Spatiotemporal Order,” into the dynamics of the nuclear spins, successfully storing more than 190 characters.
Moon emphasized the intriguing potential of this research, stating, “There isn’t an immediate, straightforward application yet, but the idea itself is fascinating that disorder in a non-periodic drive can actually store information while preserving long-term order.” He likened this phenomenon to the structural information carried by local randomness in ice.
Looking to the future, the research team plans to explore alternative materials beyond diamond, including pentacene-doped molecular crystals, which may enhance sensitivity through hydrogen-1 nuclear spins. They aim to leverage the tunable disorder in these systems to develop practical quantum sensors or memory devices that utilize stability in the temporal domain.
This groundbreaking research expands the understanding of non-equilibrium temporal order, pushing the boundaries of knowledge in the field of condensed matter physics. The findings pave the way for further investigations into complex systems and their potential applications in quantum technology.
