Researchers have made a groundbreaking discovery in the field of quantum physics, observing a new form of temporal order known as the time rondeau crystal. This phase of matter, described in a study published in Nature Physics, combines long-range temporal order with short-time disorder. The term “rondeau” is inspired by a classical musical form characterized by repeating themes and contrasting variations, akin to the behavior observed in this crystal.
The study’s co-author, Leo Moon, a Ph.D. student in Applied Science and Technology at UC Berkeley, noted that the research was driven by the interplay of order and variation found in both art and nature. “Repetitive periodic patterns naturally arise in early art forms due to their simplicity,” he explained, “while more advanced music and poetry build intricate variations atop a monotonous background.” This concept resonates beyond aesthetics, as even common substances like ice demonstrate this duality, with structured oxygen atoms and randomly arranged hydrogen nuclei.
Until now, investigations into non-periodic temporal order primarily focused on deterministic patterns, such as quasicrystals. The time rondeau crystal represents a significant advancement, being the first to merge stroboscopic order with controllable random disorder.
Creating the Rondeau Crystal
The researchers employed carbon-13 nuclear spins in diamond as a quantum simulator. This system consisted of randomly positioned nuclear spins at room temperature, interacting through long-range dipole-dipole couplings. The team began by hyperpolarizing the carbon-13 nuclear spins using a technique that leverages nitrogen-vacancy (NV) centers, which are defects in the diamond lattice. When exposed to laser illumination, these NV centers become spin-polarized, a polarization that can be transferred to surrounding nuclear spins via microwave pulses.
This hyperpolarization process, lasting approximately 60 seconds, significantly enhanced the nuclear spin polarization, boosting it nearly 1,000-fold above its thermal equilibrium value. This strong signal enabled researchers to track the system over extended periods. Following this, they applied advanced microwave pulse sequences, combining protective “spin-locking” pulses with precisely timed polarization-flipping pulses, to create the rondeau order.
Moon highlighted the advantages of using diamond for this research, stating, “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 researchers employed what they termed random multipolar drives (RMDs), structured sequences where randomness can be systematically controlled. During the drive cycle, the nuclear spins flipped their polarization in a predictable manner, revealing the periodic behavior characteristic of time crystals. Between these regular measurements, the polarization exhibited random fluctuations, further demonstrating the unique nature of the rondeau order.
Observing Temporal Order and Disorder
The team successfully observed the rondeau order maintain itself for over 170 periods, translating to more than four seconds. The discrete Fourier transform of the dynamics provided compelling evidence for this new phase, revealing a smooth, continuous distribution across all frequencies, contrasting with the sharp peaks seen in conventional discrete time crystals. This “smoking gun” signature confirmed the coexistence of temporal order and disorder.
“Rondeau order shows that order and disorder don’t have to be opposites—they can coexist in a stable, driven quantum system,” Moon explained. The team also achieved control over the system’s behavior, mapping out an extensive phase diagram of rondeau order stability by varying drive parameters. The lifetime of the order could be adjusted by modifying the drive period and pulse imperfections.
In an intriguing development, researchers demonstrated that information could be encoded within the temporal disorder. By engineering specific sequences of drive pulses, they successfully encoded the paper’s title, “Experimental observation of a time rondeau crystal. Temporal Disorder in Spatiotemporal Order,” into the micromotion dynamics of the nuclear spins, storing over 190 characters. This innovative approach indicates that information can be stored in time rather than space.
Moon remarked on the potential implications 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-time order.” He drew an analogy to ice, which has ordered oxygen positions but disordered hydrogen bonds, suggesting that local randomness can carry structural information.
The researchers believe that the tunability of disorder within these systems could pave the way for the development of quantum sensors that are selectively sensitive to specific frequency ranges. This work significantly expands the observed landscape of non-equilibrium temporal order, moving beyond conventional time crystals. Utilizing the same experimental platform, the team also realized related phenomena with deterministic aperiodic drives, such as the Thue-Morse and Fibonacci sequences, creating time aperiodic crystals and time quasicrystals alongside the rondeau order.
Looking forward, Moon mentioned that the team is exploring alternative material platforms beyond diamond, including pentacene-doped molecular crystals, where hydrogen-1 nuclear spins may offer enhanced sensitivity. “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,” he concluded.
This research marks a significant step forward in the understanding of quantum materials and their potential applications, highlighting the innovative spirit of modern science.
