In a groundbreaking study published in Nature Physics, researchers have successfully observed a new phase of matter known as the time rondeau crystal. This unique phase demonstrates a fascinating coexistence of long-range temporal order with short-time disorder. The discovery marks a significant advancement in the understanding of temporal phenomena, contributing to the broader field of quantum physics.
The concept of the time rondeau crystal draws its name from the classical musical form, where a recurring theme alternates with contrasting variations. In this context, the crystal exhibits periodic behavior during specific measurement intervals, while allowing for controllable random fluctuations between those moments. This duality mirrors patterns found in both nature and art, as explained by Leo Moon, a co-author of the study and a third-year Applied Science and Technology Ph.D. student at UC Berkeley.
Moon noted, “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.” The researchers highlight that even commonplace substances, such as ice, showcase this duality, with oxygen atoms forming a crystalline lattice while hydrogen nuclei remain randomly arranged.
The study builds on previous work involving time crystals, which exhibit long-lived periodic oscillations and break time-translation symmetry. Prior explorations of non-periodic temporal order had primarily focused on deterministic patterns like quasicrystals. The time rondeau crystal is the first to combine stroboscopic order with controllable random disorder, offering new insights into temporal dynamics.
Creating a New Phase of Matter
For their experiment, the researchers employed carbon-13 nuclear spins in diamond as a quantum simulator. The system featured randomly positioned nuclear spins at room temperature that interacted through long-range dipole-dipole couplings. Initially, the team hyperpolarized the carbon-13 nuclear spins using a method that leverages nitrogen-vacancy (NV) centers—defects in the diamond lattice where a nitrogen atom is adjacent to an empty site.
By illuminating these NV centers with a laser, the researchers achieved spin polarization, which was then transferred to the surrounding nuclear spins through microwave pulses. This hyperpolarization process significantly enhanced the nuclear spin polarization, boosting it nearly 1,000-fold above its thermal equilibrium value, allowing for a signal that could be monitored over extended periods.
To create the rondeau order, the researchers applied sophisticated microwave pulse sequences, combining protective “spin-locking” pulses with polarization-flipping pulses. This structured yet partially random driving pattern facilitated the emergence of the new temporal phase. The team utilized an innovative control system featuring an arbitrary waveform generator capable of executing over 720 different pulses in a single run.
Moon remarked, “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 stability of diamond, coupled with its resistance to chemical reactions and temperature changes, enhances the reliability of the experimental setup.
The researchers introduced a system they termed random multipolar drives (RMD), allowing for structured sequences with systematically controllable randomness. During regular intervals of the drive cycle, the nuclear spins flipped their polarization deterministically, exhibiting the periodic behavior characteristic of time crystals. Between these measurements, the polarization fluctuated randomly, demonstrating no predictable pattern.
Evidence of Rondeau Order
The team successfully observed the rondeau order for more than 170 periods, maintaining stability for over four seconds. The discrete Fourier transform of the dynamics provided crucial evidence for this new phase. Unlike conventional discrete time crystals that exhibit a single sharp peak in their frequency spectrum, the time rondeau crystal displayed a smooth, continuous distribution across all frequencies.
“This ‘smoking gun’ signature confirms the coexistence of temporal order and disorder,” said Moon. The research team was able to control the system’s behavior by varying driving parameters, enabling the mapping of an extensive phase diagram illustrating the stability of rondeau order.
The lifetime of the order could be adjusted by modifying the drive period and pulse imperfections, with heating rates following predictable scaling laws.
In a novel twist, the researchers demonstrated that information could be encoded in the temporal disorder. By engineering specific sequences of drive pulses, they successfully encoded the title of their paper, “Experimental observation of a time rondeau crystal. Temporal Disorder in Spatiotemporal Order,” into the micromotion dynamics of the nuclear spins, effectively storing over 190 characters. This approach illustrates that information can be retained not in space but through time, based on the orientation of the spins at specific moments.
Moon expressed enthusiasm about the implications of this research, stating, “While there isn’t an immediate, straightforward application yet, the idea itself is fascinating that disorder in a non-periodic drive can actually store information while preserving long-time order.” He compared the phenomenon to the structural information stored in ice, where oxygen positions are ordered, but hydrogen bonds remain disordered.
The researchers suggest that the tunable nature of this disorder may make the system promising for developing quantum sensors that are selectively sensitive to specific frequency ranges. This work broadens the landscape of non-equilibrium temporal order beyond traditional time crystals and includes related phenomena with deterministic aperiodic drives like the Thue-Morse and Fibonacci sequences.
Looking ahead, Moon indicated that the research team is exploring alternative material platforms beyond diamond, including pentacene-doped molecular crystals, which could enhance sensitivity through hydrogen-1 nuclear spins. He concluded, “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 research represents a significant step in understanding and utilizing temporal phenomena, paving the way for future innovations in quantum technology.
