Scientists observe a new form of temporal order

In a new study published in Natural physicsResearchers have made the first experimental observation of a temporal rondeau crystal, a new phase of matter where long-range temporal order coexists with short-term disorder.

Named after the classical musical form where a repeating theme alternates with contrasting variations (such as Mozart’s Rondo alla Turca), the temporal rondeau crystal exhibits perfectly periodic behavior at specific bar times while showing controllable random fluctuations between these intervals.

“The motivation for this research comes from how order and variation coexist in art and nature,” explained Leo Moon, a third-year PhD in applied science and technology. student at UC Berkeley and co-author of the study. “Repetitive periodic patterns appear naturally in early art forms due to their simplicity, while more advanced music and poetry create complex variations against a monotonous background.”

The analogy extends beyond aesthetics and art. Even familiar substances like ice exhibit this duality: the oxygen atoms form a crystal lattice while the hydrogen nuclei remain randomly arranged. Similarly, time crystals discovered over the past decade break the symmetry of time translation by exhibiting long-duration periodic oscillations.

However, until now, explorations of nonperiodic time order have focused on deterministic models, such as quasicrystals. The rondeau crystal is the first to combine stroboscopic order with controllable random disorder.

Create a new phase of matter

The researchers used the nuclear spins of carbon-13 in diamond as a quantum simulator. The system consisted of randomly positioned nuclear spins at room temperature, interacting via long-range dipole-dipole couplings.

The researchers began by hyperpolarizing the nuclear spins of carbon-13 using a technique that exploits nitrogen vacancy (NV) centers, which are defects in diamond where a nitrogen atom sits next to an empty lattice site.

When illuminated by a laser, these NV centers become spin polarized, and this polarization can be transferred to surrounding nuclear spins via microwave pulses. This 60-second process increased the nuclear spin polarization nearly 1,000 times above its thermal equilibrium value, creating a powerful signal that could be tracked for long periods of time.

Following this, sophisticated microwave pulse sequences were applied, combining protective “spin lock” pulses with strategically timed polarization reversal pulses. This structured but partially random pattern of conduct created the rondeau order.

The researchers used a new control system, which uses an arbitrary waveform generator with extensive sequence memory. This meant the system could execute more than 720 different pulses in one go, which is essential for creating the structured but non-periodic drives that generate the rondeau order in the crystal.

“The diamond lattice with carbon-13 nuclear spins provides an ideal setting for exploring these exotic time phases, because it naturally combines stability, strong interactions and easy reading,” Moon explained. “Diamond itself is incredibly stable: it does not react chemically, it is insensitive to temperature changes and it protects the towers well from external noise.”

The researchers deployed what they call random multipolar drives, or RMDs. These are structured sequences where randomness can be systematically controlled.

At regular intervals during the training cycle, the nuclear spins reversed their polarization deterministically, exhibiting the periodic behavior characteristic of time crystals. But halfway between these regular measurements, the polarization fluctuated randomly, showing no predictable pattern. This coexistence of long-range predictable order and short-term random fluctuations is the hallmark of rondeau order.

The smoking gun

The team observed that this roundel order was maintained for more than 170 periods, or more than four seconds.

The discrete Fourier transform of the dynamics provided proof of the new phase. Unlike conventional discrete time crystals, which exhibit a single sharp peak in their frequency spectrum, the time rondeau crystal exhibited a smooth, continuous distribution across all frequencies.

This “irrefutable” signature confirmed the coexistence of temporal order and disorder.

“The Rondeau order shows that order and disorder do not have to be opposites: they can actually coexist in a stable, driven quantum system,” Moon said.

The researchers managed to control the behavior of the system. Varying the drive parameters allowed them to plot a detailed phase diagram of the roundel order stability. The lifetime could be adjusted by adjusting the driving period and pulse imperfections. Heating rates followed the expected quadratic and linear scaling laws.

Enlarge the landscape

The team also demonstrated that information could be encoded in temporal disorder.

By designing specific sequences of motor pulses, they encoded the paper title, “Experimental observation of a temporal rondeau crystal. Temporal disorder in spatiotemporal order,” in the dynamics of nuclear spin micromotions, storing more than 190 characters.

In other words, information is stored not in space but in time, coded according to whether the spins point up or down at specific times in each cycle.

“There is no direct, immediate application yet, but the idea itself is fascinating: disorder in a non-periodic drive can actually store information while preserving order in the long term,” Moon said. “It’s a bit like the analogy between water and ice: the ice has ordered the oxygen positions but has disordered the hydrogen bonds, and this local randomness contains structural information.”

The researchers suggest that the tunability of the disorder could make this platform attractive for designing quantum sensors selectively sensitive to specific frequency ranges.

The work expands the observed landscape of non-equilibrium temporal order beyond conventional time crystals. Using the same experimental platform, the team also demonstrated related phenomena with deterministic aperiodic drives, including the Thue-Morse sequence and the Fibonacci sequence, experimentally realizing aperiodic time crystals and time quasicrystals alongside rondeau order.

Looking ahead, Moon mentioned that the team is exploring alternative material platforms beyond diamond, including pentacene-doped molecular crystals where hydrogen-1 nuclear spins provide increased sensitivity.

“On a more applied level, exploiting tunable disorder in such systems could pave the way for practical quantum sensors or memory devices exploiting stability in the time domain,” Moon noted.

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