Scientists observe a new form of temporal order

In a new study published in Nature Physics, researchers achieved the first experimental observation of a time rondeau crystal—a novel phase of matter where long-range temporal order coexists with short-time disorder.

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

“The motivation for this research stems from how order and variation coexist across art and nature,” explained Leo Moon, a third-year Applied Science and Technology Ph.D. student at UC Berkeley and co-author of the study. “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 analogy extends beyond aesthetics and art. Even familiar substances like ice exhibit this duality—oxygen atoms form a crystalline lattice while hydrogen nuclei remain randomly arranged. Similarly, time crystals, discovered in the past decade, break time-translation symmetry by exhibiting long-lived periodic oscillations.

However, until now, explorations of non-periodic temporal order have focused on deterministic patterns, such as quasicrystals. The rondeau crystal is the first to combine stroboscopic order with controllable random disorder.

Creating a new phase of matter

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

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

When illuminated with a laser, these NV centers become spin-polarized, and this polarization can be transferred to the surrounding nuclear spins through microwave pulses. This 60-second process boosted the nuclear spin polarization nearly 1,000-fold above its thermal equilibrium value, creating a strong signal that could be tracked for extended periods.

Following this, sophisticated microwave pulse sequences were applied, combining protective “spin-locking” pulses with strategically timed polarization-flipping pulses. This structured but partially random driving pattern created the rondeau order.

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

“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,” explained Moon. “Diamond itself is incredibly stable—it doesn’t react chemically, it’s insensitive to temperature changes, and it shields the spins well from outside noise.”

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

At regular intervals during the drive cycle, the nuclear spins flipped 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 predictable long-range order and random short-time fluctuations is the hallmark of rondeau order.

The smoking gun

The team observed this rondeau order maintain itself for more than 170 periods, more than four seconds.

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

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 actually coexist in a stable, driven quantum system,” said Moon.

Researchers achieved control over the system’s behavior. Varying the drive parameters allowed them to map out an extensive phase diagram of rondeau order stability. The lifetime could be tuned by adjusting the drive period and pulse imperfections. Heating rates followed predicted quadratic and linear scaling laws.

Expanding the landscape

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

By engineering 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 micromotion dynamics of the nuclear spins, storing more than 190 characters.

In other words, information is stored not in space but in time, encoded in whether the spins point up or down at specific moments during each cycle.

“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,” Moon said. “It’s a bit like the analogy between water and ice: ice has ordered oxygen positions but disordered hydrogen bonds, and that local randomness carries structural information.”

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

The work broadens 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 Fibonacci sequence, experimentally realizing time aperiodic crystals and time quasicrystals alongside the 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 offer enhanced sensitivity.

“On a more applied front, 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,” Moon noted.

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