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arXiv:2404.05620 · Nature Physics

Experimental observation of a time rondeau crystal

Leo Joon Il Moon, Paul M. Schindler, Yizhe Sun, Emanuel Druga, Johannes Knolle, Roderich Moessner, Hongzheng Zhao, Marin Bukov, Ashok Ajoy

Published Oct 14, 2025• 12 citations
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Abstract

Abstract Conventional phases of matter can be characterized by the symmetries they break, one example being water ice whose crystalline structure breaks the continuous translation symmetry of space. Recently, breaking of time-translation symmetry was observed in non-equilibrium systems, producing so-called time crystals. Here we investigate different kinds of partial temporal ordering, stabilized by non-periodic yet structured drives, which we call the rondeau order. Using carbon-13 nuclear spins in diamond as a quantum simulator, we use microwave driving fields to create tunable short-time disorder in a system exhibiting long-time stroboscopic order. Our spin control architecture allows us to implement a family of driving fields including periodic, aperiodic and structured random drives. We use a high-throughput read-out scheme to continuously observe the spin polarization and its rondeau order, with controllable lifetimes exceeding 4 s. Using degrees of freedom associated with the short-time temporal disorder of rondeau order, we demonstrate the capacity to encode information in the response of observables. Our work broadens the landscape of observed non-equilibrium temporal order, and raises the prospect for the potential applications of driven quantum matter.

DOI
10.1038/s41567-025-03028-y

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Abstract Conventional phases of matter can be characterized by the symmetries they break, one example being water ice whose crystalline structure breaks the continuous translation symmetry of space. Recently, breaking of time-translation symmetry was observed in non-equilibrium systems, producing so-called time crystals. Here we investigate different kinds of partial temporal ordering, stabilized by non-periodic yet structured drives, which we call the rondeau order. Using carbon-13 nuclear spins in diamond as a quantum simulator, we use microwave driving fields to create tunable short-time disorder in a system exhibiting long-time stroboscopic order. Our spin control architecture allows us to implement a family of driving fields including periodic, aperiodic and structured random drives. We use a high-throughput read-out scheme to continuously observe the spin polarization and its rondeau order, with controllable lifetimes exceeding 4 s. Using degrees of freedom associated with the short-time temporal disorder of rondeau order, we demonstrate the capacity to encode information in the response of observables. Our work broadens the landscape of observed non-equilibrium temporal order, and raises the prospect for the potential applications of driven quantum matter.
A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in crystals in space. Lots of experiments report the transition from a thermal equilibrium phase to time crystal phase. However, there is no experimental method to probe the bifurcation effect of distinct time crystals in quantum many-body systems. Here, in a driven and dissipative many-body Rydberg atom system, we observe multiple continuous dissipative time crystals and emergence of more complex temporal symmetries beyond the single time crystal phase. Bifurcation of time crystals in strongly interacting Rydberg atoms is observed; the process manifests as a transition from a time crystal state of long temporal order to one of short temporal order, or vice versa. By manipulating the driving field parameters, we observe the time crystal's bistability and a hysteresis loop. These investigations indicate new possibilities for control and manipulation of the temporal symmetries of non-equilibrium systems.
Driven systems offer the potential to realize a wide range of non-equilibrium phenomena that are inaccessible in static systems, such as the discrete time crystals. Time rondeau crystals with a partial temporal order have been proposed as a distinctive prethermal phase of matter in systems driven by structured random protocols. Yet, heating is inevitable in closed systems and time rondeau crystals eventually melt. We introduce dissipation to counteract heating and demonstrate stable time rondeau crystals, which persist indefinitely, in a many-body interacting system. A key ingredient is synchronization in the non-interacting limit, which allows for stable time rondeau order without generating excessive heating. The presence of many-body interaction competes with synchronization and a de-synchronization phase transition occurs at a finite interaction strength. This transition is well captured via a linear stability analysis of the underlying stochastic processes.
A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in conventional crystals. Lots of experiments report the transition from a thermal equilibrium phase to a time crystal phase. However, there is no experimental method to probe the bifurcation effect of distinct continuous time crystals in quantum many-body systems. Here, in a driven and dissipative many-body Rydberg atom system, we observe multiple continuous dissipative time crystals and emergence of more complex temporal symmetries beyond the single time crystal phase. Bifurcation of time crystals in strongly interacting Rydberg atoms is observed; the process manifests as a transition from a time crystal of long periodicity to a time crystal of short periodicity, or vice versa. By manipulating the driving field parameters, we observe the time crystal’s bistability and a hysteresis loop. These investigations indicate new possibilities for control and manipulation of the temporal symmetries of non-equilibrium systems. The time crystal is an exotic phase of matter where time-translational symmetry is broken. Here, the authors observe multiple continuous dissipative time crystals and bifurcation of time crystals in driven and dissipative Rydberg atomic gas.
Discrete time quasicrystals (DTQC) constitute a class of non-equilibrium matter characterized by temporal order without strict periodicity, in contrast to conventional time crystals. Investigating these phenomena is essential for expanding our fundamental understanding of far-from-equilibrium quantum matter and spontaneous symmetry breaking beyond periodic regimes. Here, we experimentally observe a DTQC in a driven-dissipative ensemble of strongly interacting Rydberg atoms, displaying non-equilibrium dynamical response with a different finite Abelian group symmetry Zm×Zn{{\mathbb{Z}}}_{m}\times {{\mathbb{Z}}}_{n}Zm​×Zn​. By applying a quasiperiodic drive using a dual-frequency drive with incommensurate frequencies, we demonstrate that the system exhibits a robust subharmonic response at multiple incommensurate frequencies, signifying the emergence of a DTQC phase. We map the full phase diagram of the system, which includes the DTQC phase, and demonstrate its rigidity against perturbations in both RF field intensity and laser detuning. Moreover, we observe a cyclic group symmetry effect that constrains the construction of Z2×Z3{{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{3}Z2​×Z3​-symmetric DTQC. This work establishes a versatile platform for studying non-equilibrium phases of matter and provides insights into the dynamics of time-translation symmetry breaking in quantum many-body systems. Time-crystal phases have raised both theoretical and experimental interest across various platforms. Here, the authors report the observation of a discrete time-quasicrystal in a driven-dissipative ensemble of interacting Rydberg atoms, advancing the understanding of symmetry breaking in these systems.
The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the many-body–localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.
A discrete time crystal is an out-of-equilibrium phase of matter characterized by the spontaneous breaking of discrete time-translation symmetry. Using extensive numerical simulations based on matrix-product-state methods, we provide evidence for discrete time-crystalline behavior in strongly disordered spin chains with Heisenberg interactions, including the isotropic point, subject to periodic driving. Starting from a many-body localized regime, we observe that rotations induced by delta kicks produce a pronounced subharmonic response at half the drive frequency in spin observables. We investigate the stability of this response against rotation-angle errors through entanglement entropy, quantum Fisher information, short-range spin correlations, and restricted-control ergotropy. Increasing the rotation error reveals an intermediate dynamical regime separating the time-crystalline and Floquet-localized responses. In this regime, most observables exhibit signatures of weakly correlated dynamics reminiscent of Anderson localization.