Time-Quasicrystals Dynamically Protected Topological Phases in Driven Dissipative Systems

The classification of phases of matter has been revolutionised by topological order and nonequilibrium phenomena such as time crystals. However, a unified framework connecting temporal order, topology, and dissipation remains elusive. Here we introduce the concept of "Time-Quasicrystals"-non-equilibrium topological phases that exhibit quasi-periodic temporal order protected by dissipative dynamics. These phases emerge in driven dissipative quantum systems through the interplay of Floquet engineering and non-local dissipation, leading to an effective non-Hermitian Floquet Hamiltonian with topological edge modes in the frequency domain. We demonstrate three hallmarks of Time-Quasicrystals: (1) fractal-like temporal correlations with multiple incommensurate frequencies, (2) a quantised topological invariant robust against disorder, and (3) algebraically decaying memory of phase perturbations. We provide explicit experimental realisations in Rydberg atom arrays and circuit quantum electrodynamics platforms. Our work establishes Time-Quasicrystals as a bridge between topological phases, time crystals, and quantum simulation, opening pathways to dissipativeprotected quantum memory and novel non-equilibrium quantum phenomena.The classification of phases of matter has been revolutionised by topological order and nonequilibrium phenomena such as time crystals. However, a unified framework connecting temporal order, topology, and dissipation remains elusive. Here we introduce the concept of "Time-Quasicrystals"-non-equilibrium topological phases that exhibit quasi-periodic temporal order protected by dissipative dynamics. These phases emerge in driven dissipative quantum systems through the interplay of Floquet engineering and non-local dissipation, leading to an effective non-Hermitian Floquet Hamiltonian with topological edge modes in the frequency domain. We demonstrate three hallmarks of Time-Quasicrystals: (1) fractal-like temporal correlations with multiple incommensurate frequencies, (2) a quantised topological invariant robust against disorder, and (3) algebraically decaying memory of phase perturbations. We provide explicit experimental realisations in Rydberg atom arrays and circuit quantum electrodynamics platforms. Our work establishes Time-Quasicrystals as a bridge between topological phases, time crystals, and quantum simulation, opening pathways to dissipativeprotected quantum memory and novel non-equilibrium quantum phenomena.

Mar 17, 20260 citations

Dissipative Floquet Time Quasicrystals with Topological Temporal Order

S. N. PRAJAPATI

Abstract The discovery of time crystals and topological phases has fundamentally altered our understanding of quantum matter, yet a unified framework that combines temporal quasi-order, topological protection, and engineered dissipation remains a central challenge. Here we introduce Floquet-engineered dissipative time quasicrystals (FDTCs) —a class of nonequilibrium topological phases that emerge from the synergy of quasi-periodic driving, non-local dissipation, and non-Hermitian topology. Using a combination of Floquet-Lindblad theory and frequency-space topology, we demonstrate that FDTCs exhibit three defining hallmarks: (i) fractal temporal correlations with multiple incommensurate frequencies, (ii) a quantized topological invariant robust against disorder, and (iii) algebraically decaying memory of phase perturbations—a signature of intrinsic protection. We establish a general theoretical framework mapping quasi-periodically driven dissipative systems to non-Hermitian tight-binding models on synthetic frequency lattices, revealing topological edge modes in the frequency domain that manifest as persistent temporal order. We provide explicit experimental blueprints for two leading quantum platforms: parametrically driven superconducting qubit arrays and Rydberg atom chains with structured dissipation. Numerical simulations validate the phase diagram, showing that FDTCs occupy a distinct region bounded by trivial dissipative dynamics, conventional time crystals, and thermal phases. Our work establishes FDTCs as a bridge between topological matter, non-equilibrium physics, and quantum simulation, opening pathways to dissipationprotected quantum memory, topologically robust frequency combs, and novel non-Hermitian quantum technologies.Abstract The discovery of time crystals and topological phases has fundamentally altered our understanding of quantum matter, yet a unified framework that combines temporal quasi-order, topological protection, and engineered dissipation remains a central challenge. Here we introduce Floquet-engineered dissipative time quasicrystals (FDTCs) —a class of nonequilibrium topological phases that emerge from the synergy of quasi-periodic driving, non-local dissipation, and non-Hermitian topology. Using a combination of Floquet-Lindblad theory and frequency-space topology, we demonstrate that FDTCs exhibit three defining hallmarks: (i) fractal temporal correlations with multiple incommensurate frequencies, (ii) a quantized topological invariant robust against disorder, and (iii) algebraically decaying memory of phase perturbations—a signature of intrinsic protection. We establish a general theoretical framework mapping quasi-periodically driven dissipative systems to non-Hermitian tight-binding models on synthetic frequency lattices, revealing topological edge modes in the frequency domain that manifest as persistent temporal order. We provide explicit experimental blueprints for two leading quantum platforms: parametrically driven superconducting qubit arrays and Rydberg atom chains with structured dissipation. Numerical simulations validate the phase diagram, showing that FDTCs occupy a distinct region bounded by trivial dissipative dynamics, conventional time crystals, and thermal phases. Our work establishes FDTCs as a bridge between topological matter, non-equilibrium physics, and quantum simulation, opening pathways to dissipationprotected quantum memory, topologically robust frequency combs, and novel non-Hermitian quantum technologies.

Apr 6, 20260 citations

Experimental Realization of Discrete Time Quasicrystals

G. He, Bingtian Ye, Ruotian Gong +5 more

Floquet (periodically driven) systems can give rise to unique nonequilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: What other novel phases can manifest when the constraint of time periodicity is relaxed? In this study, we explore quantum systems subjected to a quasiperiodic drive. Leveraging a strongly interacting spin ensemble in diamond, we identify the emergence of long-lived discrete time quasicrystals. Unlike conventional time crystals, time quasicrystals exhibit robust subharmonic responses at multiple incommensurate frequencies. Furthermore, we show that the multifrequency nature of the quasiperiodic drive allows for the formation of diverse patterns associated with different discrete time quasicrystalline phases. Our findings demonstrate the existence of nonequilibrium phases in quasi-Floquet settings, significantly broadening the catalog of novel phenomena in driven many-body quantum systems.Floquet (periodically driven) systems can give rise to unique nonequilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: What other novel phases can manifest when the constraint of time periodicity is relaxed? In this study, we explore quantum systems subjected to a quasiperiodic drive. Leveraging a strongly interacting spin ensemble in diamond, we identify the emergence of long-lived discrete time quasicrystals. Unlike conventional time crystals, time quasicrystals exhibit robust subharmonic responses at multiple incommensurate frequencies. Furthermore, we show that the multifrequency nature of the quasiperiodic drive allows for the formation of diverse patterns associated with different discrete time quasicrystalline phases. Our findings demonstrate the existence of nonequilibrium phases in quasi-Floquet settings, significantly broadening the catalog of novel phenomena in driven many-body quantum systems.

arXiv:2403.17842Physical Review XMar 12, 202529 citations

Observation of discrete time quasicrystal in Rydberg atomic gases

Dong-Yang Zhu, Zheng-Yuan Zhang, Qi-Feng Wang +17 more

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 ${{\mathbb{Z}}}_{m}\times {{\mathbb{Z}}}_{n}$ . 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 ${{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{3}$ -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.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 $${{\mathbb{Z}}}_{m}\times {{\mathbb{Z}}}_{n}$$. 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 $${{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{3}$$-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.

arXiv:2509.21248Nature CommunicationsJul 29, 20261 citation

Dissipation stabilizes Dicke Time Quasicrystals

Sk Anisur, Shuva Mondal, Tanaya Ray +1 more

Quasi-periodic driving protocols provide a powerful route to realize novel non-equilibrium phases of matter beyond the Floquet paradigm. However, these protocols inevitably lead to infinite-temperature heat death in isolated systems, which poses a major challenge to their experimental realization. We demonstrate that dissipation can be harnessed to stabilize quasi-periodically driven systems, enabling the realization of robust non-equilibrium phases. Using the paradigmatic open Dicke model, we provide a blueprint for realizing a stable time quasicrystal (TQC) by Fibonacci driving. This TQC is characterized by a robust sub-harmonic quasi-periodic response that is dictated by, but qualitatively distinct from the external Fibonacci drive. By directly analyzing the time evolution in the thermodynamic limit, we establish the existence of TQC order in this system for a wide parameter regime. We trace the origin of the stability of the TQC to the attractor structure induced by dissipation. Strikingly, the TQC order persists in the deep quantum regime with as few as two qubits. We systematically study the dependence of the TQC lifetime, $τ^{\ast}$ , on the number of qubits and demonstrate that $τ^{\ast}$ increases monotonically with the system size. Crucially, the TQC is not observed in the absence of dissipation. Our work establishes dissipation as a mechanism for stabilizing non-equilibrium phases of matter under quasi-periodic drive.Quasi-periodic driving protocols provide a powerful route to realize novel non-equilibrium phases of matter beyond the Floquet paradigm. However, these protocols inevitably lead to infinite-temperature heat death in isolated systems, which poses a major challenge to their experimental realization. We demonstrate that dissipation can be harnessed to stabilize quasi-periodically driven systems, enabling the realization of robust non-equilibrium phases. Using the paradigmatic open Dicke model, we provide a blueprint for realizing a stable time quasicrystal (TQC) by Fibonacci driving. This TQC is characterized by a robust sub-harmonic quasi-periodic response that is dictated by, but qualitatively distinct from the external Fibonacci drive. By directly analyzing the time evolution in the thermodynamic limit, we establish the existence of TQC order in this system for a wide parameter regime. We trace the origin of the stability of the TQC to the attractor structure induced by dissipation. Strikingly, the TQC order persists in the deep quantum regime with as few as two qubits. We systematically study the dependence of the TQC lifetime, $τ^{\ast}$, on the number of qubits and demonstrate that $τ^{\ast}$ increases monotonically with the system size. Crucially, the TQC is not observed in the absence of dissipation. Our work establishes dissipation as a mechanism for stabilizing non-equilibrium phases of matter under quasi-periodic drive.

quant-pharXiv:2602.05994Feb 6, 20260 citations

Topological Thermodynamics of Driven Dissipative Quantum Materials

Revista, Zen, PHYSICS, 10

This paper explores topological thermodynamics in driven dissipative quantum materials, a field at the intersection of non-equilibrium statistical mechanics, quantum topology, and condensed matter physics. We review theoretical frameworks and experimental advancements, highlighting how driving forces and dissipative processes influence the formation, stability, and characterization of topological phases. A special focus is placed on Floquet engineering for open quantum systems, where periodic driving and environmental coupling lead to novel non-equilibrium steady states with exotic topological properties. We discuss challenges in defining thermodynamic quantities like temperature and entropy in these far-from-equilibrium settings and examine how topological invariants manifest in dissipative dynamics and transport. The paper uniquely synthesizes advancements in periodically driven, open quantum systems by critically examining how dissipation, often seen as detrimental, can be precisely engineered to reveal or even stabilize topological order. This offers a distinct perspective on designing next-generation quantum technologies. Key theoretical tools, including generalized Floquet theory, Keldysh formalism, and non-Hermitian descriptions, are discussed alongside experimental platforms like photonic quantum gases and cold atomic systems.This paper explores topological thermodynamics in driven dissipative quantum materials, a field at the intersection of non-equilibrium statistical mechanics, quantum topology, and condensed matter physics. We review theoretical frameworks and experimental advancements, highlighting how driving forces and dissipative processes influence the formation, stability, and characterization of topological phases. A special focus is placed on Floquet engineering for open quantum systems, where periodic driving and environmental coupling lead to novel non-equilibrium steady states with exotic topological properties. We discuss challenges in defining thermodynamic quantities like temperature and entropy in these far-from-equilibrium settings and examine how topological invariants manifest in dissipative dynamics and transport. The paper uniquely synthesizes advancements in periodically driven, open quantum systems by critically examining how dissipation, often seen as detrimental, can be precisely engineered to reveal or even stabilize topological order. This offers a distinct perspective on designing next-generation quantum technologies. Key theoretical tools, including generalized Floquet theory, Keldysh formalism, and non-Hermitian descriptions, are discussed alongside experimental platforms like photonic quantum gases and cold atomic systems.

Nov 28, 20250 citations

{{\mathbb{Z}}}_{m}\times {{\mathbb{Z}}}_{n}

. 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

{{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{3}

-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.

τ^{\ast}

, on the number of qubits and demonstrate that

τ^{\ast}

increases monotonically with the system size. Crucially, the TQC is not observed in the absence of dissipation. Our work establishes dissipation as a mechanism for stabilizing non-equilibrium phases of matter under quasi-periodic drive.