Time crystals: a review

2017/04/30 by Krzysztof Sacha, Jakub Zakrzewski · 470 citations
Computer Science · Engineering · Physics and Astronomy · #Control and Stability of Dynamical Systems #Discrete time and continuous time #Domain (mathematical analysis) #Nonlinear Dynamics and Pattern Formation #Quantum many-body systems #Time domain #Translation (biology) #cond-mat.dis-nn #cond-mat.mes-hall #cond-mat.quant-gas #quant-ph

paper · pdf · doi:10.1088/1361-6633/aa8b38

published in Reports on Progress in Physics 81(1), 016401 (IOP Publishing) · VIDEO ABSTRACT: https://youtu.be/5uaUEWH0x60

openalex created_date 2017/04/28 · openalex publication_date 2017/09/08 · arxiv created 2018/01/18 · arxiv updated 2018/01/19 · openalex updated_date 2026/08/05

Abstract

Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental verifications of discrete (or Floquet) time crystals-the structures that appear in the time domain due to spontaneous breaking of discrete time translation symmetry. The struggle to observe discrete time crystals is reviewed here together with propositions that generalize this concept introducing condensed matter like physics in the time domain. We shall also revisit the original Wilczek's idea and review strategies aimed at spontaneous breaking of continuous time translation symmetry.

Citations

• Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time
• Light-induced gauge fields for ultracold atoms

Cited by

• Observation of period doubling and higher multiplicities in a driven single-spin system
• Discrete Time Crystals in Actively Mode-Locked Lasers
• Three-stage melting of a macroscopic continuous spacetime crystal
• Emergent ac Effect in Nonreciprocal Coupled Condensates
• Frequency comb behavior of time crystals in an rf-driven dissipative Rydberg system
• On prethermal time crystals from semi-holography
• Analytical quantification of strongly disordered discrete time crystals
• Classifying one-dimensional Floquet phases through two-dimensional topological order
• Tunable discrete quasi-time crystal from a single drive
• Exploring nonlinear dynamics in periodically driven time crystal from synchronization to chaotic motion
• The Boundary Time Crystal as a light source for collectively enhanced sensing
• Breakdown of adiabaticity in topological quantum liquids
• Optically-Induced Faraday-Goldstone Waves
• Harnessing Floquet dynamics for selective metrology in few-qubit systems
• Higher-order discrete time crystals in a quantum chaotic top
• Spatiotemporal crystallization of an active fluid
• Boundary Time Crystals: Beyond Mean-Field Theory
• Plasmonic metamaterial time crystal
• Fock space prethermalization and time-crystalline order on a quantum processor
• Nonlinear magnetization dynamics as a route to nonreciprocal phases, spin superfluidity, and analogue gravity
• Tunable quantum Mpemba effect in long-range interacting systems
• Localized structures in two-field systems: exact solutions in the presence of Lorentz symmetry breaking and explicit connection with geometric constraints
• Steering spin fluctuations in lattice systems via two-tone Floquet engineering
• Observation of Discrete Time Quasicrystal in Rydberg Atomic Gases
• Observation of Moiré Time Crystal in Floquet-driven Rydberg Atomic Gases
• A model for intertwined orders in cuprates
• Quantum recurrences and the arithmetic of Floquet dynamics
• Nonreciprocal and Geometric Frustration in Dissipative Quantum Spins
• Heating suppression via two-rate random and quasiperiodic drive protocols
• Space-time crystals from particle-like topological solitons
• Eight-fold classification of superconducting orders
• Analytical solution of boundary time crystals via the superspin basis
• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
• Running Quantum Computers in Discovery Mode
• Collective Excitations of Dissipative Time Crystals
• Anomalous slow-down of the bound state dynamics in a non-locally coupled quantum circuit
• Time Glasses: Symmetry Broken Chaotic Phase with a Finite Gap
• Bridging the classical and quantum regimes in a dissipative Ising chain
• Exact analysis of AC sensors based on Floquet time crystals
• Walsh-Floquet Theory of Periodic Kick Drives
• Mechanical metamaterials
• Quantum Time Crystal Clock and its Performance
• Designing open quantum systems for enabling quantum enhanced sensing through classical measurements
• Discrete time crystal for periodic-field sensing with quantum-enhanced precision
• Topological Time Crystals
• Synchronization in coherently and dissipatively coupled spinor polariton time crystals
• Time crystals in cavity-BEC systems
• Discrete time crystals detected by time-translation twist
• Floquet Many-Body Cages
• Time Crystal Platform: From Quasicrystal Structures in Time to Systems with Exotic Interactions
• Driving-induced metamorphosis of transport in arrays of coupled resonators
• Emergent limit cycles and time crystal dynamics in an atom-cavity system
• Time crystals in a shaken atom-cavity system
• Classical Many-Body Time Crystals
• Theory of coupled parametric oscillators beyond coupled Ising spins
• Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
• Polynomial filter diagonalization of large Floquet unitary operators
• Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries
• Nonreciprocal wave-mediated interactions power a classical time crystal
• Injection locking of Rydberg dissipative time crystals
• Proximate integrability and exact revivals in staggered Rydberg ladders
• Dynamical quantum phase transitions in collapse and revival oscillations of a quenched superfluid
• Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets
• Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation
• Open Quantum-System Simulation of Faraday's Induction Law via Dynamical Instabilities
• Provenance of classical Hamiltonian time crystals
• Simulating complex quantum networks with time crystals
• Observation of a Dissipative Time Crystal
• Stroboscopic aliasing in long-range interacting quantum systems
• Many-body cages: disorder-free glassiness from flat bands in Fock space, and many-body Rabi oscillations
• Floquet realization of prethermal Meissner phase in a two-leg flux ladder
• Seeding Crystallization in Time
• Regularizations of time-crystal dynamics. [europepmc]
• Simulating complex quantum networks with time crystals. [europepmc]
• Higher-order and fractional discrete time crystals in clean long-range interacting systems. [europepmc]
• Topological Atomic Chains on 2D Hybrid Structure. [europepmc]
• Space-time crystalline order of a high-critical-temperature superconductor with intrinsic Josephson junctions. [europepmc]
• Time-crystalline eigenstate order on a quantum processor. [europepmc]
• Realization of a discrete time crystal on 57 qubits of a quantum computer. [europepmc]
• Time crystal dynamics in a weakly modulated stochastic time delayed system. [europepmc]
• Nonlinear two-level dynamics of quantum time crystals. [europepmc]
• Digital quantum simulation of Floquet symmetry-protected topological phases. [europepmc]
• Thermal control of the topological edge flow in nonlinear photonic lattices. [europepmc]
• Quantum physics in connected worlds. [europepmc]
• Non-Hermitian Floquet Topological Matter-A Review. [europepmc]
• Creating and controlling global Greenberger-Horne-Zeilinger entanglement on quantum processors. [europepmc]
• Generation of patterns and higher harmonics in 1D quantum droplets in tilted and driven quasi-periodic confinements. [europepmc]
• Higher-order and fractional discrete time crystals in Floquet-driven Rydberg atoms. [europepmc]
• Spin-controlled photonics via temporal anisotropy. [europepmc]
• Bifurcation of time crystals in driven and dissipative Rydberg atomic gas. [europepmc]
• Exploring nonlinear dynamics in periodically driven time crystal from synchronization to chaotic motion. [europepmc]
• Temporal localization of optical waves supported by a copropagating quasiperiodic structure. [europepmc]
• Quasi-Discrete Time Crystals in the Quasiperiodically Driven Lipkin-Meshkov-Glick Model. [europepmc]
• Continuous time crystal coupled to a mechanical mode as a cavity-optomechanics-like platform. [europepmc]
• Observation of continuous time crystals and quasi-crystals in spin gases. [europepmc]
• Sensing with discrete time crystals. [europepmc]
• Temporal Effects of Surface Plasmon Polaritons in a Quantum Plasma Slab. [europepmc]

Related

• A Brief History of Time Crystals
• Absence of Quantum Time Crystals
• Quantum Time Crystal Clock and its Performance
• Observation of a Discrete Time Crystal
• Formation of Tesseract Time Crystals on a Quantum Computer