Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
arXiv:2103.01808 · doi:10.21468/SciPostPhys.12.3.097
Abstract
Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments.
Resubmission to SciPost. 58 pages, 8 figures. Comments are welcome
References in corpus (46)
- Many-Body Physics with Ultracold Gases
- Equilibrium states of generic quantum systems subject to periodic driving
- Strong dissipation inhibits losses and induces correlations in cold molecular gases
- Dephasing and the steady state in quantum many-particle systems
- Quantum Zeno dynamics: mathematical and physical aspects
- A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
- Emergent SU(2) dynamics and perfect quantum many-body scars
- Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics
- Ultracold fermions and the SU(N) Hubbard model
- Non-Markovian generalization of the Lindblad theory of open quantum systems
- Variational principle for steady states of dissipative quantum many-body systems
- Quantum Many-Body Scar States with Emergent Kinetic Constraints and Finite-Entanglement Revivals
- Nuclear Spin Effects in Optical Lattice Clocks
- Non-equilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission
- Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
- Quantum synchronization of two Van der Pol oscillators
- Analysis of quantum semigroups with GKS--Lindblad generators II. General
- Eta-pairing states as true scars in an extended Hubbard Model
- Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems
- Limit cycle phase in driven-dissipative spin systems
- Dissipation-induced instabilities of a spinor Bose-Einstein condensate inside an optical cavity
- Coherent multi-flavour spin dynamics in a fermionic quantum gas
- A proposal for realising quantum scars in the tilted 1D Fermi-Hubbard model
- Quantum synchronization in dimer atomic lattices
- Probing the spectral density of a dissipative qubit via quantum synchronization
- Dynamical phases and quantum correlations in an emitter-waveguide system with feedback
- Observing quantum synchronization blockade in circuit quantum electrodynamics
- Exact solutions of interacting dissipative systems via weak symmetries
- Magnetism and domain formation in SU(3)-symmetric multi-species Fermi mixtures
- Light scattering and dissipative dynamics of many fermionic atoms in an optical lattice
- Absolutely Stable Spatiotemporal Order in Noisy Quantum Systems
- Breaking strong symmetries in dissipative quantum systems: Bosonic atoms coupled to a cavity
- Transient Synchronisation and Quantum Coherence in a Bio-Inspired Vibronic Dimer
- Synchronisation phase as an indicator of persistent quantum correlations between subsystems
- Synchronization transition in dipole-coupled two-level systems with positional disorder
- Interorbital Interactions in an SU(2)xSU(6)-Symmetric Fermi-Fermi Mixture
- Dissipative nonequilibrium synchronization of topological edge states via self-oscillation
- Secure and efficient synchronization scheme for quantum key distribution
- Time Crystals in the Driven Transverse Field Ising Model under Quasiperiodic Modulation
- Exact solutions of open integrable quantum spin chains
- Synchronization Behavior in a Ternary Phase Model
- Perfect quantum-state synchronization
- Vulnerability of the Synchronization Process in the Quantum Key Distribution System
- Correspondence between dissipative phase transitions of light and time crystals
- Dynamical l-bits in Stark many-body localization
- Seeding crystallization in time
Cited by in corpus (64)
- Dissipative time crystal in a strongly interacting Rydberg gas
- Group theoretic approach to many-body scar states in fermionic lattice models
- Universality in driven open quantum matter
- Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
- Topological synchronization of quantum van der Pol oscillators
- Observing Quantum Synchronization of a Single Trapped-Ion Qubit
- Observation of quantum phase-synchronization in a nuclear spin-system
- Quantum nonreciprocal interactions via dissipative gauge symmetry
- Universal phenomenology at critical exceptional points of nonequilibrium models
- Quantum Origin of Limit Cycles, Fixed Points, and Critical Slowing Down
- Nonequilibrium Criticality at the Onset of Time-Crystalline Order
- Quantum non-stationary phenomena of spin systems in collision models
- Quantum many-body scars in spin models with multibody interactions
- Emergence and Dynamical Stability of Charge Time-Crystal in a Current-Carrying Quantum Dot Simulator
- Symmetries and Synchronization Blockade
- Macroscopic quantum synchronization effects
- Self-organized Limit Cycles in Red-detuned Atom-cavity Systems
- Quantum thermodynamics of boundary time-crystals
- Realizing limit cycles in dissipative bosonic systems
- Dissipative time crystals originating from parity-time symmetry
- Synchronization of persistent oscillations in spin systems with non-local dissipations
- Half-integer vs. integer effects in quantum synchronization of spin systems
- Symmetry enforced entanglement in maximally mixed states
- Nonequilibrium transition between dissipative time crystals
- Dynamics of inhomogeneous spin ensembles with all-to-all interactions: breaking permutational invariance
- Measurement-Induced Quantum Synchronization and Multiplexing
- Exact eigenstates of multicomponent Hubbard models: SU() magnetic pairing, weak ergodicity breaking, and partial integrability
- Criteria for Davies Irreducibility of Markovian Quantum Dynamics
- Topological quantum synchronization of fractionalized spins
- Quantum Effects on the Synchronization Dynamics of the Kuramoto Model
- Nonstabilizerness of a Boundary Time Crystal
- Time periodicity from randomness in quantum systems
- Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak
- Self-trapping phenomenon, multistability and chaos in open anisotropic Dicke dimer
- Criticality and Rigidity of Dissipative Discrete Time Crystals in Solids
- Perfect quantum-state synchronization
- Controlling the dynamics of atomic correlations via the coupling to a dissipative cavity
- Energetic cost for speedy synchronization in non-Hermitian quantum dynamics
- Exploring Quantum Synchronization with a Composite Two-Qubit Oscillator
- Non-equilibration, synchronization, and time crystals in isotropic Heisenberg models
- Predicting the Onset of Quantum Synchronization Using Machine Learning
- Kardar-Parisi-Zhang scaling in time-crystalline matter
- Lie Algebraic Quantum Phase Reduction
- Non-equilibrium boundary driven quantum systems: models, methods and properties
- Exploiting nonequilibrium phase transitions and strong symmetries for continuous measurement of collective observables
- Quantum Synchronization of Twin Limit-Cycle Oscillators
- Transfer of quantum states and stationary quantum correlations in a hybrid optomechanical network
- Impact of quantum noise on phase transitions in an atom-cavity system with limit cycles
- Torus bifurcation of a dissipative time crystal
- Opening Krylov space to access all-time dynamics via dynamical symmetries
- The time crystal phase emerges from the qubit network under unitary random operations
- Quantum synchronization in one-dimensional topological systems
- Time Crystals from single-molecule magnet arrays
- Protecting coherence from the environment via Stark many-body localization in a Quantum-Dot Simulator
- Quantum synchronization in an all-optical stroboscopic quantum simulator
- Boundary dissipative spin chains with partial solvability inherited from system Hamiltonians
- Symmetry-induced fragmentation and dissipative time crystal
- Quantum spin van der Pol oscillator -- a spin-based limit-cycle oscillator exhibiting quantum synchronization
- Stability of emergent time periodicity in a few-body interacting system
- Synchronized Aharonov-Bohm Motifs via Engineered Dissipation
- Auxiliary-state facilitated phase synchronization phenomena in isolated spin systems
- Signatures of Environment-Induced Quantum Synchronization Transitions via Two-body Dissipator Engineering
- Synchronizing microwave cQED limit-cycle oscillators
- Quantum limit cycles and synchronization from a measurement perspective