Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model

Abstract

Scrambling of quantum information is the process by which information initially stored in the local degrees of freedom of a quantum many-body system spreads over its many-body degrees of freedom, becoming inaccessible to local probes and thus apparently lost. Scrambling and entanglement are key concepts reconciling seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes, and have revolutionized our understanding of non-equilibrium phenomena. Here, we demonstrate that a family of fidelity out-of-time-order correlators (FOTOCs), recently measured in a trapped-ion quantum simulator via time reversal of the many-body dynamics followed by a fidelity measurement, can serve as a unifying diagnostic tool that elucidates the intrinsic connection between fast scrambling, volume law entanglement, ergodicity, quantum chaos, and the associated butterfly effect in the semiclassical dynamics of the system. We demonstrate the utility of FOTOCs by computing them in the Dicke model, an iconic model in quantum optics, recently implemented in atomic and trapped-ion setups. This model describes the coupling of a large spin to an oscillator and features rich behaviors, including a quantum phase transition and chaos. Here, we show that FOTOCs provide a direct measure of the spin-phonon Renyi entropy and quantum thermalization. Moreover, we connect the FOTOCs to the variance of simple operators, allowing us to observe fast scrambling in the parameter regime where the system's classical trajectories are chaotic, and to explicitly relate the quantum and classical Lyapunov exponents in a truly quantum many-body system. Our results open a path for the experimental use of FOTOCs to quantify fast scrambling, determine bounds on quantum information processing and to identify possible candidates of black hole analogs in controllable quantum systems.

arXiv comment17 pages, 7 figures. Additional references added to main text

References in corpus (55)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Black holes as mirrors: quantum information in random subsystems
• Quantum thermalization through entanglement in an isolated many-body system
• Fast Scramblers
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Entanglement, Non-linear Dynamics, and the Heisenberg Limit
• Quantum metrology from a quantum information science perspective
• Chaos and the Quantum Phase Transition in the Dicke Model
• Chaos in quantum channels
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Probing entanglement entropy via randomized measurements
• Phase space representation of quantum dynamics
• Fisher information and multiparticle entanglement
• Multipartite entanglement and high precision metrology
• Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Measuring the scrambling of quantum information
• Exploring Symmetry Breaking at the Dicke Quantum Phase Transition
• Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
• Dynamical phase transition in the open Dicke model
• The Lyapunov Characteristic Exponents and their computation
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Ergodic dynamics and thermalization in an isolated quantum system
• Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance
• Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
• Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems
• Measurement of many-body chaos using a quantum clock
• Loschmidt Echo for quantum metrology
• Relating out-of-time-order correlations to entanglement via multiple-quantum coherences
• Experimental observation of a phase transition in the evolution of many-body systems with dipolar interactions
• Excited-State Quantum Phase Transitions in Dicke Superradiance Models
• Verification of a many-ion simulator of the Dicke model through slow quenches across a phase transition
• Out-of-Time-Order Correlation at a Quantum Phase Transition
• Quantum chaos and effective thermalization
• Time-resolved observation of thermalization in an isolated quantum system
• Universality in volume law entanglement of pure quantum states
• Dicke model simulation via cavity-assisted Raman transitions
• Trapped Ion Quantum Information Processing with Squeezed Phonons
• Equilibration and macroscopic quantum fluctuations in the Dicke model
• Efficient entanglement criteria for discrete, continuous, and hybrid variables
• Classical chaos in atom-field systems
• Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2
• Simulating open quantum systems by applying SU(4) to quantum master equations
• Non-ergodicity in the Anisotropic Dicke model
• Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment
• Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model
• Scrambling in the Dicke model
• Boson-mediated quantum spin simulators in transverse fields: XY model and spin-boson entanglement
• Sensitivity to small perturbations in systems of large quantum spins

Cited by in corpus (145)

• Does scrambling equal chaos?
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
• Entanglement Devised Barren Plateau Mitigation
• Krylov complexity in saddle-dominated scrambling
• Barren plateaus preclude learning scramblers
• Excited-state quantum phase transitions
• Many-Body Chaos in the Sachdev-Ye-Kitaev Model
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Quantum Dynamics in Krylov Space: Methods and Applications
• Bridging entanglement dynamics and chaos in semiclassical systems
• Gauging classical and quantum integrability through out-of-time ordered correlators
• Improving Metrology with Quantum Scrambling
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Probing excited-state quantum phase transition in a quantum many body system via out-of-time-ordered correlator
• Three-level Dicke quantum battery
• Speed limits and locality in many-body quantum dynamics
• Nonlinear interferometry beyond classical limit facilitated by cyclic dynamics
• Quantum scrambling with classical shadows
• Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
• Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the Ehrenfest time-scale
• A cavity-QED simulator of slow and fast scrambling
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Observing Dynamical Quantum Phase Transitions through Quasilocal String Operators
• Out-of-time-order correlations and Floquet dynamical quantum phase transition
• Spread complexity in saddle-dominated scrambling
• Integrable and chaotic dynamics of spins coupled to an optical cavity
• The nonlinear semiclassical dynamics of the unbalanced, open Dicke model
• Quantum coherence as a signature of chaos
• Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator
• Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization
• Classical and quantum chaos in a three-mode bosonic system
• Quantum operator growth bounds for kicked tops and semiclassical spin chains
• Fast scrambling without appealing to holographic duality
• Random Matrix Theory of the Isospectral twirling
• Bound on quantum scrambling with all-to-all interactions
• Universal fluctuations and squeezing in generalized Dicke model near the superradiant phase transition
• Rényi Entropy Singularities as Signatures of Topological Criticality in Coupled Photon-Fermion Systems
• From integrability to chaos in quantum Liouvillians
• Detecting out-of-time-order correlations via quasi-adiabatic echoes as a tool to reveal quantum coherence in equilibrium quantum phase transitions
• Benchmarking Information Scrambling
• Observation of quantum thermalization restricted to Hilbert space fragments
• Out-of-time-order correlators and quantum phase transitions in the Rabi and Dicke model
• Chaos in the three-site Bose-Hubbard model -- classical vs quantum
• Scrambling and quantum chaos indicators from long-time properties of operator distributions
• Chaos and Thermalization in the Spin-Boson Dicke Model
• Quantum echo dynamics in the Sherrington-Kirkpatrick model
• Emergent decoherence induced by quantum chaos in a many-body system: A Loschmidt echo observation through NMR
• Optimal Frobenius light cone in spin chains with power-law interactions
• Inverted harmonic oscillator dynamics of the nonequilibrium phase transition in the Dicke model
• Engineering spin-spin interactions with optical tweezers in trapped ions
• Measuring out-of-time-ordered correlation functions without reversing time evolution
• Refined quantum Lyapunov exponents from replica out-of-time-order correlators
• Phase transitions of the anisotropic Dicke model
• Multifractality in quasienergy space of coherent states as a signature of quantum chaos
• Super-exponential scrambling of Out-of-time-ordered correlators
• Out-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approach
• Out-of-time-order correlator in the quantum Rabi model
• Subleading Bounds on Chaos
• Surprises in the Deep Hilbert Space of all-to-all systems: From super-exponential scrambling to slow entanglement growth
• Quantum localization measures in phase space
• Ergodicity breaking in an incommensurate system observed by OTOCs and Loschmidt Echoes: From quantum diffusion to sub-diffusion
• Thermalisation in a Bose-Hubbard dimer with modulated tunneling
• Experimental realization of the classical Dicke model
• Long-range-ordered phase in a quantum Heisenberg chain with interactions beyond nearest neighbors
• Quantum many-body dynamics on the star graph
• Dynamical route to ergodicity and quantum scarring in kicked coupled top
• Barren plateaus from learning scramblers with local cost functions
• Phase transitions of the Dicke model: a unified perspective
• Multipartite Entanglement: A Journey Through Geometry
• Quantifying scrambling in quantum neural networks
• A stroboscopic approach to trapped-ion quantum information processing with squeezed phonons
• Signatures of quantum chaos in an out-of-time-order tensor
• Energy-Resolved Information Scrambling in Energy-Space Lattices
• Many-body chaos near a thermal phase transition
• Far from equilibrium field theory for strongly coupled light and matter: dynamics of frustrated multi-mode cavity QED
• Multiparticle Entanglement Dynamics of Quantum Chaos in a Bose-Einstein condensate
• Operator growth bounds in a cartoon matrix model
• Classical and Quantum Chaos in Chirally-Driven, Dissipative Bose-Hubbard Systems
• Identification of quantum scars via phase-space localization measures
• Out of Time Order Correlations in the Quasi-Periodic Aubry-André model
• Stochastic Operator Variance: an observable to diagnose noise and scrambling
• Information propagation in one-dimensional XY-$\Gamma$ chains
• Eigenstate thermalization scaling in approaching the classical limit
• Eigenstate entanglement in integrable collective spin models
• Late-time critical behavior of local string-like observables under quantum quenches
• Post-thermalization via information spreading in open quantum systems
• Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator
• Self-trapping phenomenon, multistability and chaos in open anisotropic Dicke dimer
• Quantum geometric tensor away from Equilibrium
• Microscope for Quantum Dynamics with Planck Cell Resolution
• Space-Time Duality between Quantum Chaos and Non-Hermitian Boundary Effect
• Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit
• Classical route to ergodicity and scarring in collective quantum systems
• Power-law decay of the fraction of the mixed eigenstates in kicked top model with mixed-type classical phase space
• Quantum chaos and thermalization in the two-mode Dicke model
• Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model: Dynamical Aspects
• Chaos-induced depletion of a Bose-Einstein condensate
• Scaling at the OTOC Wavefront: free versus chaotic models
• Realizing the Hayden-Preskill Protocol with Coupled Dicke Models
• Analyticity constraints bound the decay of the spectral form factor
• Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity
• Fast quantum state preparation and bath dynamics using non-Gaussian variational ansatz and quantum optimal control
• Quantum multifractality as a probe of phase space in the Dicke model
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Statistical and dynamical aspects of quantum chaos in a kicked Bose-Hubbard dimer
• Diagnosing First and Second Order Phase Transitions with Probes of Quantum Chaos
• Quantum Geometric Tensor and Critical Metrology in the Anisotropic Dicke Model
• Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model
• Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
• Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors
• Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models
• Fast scrambling dynamics and many-body localization transition in an all-to-all disordered quantum spin model
• Entanglement Dynamics between Ising Spins and a Central Ancilla
• Out-of-Time-Order-Correlator for van der Waals potential
• Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
• Error-resilient Reversal of Quantum Chaotic Dynamics Enabled by Scramblons
• Prethermalization of light and matter in cavity-coupled Rydberg arrays
• Connecting scrambling and work statistics for short-range interactions in the harmonic oscillator
• An operational definition of quantum information scrambling
• Analysis of chaos and regularity in the open Dicke model
• Quantum reservoir probing: an inverse paradigm of quantum reservoir computing for exploring quantum many-body physics
• Verifying a quasi-classical spin model of perturbed quantum rewinding in a Fermi gas
• Transient and steady-state chaos in dissipative quantum systems
• Dzyaloshinskii-Moriya interaction as a fast quantum information scrambler
• Manifestation of strange nonchaotic attractors in extended systems: A study through out-of-time-ordered correlators
• Comment on 'Revisiting the phase transitions of the Dicke model'
• Efficient detection of chaos through the computation of the Generalized Alignment Index (GALI) by the multi-particle method
• Scrambling in the Charging of Quantum Batteries
• Quantum instability and Ehrenfest time for an inverted harmonic oscillator
• Origin and Limit of the Recovery of Damaged Information by Time Reversal
• Probing scrambling and operator size distributions using random mixed states and local measurements
• Transition to chaos in extended systems and their quantum impurity models
• Global Out of Time Order Correlators as a Signature of Scrambling Dynamics of Local Observables
• Thermalization of isolated quantum many-body system and the role of entanglement
• Quantum Signatures of Chaos in Anisotropic Quantum Rabi Model
• Permutationally invariant processes in open multiqudit systems
• Emergence and Control of Complex Behaviours in Driven Systems of Interacting Qubits with Dissipation
• Experimental observation of phase transitions of a deformed Dicke model using a reconfigurable, bi-parametric electronic platform
• Temporal Entanglement Transitions in the Periodically Driven Ising Chain
• Dynamical Quantum Phase Transitions and Many-Body Backflow in Open Quantum Systems
• Out-of-Time-Order-Correlation in perturbed quantum wells
• Exploring the properties of quantum scars in a toy model
• Enhanced Quantum Metrology via Saddle-Point Scrambling in Phase Space
• Quantum transitions, ergodicity, and quantum scars in the coupled top model