Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

Abstract

The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has been corroborated for the kicked rotor and the stadium billiard, which are one-body chaotic systems. The conjecture has not yet been validated for realistic systems with interactions. We make progress in this direction by studying the OTOC in the Dicke model, where two-level atoms cooperatively interact with a quantized radiation field. For parameters where the model is chaotic in the classical limit, the OTOC increases exponentially in time with a rate that closely follows the classical Lyapunov exponent.

6 pages, 4 figures (as published)

References in corpus (49)

• A bound on chaos
• Comments on the Sachdev-Ye-Kitaev model
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Cold atoms in cavity-generated dynamical optical potentials
• Chaos and the Quantum Phase Transition in the Dicke Model
• Dynamics of Loschmidt echoes and fidelity decay
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Environment-independent decoherence rate in classically chaotic systems
• Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
• Entanglement and the Phase Transition in Single Mode Superradiance
• Exploring Symmetry Breaking at the Dicke Quantum Phase Transition
• Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Exploring Localization in Nuclear Spin Chains
• Entanglement in the Dicke model
• Out-of-time-order correlators in quantum mechanics
• Observation of a superradiant Mott insulator in the Dicke-Hubbard model
• Scrambling and thermalization in a diffusive quantum many-body system
• Power-law out of time order correlation functions in the SYK model
• Realization of the Dicke model using cavity-assisted Raman transitions
• 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
• Some remarks on 'superradiant' phase transitions in light-matter systems
• Supermode-Density-Wave-Polariton Condensation
• Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators
• Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions
• Quantum quench influenced by an excited-state phase transition
• Measuring the Lyapunov exponent using quantum mechanics
• Comparative quantum and semi-classical analysis of Atom-Field Systems II: Chaos and regularity
• Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
• Classical chaos in atom-field systems
• Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2
• Quantum quench dynamics in Dicke superradiance models
• Dynamics of the Dicke model close to the classical limit
• Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment
• Semiclassical Identification of Periodic Orbits in a Quantum Many-Body System
• Semiclassical coherent state propagator for systems with spin
• Delocalization and quantum chaos in atom-field systems
• Exponentially fast dynamics of chaotic many-body systems
• Quantum phases and entanglement properties of an extended Dicke model
• Sensitivity to small perturbations in systems of large quantum spins
• A semiclassical study of the Jaynes-Cummings model
• Analytical description of the survival probability of coherent states in regular regimes
• Efficient basis for the Dicke Model I: theory and convergence in energy
• Efficient basis for the Dicke Model II: wave function convergence and excited states
• Monodromy in Dicke superradiance
• Chaotic Evolution in Quantum Mechanics

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• Speck of Chaos
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• Crafting the dynamical structure of synchronization by harnessing bosonic multilevel cavity QED
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• Anharmonicity-induced excited-state quantum phase transition in the symmetric phase of the two-dimensional limit of the vibron model
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• Classical route to ergodicity and scarring in collective quantum systems
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• Diagnosing Quantum Many-body Chaos in Non-Hermitian Quantum Spin Chain via Krylov Complexity
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• Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations
• Quantum multifractality as a probe of phase space in the Dicke model
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• Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems
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• Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model
• Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
• Photon waiting time distributions: a keyhole into dissipative quantum chaos
• Out-of-Time-Order-Correlator for van der Waals potential
• Analysis of chaos and regularity in the open Dicke model
• A Floquet analysis perspective of driven light-matter interaction models
• Relaxation exponents of OTOCs and overlap with local Hamiltonians
• Emergence of chaos and controlled photon transfer in a cavity-QED network
• Nonequilibrium many-body quantum dynamics: from full random matrices to real systems
• Quantum Phase Transitions in a Generalized Dicke Model
• Aspects of entanglement in non-local field theories with fractional Laplacian
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• Bipartite OTOC in open quantum systems: information scrambling and irreversibility
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