Quantum scarring in a spin-boson system: fundamental families of periodic orbits
arXiv:2009.08523 · doi:10.1088/1367-2630/abd2e6
Abstract
As the name indicates, a periodic orbit is a solution for a dynamical system that repeats itself in time. In the regular regime, periodic orbits are stable, while in the chaotic regime, they become unstable. The presence of unstable periodic orbits is directly associated with the phenomenon of quantum scarring, which restricts the degree of delocalization of the eigenstates and leads to revivals in the dynamics. Here, we study the Dicke model in the superradiant phase and identify two sets of fundamental periodic orbits. This experimentally realizable atom-photon model is regular at low energies and chaotic at high energies. We study the effects of the periodic orbits in the structure of the eigenstates in both regular and chaotic regimes and obtain their quantized energies. We also introduce a measure to quantify how much scarred an eigenstate gets by each family of periodic orbits and compare the dynamics of initial coherent states close and away from those orbits.
arXiv comment19 pages, 6 figures (as published)
References in corpus (33)
- Ultrastrong coupling regimes of light-matter interaction
- Quantum many-body scars
- Chaos and the Quantum Phase Transition in the Dicke Model
- Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
- Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa
- Realization of the Dicke model using cavity-assisted Raman transitions
- Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems
- Linear and Nonlinear Theory of Eigenfunction Scars
- Ultrastrong coupling phenomena beyond the Dicke model
- Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
- Cavity quantum electrodynamics in the non-perturbative regime
- 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
- Theoretical methods for ultrastrong light-matter interactions
- Quantum quench influenced by an excited-state phase transition
- Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions
- Dicke model simulation via cavity-assisted Raman transitions
- Comparative quantum and semi-classical analysis of Atom-Field Systems II: Chaos and regularity
- Measuring Scars of Periodic Orbits
- Classical chaos in atom-field systems
- Quantum quench dynamics in Dicke superradiance models
- Dynamical signatures of quantum chaos and relaxation timescales in a spin-boson system
- 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
- Quantum Lissajous Scars
- Semiclassical coherent state propagator for systems with spin
- Delocalization and quantum chaos in atom-field systems
- Scarring by homoclinic and heteroclinic orbits
- Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring
- Analytical description of the survival probability of coherent states in regular regimes
- Effects of scarring on quantum chaos in disordered quantum wells
- Coherent Quantum Dynamics: What Fluctuations Can Tell
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- Ubiquitous quantum scarring does not prevent ergodicity
- Scars from protected zero modes and beyond in quantum link and quantum dimer models
- Quantum scars and regular eigenstates in a chaotic spinor condensate
- Constant of motion identifying excited-state quantum phases
- Chaos in the three-site Bose-Hubbard model -- classical vs quantum
- Chaos and Thermalization in the Spin-Boson Dicke Model
- Quantum localization measures in phase space
- Chaos in a deformed Dicke model
- Identification of quantum scars via phase-space localization measures
- Quantum many-body scars from unstable periodic orbits
- From integrability to chaos: the quantum-classical correspondence in a triple well bosonic model
- Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit
- Analysis of chaos and regularity in the open Dicke model
- Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach
- Long-time signatures of chaos in large atom-light frequency ratios Rabi model