Classical chaos in atom-field systems

Chávez-Carlos, Jorge; Bastarrachea-Magnani, Miguel A.; Lerma-Hernández, Sergio; Hirsch, Jorge G.

doi:10.1103/physreve.94.022209

Cited by 67 publications

(85 citation statements)

References 45 publications

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“…Similar features appear in the classical dynamics of the DM [31,[33][34][35][36], manifested in the different behavior of trajectories in phase-space computed from the mean-field equations of motion for:x = ( Ŝ x , Ŝ y , Ŝ z , α R , α I ), where . .…”

Section: B Connections Between Scrambling Dynamics and Chaosmentioning

confidence: 59%

Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model

Lewis-Swan

Safavi-Naini

Bollinger³

et al. 2019

Nat Commun

216

197

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Scrambling is the process by which information stored in local degrees of freedom spreads over the many-body degrees of freedom of a quantum system, becoming inaccessible to local probes and apparently lost. Scrambling and entanglement can reconcile seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes. Here, we demonstrate that fidelity out-of-time-order correlators (FOTOCs) can elucidate connections between scrambling, entanglement, ergodicity and quantum chaos (butterfly effect). We compute FOTOCs for the paradigmatic Dicke model, and show they can measure subsystem Rényi entropies and inform about quantum thermalization. Moreover, we illustrate why FOTOCs give access to a simple relation between quantum and classical Lyapunov exponents in a chaotic system without finite-size effects. Our results open a path to experimental use FOTOCs to explore scrambling, bounds on quantum information processing and investigation of black hole analogs in controllable quantum systems.

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Section: B Connections Between Scrambling Dynamics and Chaosmentioning

confidence: 59%

Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model

Lewis-Swan

Safavi-Naini

Bollinger³

et al. 2019

Nat Commun

216

197

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“…We note that chaos in the basic and extended Dicke model was studied also in Refs. [13,14,[38][39][40]. Classical chaos in a general Hamiltonian (8) can be quantified by a so-called regular fraction f reg .…”

Section: Hamiltonian Eigensolutions Classical Limitmentioning

confidence: 99%

Quantum phases and entanglement properties of an extended Dicke model

2017

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We study a simple model describing superradiance in a system of two-level atoms interacting with a single-mode bosonic field. The model permits a continuous crossover between integrable and partially chaotic regimes and shows a complex thermodynamic and quantum phase structure. Several types of excited-state quantum phase transitions separate quantum phases that are characterized by specific energy dependences of various observables and by different atom-field and atom-atom entanglement properties. We observe an approximate revival of some states from the weak atom-field coupling limit in the strong coupling regime.

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“…Nuclear and molecular systems, as well as integrable and chaotic models have been considered. There has also been interesting attempts to relate the onset of chaos with ESQPTs , although this connection may in fact be due to a fortuitous choice of parameters .…”

Section: Introductionmentioning

confidence: 99%

Effects of excited state quantum phase transitions on system dynamics

Pérez‐Bernal

Santos

2016

Fortschritte der Physik

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This work is concerned with the excited state quantum phase transitions (ESQPTs) defined in Ann.Phys. 323, 1106 (2008). In many-body models that exhibit such transitions, the ground state quantum phase transition (QPT) occurs in parallel with a singularity in the energy spectrum that propagates to higher energies as the control parameter increases beyond the QPT critical point. The analysis of the spectrum has been a main tool for the detection of these ESQPTs. Studies of the effects of this transition on the system dynamics are more limited. Here, we extend our previous works and show that the evolution of an initial state with energy close to the ESQPT critical point may be extremely slow. This result is surprising, because it may take place in systems with long-range interactions, where the dynamics is usually expected to be very fast. A timely example is the one-dimensional spin-1/2 model with infinite-range Ising interaction studied in experiments with ion traps. Its Hamiltonian has a U(2) algebraic structure. More generally, the slow dynamics described here occurs in two-level bosonic or fermionic models with pairing interactions and a U(v+1) Hamiltonian exhibiting a QPT between its limiting U(v) and SO(v+1) dynamical symmetries. In this work, we compare the results for v=1, 2, and 3.Comment: 6 pages, 4 figures, accepted at the FQMT15 special volume of the Fortschritte der Physi

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Classical chaos in atom-field systems

Cited by 67 publications

References 45 publications

Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model

Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model

Quantum phases and entanglement properties of an extended Dicke model

Effects of excited state quantum phase transitions on system dynamics

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