Regularity and chaos in cavity QED

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

doi:10.1088/1402-4896/aa6640

Cited by 17 publications

(12 citation statements)

References 96 publications

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“…The participation ratio is strongly correlated with the underlying classical dynamics [53,74]. For instance, the stochastic layer appearing in the classical dynamics around the separatrix is associated with larger values of P R , which indicate states that are more delocalized in the energy eigenbasis.…”

Section: B Initial Statesmentioning

confidence: 99%

Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring

Villasenor,

Pilatowsky-Cameo,

Bastarrachea-Magnani

et al. 2020

Preprint

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We investigate the entire evolution of the Dicke model, which is a two-degree-of-freedom interacting spin-boson model of great experimental interest. Our objects of study are the quantum and classical survival probabilities of initial coherent states and the corresponding classical evolution of the Wigner distribution in phase space. We show that major aspects of the system are uncovered by analyzing its long-time dynamics, such as whether the initial state is in a regular or chaotic region, in the vicinity of a separatrix, or yet close to an unstable periodic orbit. We demonstrate that a ratio of two between the quantum and classical asymptotic values of the survival probability is a clear indicator of maximal quantum ergodicity. In this case, the quantum survival probability develops a correlation hole, that is nonexistent in its classical version and results in a longer equilibration time for the quantum dynamics. These findings are corroborated by our analytical expressions for the survival probability and the equilibration time.

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Section: B Initial Statesmentioning

confidence: 99%

Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring

Villasenor,

Pilatowsky-Cameo,

Bastarrachea-Magnani

et al. 2020

Preprint

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show abstract

“…Since a generic system usually has a structured phase space with coexistence of regular and chaotic regions rather than a featureless fully developed chaotic region, it is highly desirable to investigate such quantities that enable us to analyze the local chaotic behaviors of a quantum system. With the help of coherent states (or localized wave packets), the local chaotic behaviors of quantum systems have been extensively explored in a variety of works [42][43][44][45][46][47][48][49]. Here, by considering the kicked top model, we are interested in how to reveal the phase space structures and the degree of chaos by means of multifractality of coherent states.…”

Section: Introductionmentioning

confidence: 99%

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

Wang

Robnik

2021

Entropy

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We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.

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“…Since a generic system usually has structured phase space with coexistence of regular and chaotic regions rather than featureless fully developed chaotic region, it is therefore highly desirable to investigate such quantities which enable us to analyze the local chaotic behaviors of a quantum system. With the help of coherent states (or localized wave-packets), the local chaotic behaviors of quantum systems have been extensively explored in a variety of works [42][43][44][45][46][47][48][49]. Here, by considering the kicked top model, we are interested in how to reveal the phase space structures and the degree of chaos by means of multifractality of coherent states.…”

Section: Introductionmentioning

confidence: 99%

Multifractality in quasienergy space of coherent states as a signature of quantum chaos

Wang,

Robnik

2021

Preprint

View full text Add to dashboard Cite

We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase space averaged multifractal dimensions, which are well described by random matrix theory in strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.

show abstract

Regularity and chaos in cavity QED

Cited by 17 publications

References 96 publications

Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring

Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

Multifractality in quasienergy space of coherent states as a signature of quantum chaos

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