Quantum scarring in a spin-boson system: fundamental families of periodic orbits

Pilatowsky-Cameo, Saúl; Villaseñor, David; Bastarrachea-Magnani, Miguel A.; Lerma-Hernández, Sergio; Santos, Lea F.; Hirsch, Jorge G.

doi:10.1088/1367-2630/abd2e6

Cited by 21 publications

(20 citation statements)

References 64 publications

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“…We stress that these unstable periodic orbits are different from those that we found in Ref. [64], whose origin could be traced down to the fundamental excitations around the ground state configuration. Further studies of these new orbits may eventually reveal the properties and origin of these new families of unstable periodic orbits for the Dicke model.…”

Section: Identifying Unstable Periodic Orbitscontrasting

confidence: 82%

“…These orbits are different from the ones found in Ref. [64] and their uncovering represents a step forward in the difficult task of identifying the unstable periodic orbits underlying quantum scars. In addition, we study the dynamical properties of the unveiled orbits and use them to explain the structures of the eigenstates and their degree of localization.…”

Section: Introductioncontrasting

confidence: 65%

“…In Refs. [64,65], we studied Q 1 k (Q, P ) and verified that it allows for the visual identification of quantum scars. In Ref.…”

Section: Eigenstatesmentioning

confidence: 81%

“…The Dicke model [30] was initially introduced to explain the phenomenon of superradiance [36,43,50,80] and has since fostered a wide variety of theoretical studies, including the behavior of out-of-time-ordered correlators [24,59,63], manifestations of quantum scarring [6,29,35,64,65], non-equilibrium dynamics [1,50,51,57,58,78], and measures of quantum localization with respect to phase space [65,79]. The model is also of great interest to experiments with trapped ions [26,71], superconducting circuits [47], and cavity assisted Raman transitions [5,82].…”

Section: Dicke Modelmentioning

confidence: 99%

“…The evolution is halted when the evolved point x i (T i ) approximately returns to the initial condition x i (0). This gives an approximate period T i and an initial condition x i , which can be converged to a truly periodic condition by means of an algorithm known as the monodromy method [7,28,64,73] B2), (C2), and (D2). The mirrored orbit O D is obtained by changing the signs of the coordinates Q and q of O D .…”

Section: Identifying Unstable Periodic Orbitsmentioning

confidence: 99%

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Identification of quantum scars via phase-space localization measures

Santos

Pilatowsky-Cameo

̃nor

et al. 2022

Quantum

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There is no unique way to quantify the degree of delocalization of quantum states in unbounded continuous spaces. In this work, we explore a recently introduced localization measure that quantifies the portion of the classical phase space occupied by a quantum state. The measure is based on the α-moments of the Husimi function and is known as the Rényi occupation of order α. With this quantity and random pure states, we find a general expression to identify states that are maximally delocalized in phase space. Using this expression and the Dicke model, which is an interacting spin-boson model with an unbounded four-dimensional phase space, we show that the Rényi occupations with α>1 are highly effective at revealing quantum scars. Furthermore, by analyzing the high moments (α>1) of the Husimi function, we are able to identify qualitatively and quantitatively the unstable periodic orbits that scar some of the eigenstates of the model.

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Section: Identifying Unstable Periodic Orbitscontrasting

confidence: 82%

Section: Introductioncontrasting

confidence: 65%

“…In Refs. [64,65], we studied Q 1 k (Q, P ) and verified that it allows for the visual identification of quantum scars. In Ref.…”

Section: Eigenstatesmentioning

confidence: 81%

Section: Dicke Modelmentioning

confidence: 99%

Section: Identifying Unstable Periodic Orbitsmentioning

confidence: 99%

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Identification of quantum scars via phase-space localization measures

Santos

Pilatowsky-Cameo

̃nor

et al. 2022

Quantum

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Ubiquitous quantum scarring does not prevent ergodicity

et al. 2021

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In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born’s rules to connect quantum states with probabilities, one might then expect that all quantum states in the chaotic regime should be uniformly distributed in phase space. This simplified picture was shaken by the discovery of quantum scarring, where some eigenstates are concentrated along unstable periodic orbits. Despite that, it is widely accepted that most eigenstates of chaotic models are indeed ergodic. Our results show instead that all eigenstates of the chaotic Dicke model are actually scarred. They also show that even the most random states of this interacting atom-photon system never occupy more than half of the available phase space. Quantum ergodicity is achievable only as an ensemble property, after temporal averages are performed.

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Chaos in a deformed Dicke model

Corps¹,

Molina²,

Relaño³

2022

J. Phys. A: Math. Theor.

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The critical behavior in an important class of excited state quantum phase transitions is signaled by the presence of a new constant of motion onlyat one side of the critical energy. We study the impact of this phenomenon in the development of chaos in a modified version of the paradigmatic Dicke model of quantum optics, in which a perturbation is added that breaks the parity symmetry. Two asymmetric energy wells appear in the semiclassical limit of the model, whose consequences are studied both in the classical and in the quantum cases. Classically, Poincar ́e sections reveal that the degree of chaos not only depends on the energy of the initial condition chosen, but also on the particular energy well structure of the model. In the quantum case, Peres lattices of physical observables show that the appearance of chaos critically depends on the quantum conserved number provided by this constant of motion. The conservation law defined by this constant is shown to allow for the coexistence between chaos and regularity at the same energy. We further analyze the onset of chaos in relationwith an additional conserved quantity that the model can exhibit.

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Quantum scarring in a spin-boson system: fundamental families of periodic orbits

Cited by 21 publications

References 64 publications

Identification of quantum scars via phase-space localization measures

Identification of quantum scars via phase-space localization measures

Ubiquitous quantum scarring does not prevent ergodicity

Chaos in a deformed Dicke model

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