Quantum quench dynamics in Dicke superradiance models

Kloc, Michal; Stránský, Pavel; Cejnar, Pavel

doi:10.1103/physreva.98.013836

Cited by 70 publications

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“…In the nonrigid case, the eigenstate at the ESQPT critical energy is strongly localized in the linear limit basis state with n = 0, a fact that affects the system dynamics by slowing down the evolution. [35][36][37][38] The eigenstate at the isomerization barrier is also localized, but with a caveat, as we explain next. In the HCN-HNC case, we plot the PR for the = 0 eigenstates normalized by the vibron number N in Fig.…”

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confidence: 93%

Calculation of Transition State Energies in the HCN–HNC Isomerization with an Algebraic Model

et al. 2019

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Recent works have shown that the spectroscopic access to highly-excited states provides enough information to characterize transition states in isomerization reactions.Here, we show that the transition state of the bond breaking HCN-HNC isomerization reaction can also be achieved with the two-dimensional limit of the algebraic vibron model. We describe the system's bending vibration with the algebraic Hamiltonian and use its classical limit to characterize the transition state. Using either the coherent state formalism or a recently proposed approach by Baraban et al. [Science 2015, 350, 1338, we obtain an accurate description of the isomerization transition state. In addition, we show that the energy level dynamics and the transition state wave function structure indicate that the spectrum in the vicinity of the isomerization saddle point can be understood in terms of the formalism for excited state quantum phase transitions. Graphical TOC EntryKeywords isomerization transition state, excited state quantum phase transition, two-dimensional vibron model, HCN-HNC isomerization

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confidence: 93%

Calculation of Transition State Energies in the HCN–HNC Isomerization with an Algebraic Model

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“…[29] and excited-state quantum phase transition signatures have been experimentally observed in superconducting microwave billiards [32], different molecular systems [33,34], and spinor Bose-Einstein condensates [35]. The excited-state quantum phase transition influence on the dynamics of quantum systems has recently attracted significant attention and several remarkable dynamical effects of excited-state quantum phase transitions have been revealed [22,24,26,[36][37][38][39][40][41][42][43]. In particular, the impact of excited-state quantum phase transitions on the adiabatic dynamics of a quantum system has been recently analyzed [44], as well as the relationship between thermal phase transitions and excitedstate quantum phase transitions [45].…”

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confidence: 99%

Excited-state quantum phase transition and the quantum-speed-limit time

Wang

Pérez‐Bernal

2019

Phys. Rev. A

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We investigate the influence of an excited-state quantum phase transition on the quantum speed limit time of an open quantum system. The system consists of a central qubit coupled to a spin environment modeled by a Lipkin-Meshkov-Glick Hamiltonian. We show that when the coupling between qubit and environment is such that the latter is located at the critical energy of the excitedstate quantum phase transition, the qubit evolution shows a remarkable slowdown, marked by an abrupt peak in the quantum speed limit time. Interestingly, this slowdown at the excited-state quantum phase transition critical point is induced by the singular behavior of the qubit decoherence rate, being independent of the Markovian nature of the environment.

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“…The model has also found applications beyond superradiance in various different fields. It has been employed, for instance, in studies of ground-state and excited-state quantum phase tran-sitions [33,[40][41][42][43][44], entanglement creation [45], nonequilibrium dynamics [46][47][48][49], quantum chaos [50][51][52][53], and monodromy [54,55]. Recently, the model has received revived attention due to new experiments with ion traps [56,57] and the analysis of the OTOC [58,59].In the classical limit, the Dicke model presents regular and chaotic regions depending on the Hamiltonian parameters and excitation energies [53].…”

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Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

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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.Quantum chaos tries to bridge quantum and classical mechanics. The search for quantum signatures of classical chaos has ranged from level statistics [1,2] and the structure of the eigenstates [3,4] to the exponential increase of complexity [5,6] and the exponential decay of the overlap of two wave packets [7][8][9][10]. Recently, the pursuit of exponential instabilities in the quantum domain has been revived by the conjecture of a bound on the rate growth of the out-of-time-ordered correlator (OTOC) [11,12]. First introduced in the context of superconductivity [13], the OTOC is now presented as a measure of quantum chaos, with its growth rate being associated with the classical Lyapunov exponent. The OTOC is not only a theoretical quantity, but has also been measured experimentally via nuclear magnetic resonance techniques [14][15][16][17].The correspondence between the OTOC growth rate and the classical Lyapunov exponent has been explicitly shown in two cases of one-body chaotic systems, the kicked-rotor [18] and, after a first unsuccessful attempt [19], the stadium billiard [20]. It was also achieved for chaotic maps [21]. For interacting many-body systems, while exponential behaviors for the OTOC have been found for the Sachdev-Ye-Kitaev model [11,22] and for the Bose-Hubbard model [23,24], a direct demonstration of the quantum-classical correspondence has not yet been made. Studies in this direction include [6,[25][26][27][28][29] and [30].Here, we investigate the OTOC for the Dicke model [31,32]. Comparing with one-body systems, the model is a step up toward an explicit quantum-classical correspondence for interacting many-body systems, since it contains N atoms interacting with a quantized field.The Dicke model was originally proposed to explain the collective phenomenon of superradiance: the field mediates interatomic interactions, which causes the atoms to act collectively [31,33]. Superradiance has been experimentally studied with ultracold atoms in optical cavities [34][35][36][37][38][39]. The model has also found applications beyond superradiance in various different fields. It has been employed, for instance, in studies of ground-state and excited-state quantum phase tran-sitions [33,[40][41][42][43][44], entanglement creation [45], nonequilibrium dynamic...

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Quantum quench dynamics in Dicke superradiance models

Cited by 70 publications

References 70 publications

Calculation of Transition State Energies in the HCN–HNC Isomerization with an Algebraic Model

Calculation of Transition State Energies in the HCN–HNC Isomerization with an Algebraic Model

Excited-state quantum phase transition and the quantum-speed-limit time

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

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