Verification of a Many-Ion Simulator of the Dicke Model Through Slow Quenches across a Phase Transition

Safavi-Naini, Arghavan; Lewis-Swan, Robert J.; Bohnet, Justin; Gärttner, Martin; Gilmore, Kevin; Jordan, Elena; Cohn, Jeffrey; Freericks, J. K.; Rey, Ana María; Bollinger, John J.

doi:10.1103/physrevlett.121.040503

Cited by 135 publications

(107 citation statements)

References 59 publications

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“…Experimental attempts to measure λ L in the DM are already underway 32,48 . This can potentially make our results to be of short-term experimental relevance.…”

Section: Discussionmentioning

confidence: 99%

Scrambling in the Dicke model

Alavirad

Lavasani

2019

Phys. Rev. A

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The scrambling rate λL associated with the exponential growth of out-of-time-ordered correlators can be used to characterize quantum chaos. Here we use the Majorana Fermion representation of spin 1/2 systems to study quantum chaos in the Dicke model. We take the system to be in thermal equilibrium and compute λL throughout the phase diagram to leading order in 1/N . We find that the chaotic behavior is strongest close to the critical point. At high temperatures λL is nonzero over an extended region that includes both the normal and super-radiant phases. At low temperatures λL is nonzero in (a) close vicinity of the critical point and (b) a region within the super-radiant phase. In the process we also derive a new effective theory for the super-radiant phase at finite temperatures. Our formalism does not rely on the assumption of total spin conservation. arXiv:1808.02038v2 [cond-mat.stat-mech]

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“…Experimental attempts to measure λ L in the DM are already underway 32,48 . This can potentially make our results to be of short-term experimental relevance.…”

Section: Discussionmentioning

confidence: 99%

Scrambling in the Dicke model

Alavirad

Lavasani

2019

Phys. Rev. A

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“…Stroboscopic methods of address can be used to control ions in such a system, but most work to date has effected uniform excitation. Recent work using these systems has resulted in the creation of manybody entanglement in large 2D ion crystals of hundreds of ions [64] with application to quantum simulation of critical systems and non-equilibrium dynamics in general [65,66], as well as enhanced quantum sensing [67]. However, since it is generally more straightforward to individually manipulate ions that are part of stationary arrays, Paul traps, with oscillating electric fields in the RF range, are the main focus for researchers in QC.…”

Section: Types Of Ion Trapsmentioning

confidence: 99%

Trapped-ion quantum computing: Progress and challenges

Bruzewicz

Chiaverini

McConnell

et al. 2019

Applied Physics Reviews

1,038

644

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Trapped ions are among the most promising systems for practical quantum computing (QC). The basic requirements for universal QC have all been demonstrated with ions and quantum algorithms using few-ion-qubit systems have been implemented. We review the state of the field, covering the basics of how trapped ions are used for QC and their strengths and limitations as qubits. In addition, we discuss what is being done, and what may be required, to increase the scale of trapped ion quantum computers while mitigating decoherence and control errors. Finally, we explore the outlook for trapped-ion QC. In particular, we discuss near-term applications, considerations impacting the design of future systems of trapped ions, and experiments and demonstrations that may further inform these considerations. CONTENTS

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“…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]. This allows us to benchmark the OTOC growth against the presence and absence of chaos.…”

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confidence: 99%

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

et al. 2019

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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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Verification of a Many-Ion Simulator of the Dicke Model Through Slow Quenches across a Phase Transition

Cited by 135 publications

References 59 publications

Scrambling in the Dicke model

Scrambling in the Dicke model

Trapped-ion quantum computing: Progress and challenges

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

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