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

Lewis-Swan, Robert J.; Safavi-Naini, Arghavan; Bollinger, John J.; Rey, Ana María

doi:10.1038/s41467-019-09436-y

Cited by 224 publications

(216 citation statements)

References 69 publications

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“…This differs from the exponential growth rate of an OTOC, λ OTOC , which is rather the log of the phase space average of sensitivity squared. Since the log of the average is larger than the average of the log, we have [22][23][24][25][26][27][28]:…”

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confidence: 99%

“…Originally, it was conceived to describe N two-level atoms coupled to a single optical cavity mode. Several recent works [25,27,28] considered the OTOCs in this model. In the classical limit, its Hamiltonian H = 1 2 (q 2 + p 2 ) + x + γzq (A1) describes an SU (2) (pseudo)-spin (x, y, z) and a harmonic oscillator (p, q), interacting with a coupling constant γ > 0.…”

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confidence: 99%

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Does Scrambling Equal Chaos?

2020

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Focusing on semiclassical systems, we show that the parametrically long exponential growth of outof-time order correlators (OTOCs), also known as scrambling, does not necessitate chaos. Indeed, scrambling can simply result from the presence of unstable fixed points in phase space, even in an integrable model. We derive a lower bound on the OTOC Lyapunov exponent which depends only on local properties of such fixed points. We present several models for which this bound is tight, i.e. for which scrambling is dominated by the local dynamics around the fixed points. We propose that the notion of scrambling be distinguished from that of chaos.

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confidence: 99%

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confidence: 99%

Does Scrambling Equal Chaos?

2020

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“…The chaotic dynamics observed in the classical limit S → ∞ can be studied experimentally via the hallmark of sensitivity to perturbations. Recent theoretical and experimental work has shown that such sensitivity is accessible in quantum systems by measuring out-of-timeorder correlators (OTOCs) [1,34,[68][69][70][71][72][73], which quantify the spread of operators in time via the commutator C(t) = [V (t), W (0)] 2 . The connection to classical chaos is made clear in the semi-classical limit: for operators V = S z i , W = S z j , one can show that, to lowest order in a 1/S expansion, C(t) ∝ (∂S z i (t)/∂φ j ) 2 for a small rotation φ j at site j about the z-axis [74].…”

Section: Experimental Realitiesmentioning

confidence: 99%

Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity

et al. 2019

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We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the experimental parameters, one can tune between integrable and chaotic dynamics on the one hand, and between classical and quantum regimes on the other hand. For two special values of a spin-anisotropy parameter, the model exhibits rational-Gaudin type integrability and it is characterized by an extensive set of spin-bilinear integrals of motion, independent of the spin size. More generically, we find a novel integrable structure with conserved charges that are not purely bilinear. Instead, they develop "dressing tails" of higher-body terms, reminiscent of the dressed local integrals of motion found in Many-Body Localized phases. Surprisingly, this new type of integrable dynamics found in finite-size spin-1/2 systems disappears in the large-S limit, giving way to classical chaos. We identify parameter regimes for characterizing these different dynamical behaviors in realistic experiments, in view of the limitations set by cavity dissipation. arXiv:1904.10966v3 [cond-mat.stat-mech]

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“…A nice feature of the continuous protocol is that we obtain a total Hamiltonian that can be mapped to the original SDF-only Hamiltonian with an enhanced coupling strength. This can be useful for studies on spin-motion coupling [35]. Additionally, the gate time is not limited by the motional mode splitting and the enhancement is more advantageous for gT 30 as shown in Fig.…”

Section: Comparison To the Continuous Protocolmentioning

confidence: 99%

Stroboscopic approach to trapped-ion quantum information processing with squeezed phonons

Sawyer

Britton

et al. 2019

Phys. Rev. A

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In trapped-ion quantum information processing, interactions between spins (qubits) are mediated by collective modes of motion of an ion crystal. While there are many different experimental strategies to design such interactions, they all face both technical and fundamental limitations to the achievable coherent interaction strength. In general, obtaining strong interactions and fast gates is an ongoing challenge. Here, we extend previous work [Phys. Rev. Lett. 112, 030501 (2019)] and present a general strategy for enhancing the interaction strengths in trapped-ion systems via parametric amplification of the ions' motion. Specifically, we propose a stroboscopic protocol using alternating applications of parametric amplification and spin-motion coupling. In comparison with the previous work, we show that the current protocol can lead to larger enhancements in the coherent interaction that increase exponentially with the gate time.

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

Cited by 224 publications

References 69 publications

Does Scrambling Equal Chaos?

Does Scrambling Equal Chaos?

Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity

Stroboscopic approach to trapped-ion quantum information processing with squeezed phonons

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