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Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

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TLDR
The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos and is studied in the Dicke model, where two-level atoms cooperatively interact with a quantized radiation field.
Abstract
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.

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

TL;DR: It is demonstrated that fidelity out-of-time-order correlators (FOTOCs) can elucidate connections between scrambling, entanglement, ergodicity and quantum chaos (butterfly effect) and establish quantitative relationships between experimentally-measureable correlators, the Rényi entropy and Lyapunov exponents in the Dicke model.
Journal ArticleDOI

Positive quantum Lyapunov exponents in experimental systems with a regular classical limit

TL;DR: In this article, it was shown that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime, and the same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable.
Journal ArticleDOI

Quantum versus classical many-body batteries

TL;DR: In this article, the authors studied three examples of quantum-mechanical many-body batteries with rigorous classical analogs and found that the answer is model dependent and depends on the value of the coupling constant that controls the interaction between the charger and the battery itself.
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Does Scrambling Equal Chaos

TL;DR: In this article, the authors show that scrambling can simply result from the presence of unstable fixed points in phase space, even in a classically integrable model, and derive a lower bound on the Lyapunov exponent, which depends only on local properties of such fixed points.
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Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model

TL;DR: In this paper, a family of fidelity out-of-time-order correlators (FOTOCs) is proposed to quantify fast scrambling, determine bounds on quantum information processing and to identify possible candidates of black hole analogs in controllable quantum systems.
References
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Coherence in Spontaneous Radiation Processes

TL;DR: In this article, the authors considered a radiating gas as a single quantum-mechanical system, and the energy levels corresponding to certain correlations between individual molecules were described, where spontaneous emission of radiation in a transition between two such levels leads to the emission of coherent radiation.
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A bound on chaos

TL;DR: In this paper, a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom is given, based on plausible physical assumptions, establishing this conjecture.
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Remarks on the Sachdev-Ye-Kitaev model

TL;DR: In this paper, the authors studied the quantum mechanical model of $N$ Majorana fermions with random interactions of a few Fermions at a time (Sachdev-Ye-Kitaev model) in the large N$ limit.
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Dicke quantum phase transition with a superfluid gas in an optical cavity

TL;DR: In this paper, the Dicke phase transition in an open system formed by a Bose-Einstein condensate coupled to an optical cavity has been realized, and the phase transition is driven by infinitely long-range interactions between the condensed atoms, induced by two-photon processes involving the cavity mode and a pump field.
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A bound on chaos

TL;DR: In this paper, a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom is given. But this bound depends on the assumption that the influence of chaos on the commutator can develop no faster than exponentially with Lyapunov exponent.
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