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arXiv:2407.09802 · Communications in Theoretical Physics

Long-time signatures of chaos in large atom-light frequency ratios Rabi model

Shangyun Wang, Songbai Chen, Jiliang Jing

Published Mar 24, 2025• 0 citations
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Abstract

Abstract As one of the famous effects in the quantum Rabi model (QRM), Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts, such as quantum collapse and revival effects. In this paper, we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model. It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions, and the Husimi Q function are more dispersed in phase space. Moreover, we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space. Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.

DOI
10.1088/1572-9494/adc3f9

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Abstract As one of the famous effects in the quantum Rabi model (QRM), Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts, such as quantum collapse and revival effects. In this paper, we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model. It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions, and the Husimi Q function are more dispersed in phase space. Moreover, we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space. Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.
Abstract Quantum chaos is an intriguing topic and has attracted a great deal of interests in quantum mechanics and black hole physics. Recently, the exponential growth of out‐of‐time‐ordered correlator (OTOC) has been proposed to diagnose quantum chaos and verify the correspondence principle. Here, good correspondence is found between the linear entanglement entropy and the semiclassical phase space structures in the anisotropic quantum Rabi model. The Loschmidt echo in the chaotic sea decays more faster than that in the stable island. However, the OTOCs grow exponentially at early times for the initial states centered both in the chaotic and stable regions. The exponential growth of the OTOC is attributed to quantum collapse that provides a novel mechanism of yielding exponential growth of the OTOC in quantum systems. Moreover, the quantum collapse effect is more obvious for the initial states centered in the chaotic one. The results show that in the anisotropic quantum Rabi model, the linear entanglement entropy, and Loschmidt echo are more effective than OTOC for diagnosing quantum chaotic signals.
Testing the correspondence principle in nonlinear quantum systems is a fundamental pursuit in quantum physics. In this paper, we employed mean field approximation theory to study the semiclassical dynamics in the Rabi-Stark model (RSM) and showed that the nonlinear Stark coupling significantly modulates the semiclassical phase space structure. By analyzing the linear entanglement entropy of coherent states prepared in the classical chaotic and regular regions of the semiclassical phase space, we demonstrate that quantum-classical correspondence can be achieved in the RSM with large atom-light frequency ratios. While this correspondence fails in the resonant Rabi model because its truncated photon number is insufficient to approach the large quantum number limit, we discovered that in the resonant RSM when the nonlinear Stark coupling U→±1U \to \pm 1U→±1, the time-averaged linear entanglement entropy correlates strongly with the semiclassical phase space. In particular, when U→−1U \to -1U→−1, the truncated photon number in the resonant RSM is very close to that in the resonant Rabi model, but the time-averaged linear entanglement entropy still corresponds well with the semiclassical phase space. This result demonstrates that quantum-classical correspondence can be realized in the few-body resonant RSM.
We investigate signatures of chaos and equilibration in the quantum Rabi model, which exhibits a quantum phase transition when the ratio of the atomic level-splitting to bosonic frequency grows to infinity. We show that the out-of-time-order correlator derived from the Loschmidt echo signal quickly saturates in the normal phase and undergoes exponential growth in the superradiant phase, which is associated with the onset of quantum chaos. Furthermore, we show that the effective time-averaged dimension of the quantum Rabi system can be large compared with the spin system size, which leads to suppression of the temporal fluctuations and equilibration of the spin system.
Identifying the quantum signatures of classical chaos remains a central question in quantum physics, and quantum scrambling provides a new perspective on this correspondence. We study two distinct limits of the same model to examine how the correspondence between chaos and scrambling changes across different regimes. The thermodynamic-limit anisotropic Dicke model exhibits a close correspondence between chaos and scrambling, whereas this correspondence breaks down in the large-frequency-ratio limit of the anisotropic Rabi model (ARM). The contrasting chaotic behavior in the two limits originates from the different numbers of classical degrees of freedom, whereas their similar scrambling behavior stems from eigenstate delocalization. This implies that, in the large-frequency-ratio limit, eigenstate delocalization alone is insufficient to qualify the ARM as a classically chaotic model. This finding suggests that identifying chaos in quantum systems requires jointly considering the classical degrees of freedom and eigenstate delocalization.
The relationship between classically chaotic dynamics and the entanglement properties of the corresponding quantum system is examined in the semiclassical limit. Numerical results are computed for a modified kicked top, keeping the classical dynamics constant while investigating the entanglement for several versions of the corresponding quantum system characterized by a different value of the effective Planck constant ℏ eff. Our findings indicate that as ℏ eff → 0, the apparent signatures of classical chaos in the entanglement properties, such as characteristic oscillations in the time-dependence of the linear entropy, can also be obtained in the regular regime. These results suggest that entanglement is not a universal marker of chaotic dynamics of the corresponding classical system.
Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section - it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudo-random states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. Continuing on our journey to find the footprints of chaos in the quantum world, we explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. We find an increase in the rate of information gain and hence higher fidelities in the process when the Floquet maps employed increase in chaoticity. We make predictions for the information gain using random matrix theory in the fully chaotic regime and show a remarkable agreement between the two. The last part of this thesis is devoted to the study of the nature of quantum correlations themselves. We present an operational interpretation of quantum discord based on the quantum state merging protocol. Quantum discord is the markup in the cost of quantum communication in the process of quantum state merging, if one discards relevant prior information.