Identifying quantum chaos in Floquet systems with mixed classical phase spaces requires robust experimentally accessible signatures. We investigate the time-averaged quantum Fisher information (QFI) and the fidelity out-of-time-ordered correlator (FOTOC) of continuous periodically driven systems. We uncover two distinct power-law scalings of the time-averaged QFI with respect to system size: the standard quantum limit and the Heisenberg limit. These scalings correspond to initial states localized in the regular and chaotic regions of the classical phase space, respectively. Remarkably, we show that the time-averaged FOTOC can accurately identify the transition from mixed phase space to fully chaotic sea (at a critical driving strength Bx≈5.3) as verified by the maximum Lyapunov exponent. The results suggest that both time-averaged QFI and FOTOC can be used as excellent quantum signatures for probing mixed phase-space structures and our adopted protocol for measuring the FOTOC eliminates the need for time-reversal operations. This work establishes a practical framework for investigating quantum chaos in Floquet systems, bridging theoretical insights with experimental applications.
Identifying quantum chaos in Floquet systems with mixed classical phase spaces requires robust experimentally accessible signatures. We investigate the time-averaged quantum Fisher information (QFI) and the fidelity out-of-time-ordered correlator (FOTOC) of continuous periodically driven systems. We uncover two distinct power-law scalings of the time-averaged QFI with respect to system size: the standard quantum limit and the Heisenberg limit. These scalings correspond to initial states localized in the regular and chaotic regions of the classical phase space, respectively. Remarkably, we show that the time-averaged FOTOC can accurately identify the transition from mixed phase space to fully chaotic sea (at a critical driving strength Bx≈5.3) as verified by the maximum Lyapunov exponent. The results suggest that both time-averaged QFI and FOTOC can be used as excellent quantum signatures for probing mixed phase-space structures and our adopted protocol for measuring the FOTOC eliminates the need for time-reversal operations. This work establishes a practical framework for investigating quantum chaos in Floquet systems, bridging theoretical insights with experimental applications.
We investigate both classical and quantum chaotic dynamics of a two-mode Bose-Einstein condensate driven by a continuously periodic field. We calculate the quantities, including quantum Fisher information (QFI), fidelity, and linear entropy, to characterize the quantum chaos and compare these quantities with the maximum Lyapunov exponent (MLE) of the corresponding classical system. The behaviors of the quantum quantities and the classical quantity show a strong correspondence regardless of the classical regular and chaotic regions in the parameter space. A quantitative link between the MLE and the short-time dynamics of the QFI is established. Particularly, we find that our continuously driven model is significantly superior to other models in accelerating entanglement generation through chaos, which is evidenced by the shorter time required for the QFI to reach the Heisenberg limit. We briefly discuss the underlying mechanism of this finding and its application in saving time costs and improving measurement accuracy as well.
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.
The periodically modulated Bose-Hubbard dimer model offers an experimentally realizable and highly tunable platform for observing the scrambling of quantum information and the apparent thermalization of isolated, interacting quantum many-body systems. In this work we apply fidelity out-of-time correlators (FOTOCs) to establish connections between the thermalization in the Floquet system, the exponential growth of FOTOCs as quantified by a nonzero quantum Lyapunov exponent, and the underlying classical transition from regular to chaotic dynamics in the dimer. Moreover, we demonstrate that a nonzero quantum Lyapunov exponent can also be inferred from measures quantifying the delocalization of the Floquet modes of the system such as the Shannon entropy, which approaches unity if the system thermalizes to the periodic Gibbs ensemble prediction.
Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated theoretically for some systems and there are several projects to do the same experimentally. The Dicke model, in particular, which has a regular and a chaotic regime, is currently under intense investigation by experiments with trapped ions. We show, however, that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime. The same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable. The exponential behavior in these cases are due to unstable stationary points, not to chaos.
In this work, we show, that relative oscillations in asymptotic times of microcanonical Out-of-Time-Order correlators (OTOCs) are suppressed by chaos with the size of the sys- tem. Therefore they can serve as an indicator of quantum chaos in quantum systems. We demonstrate this phenomenon on numerical results of the Out-of-Time-Order correlators from a model with hamiltonian based on the u(3) algebra. Firstly we prove, that this model can be used not only for the description of molecular vibrations, but also Bose- Einstein condensate. Then we employ several methods for the analysis of both quantum and classical chaos, namely spectral statistics such as Nearest Neighbour Spacing Distri- bution and Brody distribution, Inverse Participation Ratio, Poincaré sections, Lyapunov exponent, and the chaotic fraction of classical phase space. We compare these results with relative oscillations of microcanonical Out-of-Time-Order correlators and show, that their suppression corresponds with the chaoticity of the quantum system and the fraction of chaotic regions of the classical phase space. 1
We study operator growth in a bipartite kicked coupled tops (KCTs) system using out-of-time ordered correlators (OTOCs), which quantify "information scrambling" due to chaotic dynamics and serve as a quantum analog of classical Lyapunov exponents. In the KCT system, chaos arises from the hyper-fine coupling between the spins. Due to a conservation law, the system's dynamics decompose into distinct invariant subspaces. Focusing initially on the largest subspace, we numerically verify that the OTOC growth rate aligns well with the classical Lyapunov exponent for fully chaotic dynamics. While previous studies have largely focused on scrambling in fully chaotic dynamics, works on mixed-phase space scrambling are sparse. We explore scrambling behavior in both mixed-phase space and globally chaotic dynamics. In the mixed-phase space, we use Percival's conjecture to partition the eigenstates of the Floquet map into "regular" and "chaotic." Using these states as the initial states, we examine how their mean phase space locations affect the growth and saturation of the OTOCs. Beyond the largest subspace, we study the OTOCs across the entire system, including all other smaller subspaces. For certain initial operators, we analytically derive the OTOC saturation using random matrix theory (RMT). When the initial operators are chosen randomly from the unitarily invariant random matrix ensembles, the averaged OTOC relates to the linear entanglement entropy of the Floquet operator, as found in earlier works. For the diagonal Gaussian initial operators, we provide a simple expression for the OTOC.