Quantum chaos measures for Floquet dynamics

Sarben Sarkar, J.S. Satchell

Shohini Ghose, R. Stock, Poul Jessen +2 more

We analyze the interplay of chaos, entanglement, and decoherence in a system of qubits whose collective behavior is that of a quantum kicked top. The dynamical entanglement between a single qubit and the rest can be calculated from the mean of the collective spin operators. This allows the possibility of efficiently measuring entanglement dynamics in an experimental setting. We consider a deeply quantum regime and show that signatures of chaos are present in the dynamical entanglement for parameters accessible in an experiment that we propose using cold atoms. The evolution of the entanglement depends on the support of the initial state on regular versus chaotic Floquet eigenstates, whose phase-space distributions are concentrated on the corresponding regular or chaotic eigenstructures. We include the effect of decoherence via a realistic model and show that the signatures of chaos in the entanglement dynamics persist in the presence of decoherence. In addition, the classical chaos affects the decoherence rate itself.

Neil Dowling, Kavan Kishore Modi

Chaotic systems are highly sensitive to a small perturbation and are ubiquitous throughout the biological sciences, the physical sciences, and even the social sciences. Taking this as the underlying principle, we construct an operational notion for quantum chaos. Namely, we demand that the future state of a many-body isolated quantum system is sensitive to past multitime operations on a small subpart of that system. By “sensitive,” we mean that the resultant states from two different perturbations cannot easily be transformed into each other. That is, the pertinent quantity is the complexity of the effect of the perturbation within the final state. From this intuitive metric, which we call the butterfly-flutter fidelity, we use the language of multitime quantum processes to identify a series of operational conditions on chaos; in particular, the scaling of the spatiotemporal entanglement. Our criteria already contain the routine notions, as well as the well-known diagnostics for quantum chaos. This includes the Peres-Loschmidt echo, dynamical entropy, tripartite mutual information, and local-operator entanglement. We hence present a unified framework for these existing diagnostics within a single structure. We also go on to quantify how several mechanisms, such as evolution generated from random circuits, lead to quantum chaos. Our work paves the way to systematically study many-body dynamical phenomena such as many-body localization, measurement-induced phase transitions, and Floquet dynamics. Published by the American Physical Society 2024

G. P. Berman

Sandro Wimberger

Anton Kapustin, Daniil Radamovich

We study the ergodic properties of a unitary Floquet dynamics arising from the repeated application of a translationally-invariant Clifford Quantum Cellular Automata to an infinite system of qubits in d dimensions. One expects that if the QCA does not exhibit any periodicity, a generic initial state of qubits will thermalize, that is, approach the infinite-temperature state. We show that this is true for many classes of states, both pure and mixed. In particular, this is true for all initial states that are short-range entangled and close to the equilibrium state. We also point out a subtle distinction between weak and strong thermalization.