Measurement and feedback-driven adaptive dynamics in the classical and quantum kicked top

TL;DR

This paper explores how stochastic feedback control can stabilize and manipulate the dynamics of the classical and quantum kicked top, revealing insights into quantum chaos, semiclassical approximations, and information encoding.

Contribution

It demonstrates the application of stochastic feedback protocols across classical, semiclassical, and quantum regimes of the kicked top, highlighting their effectiveness and limitations.

Findings

Control protocols stabilize unstable orbits in classical and quantum regimes.

Low-moment observables are well captured by semiclassical approximations.

Control induces rapid purification, reducing the system's quantum information capacity.

Abstract

In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these control protocols in classical, semiclassical, and quantum regimes to the kicked top, a paradigmatic model of quantum chaos. The quantum kicked top, modeled as the dynamics of a spin-S object, naturally interpolates between these regimes with the spin size S acting as an effective Planck constant. We show that the dynamics of the kicked top in classical, semiclassical, and fully quantum limits can all be controlled using stochastic feedback protocols. Comparing the full quantum dynamics to a truncated Wigner approximation that captures quantum noise but neglects interference beyond the Ehrenfest time, we find that low-moment observables are largely accounted for semiclassically, while the remaining discrepancy in higher moments is consistent with contributions from interference and possibly nonlinearities in rare trajectories that explore the compact phase space. We also find rapid purification in the numerics studied for all rates of control considered, suggesting that control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.