# Simulating nonlinear dynamics of collective spins via quantum measurement and feedback

## TL;DR

This paper presents a measurement-based feedback method to simulate and analyze the transition from quantum to classical chaos in spin ensembles, demonstrating robustness against decoherence.

## Contribution

The authors introduce a novel measurement and feedback scheme to simulate quantum many-body dynamics and explore quantum chaos in a realistic experimental setup.

## Key findings

- Quantum trajectories can recover classical chaos in certain regimes.
- Transition from quantum noise to deterministic chaos characterized by Lyapunov exponents.
- Scheme remains robust under decoherence effects.

## Abstract

We study a method to simulate quantum many-body dynamics of spin ensembles using measurement-based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by classical Lyapunov exponents. We also analyze the effects of decoherence, and show that the proposed scheme represents a robust method to explore the emergence of chaos from complex quantum dynamics in a realistic experimental platform based on an atom-light interface.