Feedback-based simulation of quantum nonlinear dynamics: The Quantum Kicked Top in an ensemble of two-level atoms.

We study the implementation of a measurement-based feedback scheme to realize quantum nonlinear dynamics. We specifically study the Quantum Kicked Top (QKT), a standard paradigm of quantum chaos, in the context of an ensemble of spins. The scheme uses a sequence of (not-so) weak measurements of a collective spin variable and global rotations conditioned on the measurement outcome. We show that the resulting dynamics, ensemble averaged over many realizations, is governed by a combination of the QKT Hamiltonian and a non-unitary channel which vanishes in the semiclassical limit, recovering the Classical Kicked Top. We also analyze individual quantum trajectories, where we explore the emergence of chaotic behaviour and revisit the role of the measurement process in the quantum-to-classical transition.