Quantum Chaos and Entanglement in Ion Crystals

Trapped ion crystals are a  powerful platform for quantum simulation of
spin and spin–boson models. In this talk, I will present our recent
experimental realization of the Dicke model in a two-dimensional crystal
of about 100 trapped ions. Despite its apparent simplicity, this model
hosts a wealth of complex behaviors that have remained largely
unexplored experimentally.  I will discuss  evidence of the dynamical
phase transition between ferromagnetic and paramagnetic regimes, of the
emergence of chaos as phonons actively participate in the dynamics, and
clear signatures of quantum fluctuations, entanglement, and
non-integrability. Starting from unstable classical fixed points, we
directly observe dynamics triggered by quantum noise, including
exponential decay of magnetization, quantum collapses and revivals, and
the formation of correlated spin–phonon excitations.

Our measurements are in excellent agreement with simulations
incorporating leading quantum fluctuations, revealing two-mode squeezing
between spins and phonons and variance reduction below the standard
quantum limit. These results demonstrate that ion crystals provide a
scalable platform for non-equilibrium phonon–matter dynamics, offering
new opportunities to explore quantum scrambling, entanglement-enhanced
metrology, and information recovery protocols.