Quantum Chaos and Entanglement in a Trapped Ion Crystal

Trapped ion crystals are a  powerful platform for quantum simulation of spin and spin–boson models. In this talk, I will report on  a recent experimental realization of the Dicke model in a two-dimensional crystal in a Penning trap with  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, I will discuss how we can  directly observe dynamics triggered by quantum noise, including an  exponential decay of the  total  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 of  3 dB below the standard quantum limit and 5 dB below the thermal bound. 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.