Simulating the Dicke model with hundreds of ions in a Penning trap

Through control of both the spin and motional degrees of freedom, trapped ions provide opportunities for simulating spin-boson models. Of particular interest is the Dicke model, which describes the collective interaction of many spins with a single harmonic oscillator. The Dicke model exhibits interesting features such as non-integrability, chaos, and dynamical phase transitions. Here we summarize recent experimental work simulating non-equilibrium dynamics of the Dicke model with single-plane crystals of several hundred ions stored in a Penning ion trap. The collective spin of the trapped ion crystal consisting of several hundred Be+ ions is coupled to the crystal center-of-mass mode through a spin-dependent optical dipole force. A transverse field interaction that competes with the spin-motion coupling is implemented with microwaves resonant with the ion qubit transition. A nice feature of employing tapped ions for simulating spin-boson models is the weak damping of the center-of-mass mode, which has been measured to be longer than hundreds of ms in our system