Photon-mediated correlated hopping in a synthetic ladder

Abstract: Cavity QED systems are emerging as leading platforms for quantum simulation of tunable long-range interacting spin models and spin-boson models featuring rich steady-state and non-equilibrium many-body behaviors. We propose a new direction that uses multilevel atoms in an optical cavity as a toolbox to engineer new types of bosonic models, which features correlated hopping processes in a synthetic two-leg ladder spanned by atomic ground states. The underlying mechanisms responsible for correlated hopping are collective cavity-mediated interactions that dress a manifold of excited levels in the far detuned limit. We study a variety of many-body phenomena that can be realized in this system, including dynamical phase transitions in pair production processes, chiral transport that is tunable via laser detunings and initial state preparation, and correlation spreading and emergent light-cone transport in the synthetic ladder. We also discuss a feasible experimental implementation using long-lived alkaline earth atoms.