The quantum Rabi model describing the fundamental interaction between light and matter is a cornerstone of quantum physics. It predicts exotic phenomena like quantum phase transitions and ground-state entanglement in the ultrastrong-coupling (USC) regime, where coupling strengths are comparable to subsystem energies. Despite progress in many experimental platforms, the few experiments reaching USC have been limited to spectroscopy: demonstrating USC dynamics remains an outstanding challenge. Here, we employ a circuit QED chip with moderate coupling between a resonator and transmon qubit to realise accurate digital quantum simulation of USC dynamics. We advance the state of the art in solid-state digital quantum simulation by using up to 90 second-order Trotter steps and probing both subsystems in a combined Hilbert space dimension ∼80, demonstrating the Schr\"odinger-cat like entanglement and build-up of large photon numbers characteristic of deep USC. This work opens the door to exploring extreme USC regimes, quantum phase transitions and many-body effects in the Dicke model.
@article{arxiv.1610.10065,
title = {Experimentally simulating the dynamics of quantum light and matter at ultrastrong coupling},
author = {N. K. Langford and R. Sagastizabal and M. Kounalakis and C. Dickel and A. Bruno and F. Luthi and D. J. Thoen and A. Endo and L. DiCarlo},
journal= {arXiv preprint arXiv:1610.10065},
year = {2017}
}