Ultrastrong Jaynes-Cummings Model

We propose a reliable scheme to realize the ultrastrong Jaynes-Cummings (JC) model by simultaneously modulating the resonance frequencies of the two-level system and the bosonic mode in the ultrastrong quantum Rabi model. We find that in both the high- and low-frequency modulation regimes, the counter-rotating terms can be completely suppressed without reducing the coupling strength of the rotating-wave terms, and hence the ultrastrong JC Hamiltonian is achieved. The ultrastrong JC interaction can not only be used to implement ultrafast quantum operations, but also will open up a new route to the demonstration of quantum phase transition associated with the JC Hamiltonian across the deep-strong coupling point. Some discussions on the experimental implementation of this scheme with circuit-QED systems are presented.