  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.
