  We investigate theoretically quantum effects of a cavity-atom system in which
the upper two levels of a cascade-type three-level atom interact with a cavity
field mode in the ultrastrong coupling regime. By exploiting the virtual
photons carried by atom-cavity dressed states, we indicate how two external
driving fields induce Raman transitions such that a continuous conversion of
virtual photons into real photons can be achieved with a high probability. We
present analytical and numerical solutions of the system. In addition, we show
that the converted photons exhibit a bunching behavior in the steady state. Our
scheme demonstrates that atom-cavity dressed states in the ultrastrong coupling
regime can serve as intermediate states to invoke nonlinear optical processes.
