  High power measurement-induced cavity response is investigated in the |g>,
|e>, and |f> states of a transmon. All the states exhibit photon blockades
above a certain critical value, a phenomenon that has previously been
understood based on the bistability of semiclassical Duffing oscillators. The
measurement-induced state transition (MIST) to high-level transmon states is
expected to be one contributor to the bistability; however, the critical values
measured in the |e> and |f> states are not coincident with the MIST. To
understand this discrepancy, we utilize the recently developed semiclassical
dynamics model of a cavity photon state. The appearance of dim and bright
cavity states obtained from the model's steady-state solution leads to the
photon blockades at lower critical photon numbers, and this can explain the
response of the bistable region in the |e> and |f> states.
