  We demonstrate the capability of complete thresholdless lasing operation
between dressed states of a two-level atom located inside a microscopic cavity
engineered in a photonic band-gap material. We distinguish between threshold
and thresholdless behaves by analyzing the Mandel's Q parameter for the cavity
field. We find that the threshold behave depends on whether the spontaneous
emission is or is not present on the lasing transition. In the presence of the
spontaneous emission, the mean photon number of the cavity field exhibits
threshold behavior indicating that the system may operate as an ordinary laser.
When the spontaneous emission is eliminated on the lasing transition, no
threshold is observed for all values of the pumping rate indicating the system
becomes a thresholdless laser. Moreover, we find that under a thresholdless
operation, the mean photon number can increase nonlinearly with the pumping
rate, and this process is accompanied by a sub-Poisson statistics of the field.
This suggests that the nonclassical statistics can be used to distinguish a
nonlinear operation of the dressed-atom laser.
