The stationary state of a single-atom (single-qubit) laser is shown to be a
phase-averaged nonlinear coherent state - an eigenstate of a specific deformed
annihilation operator. The solution found for the stationary state is unique
and valid for all regimes of the single-qubit laser operation. We have found
the parametrization of the deformed annihilation operator which provides
superconvergence in finding the stationary state by iteration. It is also shown
that, contrary to the case of the usual laser with constant Einstein
coefficients describing transition probabilities, for the single-atom laser the
interaction-induced transition probabilities effectively depend on the field
intensity