  We study the emission spectrum of a qubit under deep strong driving in the
high-frequency dispersive regime when the driving frequency and strength exceed
significantly the qubit transition frequency. Closed-form expressions for the
steady-state first-order field correlation function and the multiphoton
emission spectrum are obtained. The spectrum comprises a series of narrow
delta-like lines that stem from coherent processes and Lorenzian peaks that
result from the incoherent scattering of photons. The oscillating dependence of
the widths of the emission lines on the driving strength is predicted. We show
how the features of this dependence are governed by the qubit dephasing and
relaxation rates.
