  Strongly driven systems of emitters offer an attractive source of light over
broad spectral ranges up to the X-ray region. A key limitation of these systems
is that the light they emit is for the most part classical. We challenge this
paradigm by building a quantum-optical theory of strongly driven many-body
systems, showing that the presence of correlations among the emitters creates
emission of nonclassical many-photon states of light. We consider the example
of high-harmonic generation (HHG), by which a strongly driven system emits
photons at integer multiples of the drive frequency. In the conventional case
of uncorrelated emitters, the harmonics are in an almost perfectly multi-mode
coherent state lacking any correlation between harmonics. By contrast, a
correlation of the emitters prior to the strong drive is converted onto
nonclassical features of the output light, including doubly-peaked photon
statistics, ring-shaped Wigner functions, and quantum correlations between
harmonics. We propose schemes for implementing these concepts, creating the
correlations between emitters via an interaction between them or their joint
interaction with the background electromagnetic field (as in superradiance). By
tuning the time at which these processes are interrupted by the strong drive,
one can control the amount of correlations between the emitters, and
correspondingly the deviation of the emitted light from a classical state. Our
work paves the way towards the engineering of novel many-photon states of light
over a broadband spectrum of frequencies, and suggests HHG as a diagnostic tool
for characterizing correlations in many-body systems with attosecond temporal
resolution.
