  We study the effect of electron-electron correlations on the quantum state of
the light emitted from high-harmonic generation (HHG). The quantum state of the
emitted light is obtained by using a fully quantum mechanical description of
both the optical modes as well as the electronic system. This is different from
the usual semiclassical description of HHG, which only treats the electronic
target system quantum mechanically. Using the generic Fermi-Hubbard model, the
strength of the electron-electron correlation can be treated as a parameter
enabling us to investigate the two limiting cases of a completely uncorrelated
phase and a correlated Mott-insulating phase. In the completely uncorrelated
phase, the model reduces to a single-band tight-binding model in which only
intraband currents contribute to the spectrum. In this limit, we analytically
find that the emitted light is in a classical coherent state. In the
Mott-insulating phase, a consideration of the photon statistics and squeezing
of the emitted photonic state shows that the inter-Hubbard-subband current
generates nonclassical light. In this sense, we show that electron-electron
correlation can induce the generation of nonclassical states of light.
