  We analytically describe the strong-field light-electron interaction using a
quantized coherent laser state with arbitrary photon number. We obtain a
light-electron wave function which is a closed-form solution of the
time-dependent Schrodinger equation (TDSE). This wave function provides
information about the quantum optical features of the interaction not
accessible by semi-classical theories. With this approach we can reveal the
quantum optical properties of high harmonic generation (HHG) process in gases
by measuring the photon statistics of the transmitted infrared (IR) laser
radiation. This work can lead to novel experiments in high-resolution
spectroscopy in extreme-ultraviolet (XUV) and attosecond science without the
need to measure the XUV light, while it can pave the way for the development of
intense non-classical light sources.
