  We present a theoretical demonstration on the generation of entangled
coherent states and of coherent state superpositions, with photon numbers and
frequencies orders of magnitude higher than those provided by the current
technology. This is achieved by utilizing a quantum mechanical multimode
description of the single- and two-color intense laser field driven process of
high harmonic generation in atoms. It is found that all field modes involved in
the high harmonic generation process are entangled, and upon performing a
quantum operation, leads to the generation of high photon number optical cat
states spanning from the far infrared to the extreme-ultraviolet spectral
region. This provides direct insights into the quantum mechanical properties of
the optical field in intense laser matter interaction. Finally, these states
can be considered as a new resource for fundamental tests of quantum theory,
quantum information processing or sensing with non-classical states of light.

Quantum Physics;Atomic Physics;Optics