  Squeezing of optical fields, used as a powerful resource for many
applications, and the radiation properties in the process of high harmonic
generation have thus far been considered separately. In this Letter, we want to
clarify that the joint quantum state of all the optical field modes in the
process of high harmonic generation is in general entangled and squeezed. We
show that this is already the case in the simplest scenario of driving
uncorrelated atoms by a classical laser light field. The previous observation
of product coherent states after the high harmonic generation process is a
consequence of the assumption that the ground state depletion can be neglected,
which is related to vanishing dipole moment correlations. Furthermore, we
analyze how the resulting quadrature squeezing in the fundamental laser mode
after the interaction can be controlled and explicitly show that all field
modes are entangled.
