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Squeezing of optical fields, used as a powerful resource for manyapplications, and the radiation properties in the process of high harmonicgeneration have thus far been considered separately. In this Letter, we want toclarify that the joint quantum state of all the optical field modes in theprocess of high harmonic generation is in general entangled and squeezed. Weshow that this is already the case in the simplest scenario of drivinguncorrelated atoms by a classical laser light field. The previous observationof product coherent states after the high harmonic generation process is aconsequence of the assumption that the ground state depletion can be neglected,which is related to vanishing dipole moment correlations. Furthermore, weanalyze how the resulting quadrature squeezing in the fundamental laser modeafter the interaction can be controlled and explicitly show that all fieldmodes are entangled.

Entanglement and squeezing of the optical field modes in high harmonic generation