Strong field Cooper minimum in High Harmonic Generation

The Cooper minimum is a prominent dip in the VUV photoionization spectrum in Ar caused by a cancellation of the radial integral in the transition matrix element between the atomic ground state and the continuum. The minimum is accompanied by a $\pi$ phase jump in the matrix element [1]. The recombination step of High Harmonic Generation (HHG) can be described by the inverse photoionization matrix element. We observe a similar minimum in the HHG spectrum of argon, which we associate with the Cooper minimum. We have measured the spectral phase of the harmonics and observe the expected spectral phase jump of $\pi$ around this spectral minimum. This HHG Cooper minimum is shifted from the photoionization Cooper minimum by about 5 eV. Calculations show that this shift is due to strong-field mixing of the continuum states during the recombination step in HHG. The results show the opportunity for controlled attosecond pulse shaping. [1] J. W. Cooper, Physical Review 128, 681 (1962)