It is assumed in standard cosmology that the Universe underwent a period of inflation in its earliest phase, providing the seeds for structure formation through vacuum fluctuations of the inflaton scalar field. These fluctuations get stretched by the quasi-exponential expansion of the Universe and become squeezed. From an observational point of view, if we consider Gaussian states, the expectation value of physical quantities on a squeezed state is indistinguishable from a classical average of a stochastic distribution. This renders cosmological perturbations arising from quantum fluctuations of free fields effectively identical to those with a classical origin. The cosmological squeezing has been largely studied in the literature, however most works have focused on nearly free fields. In this talk I will consider the effect of self-interactions of axion-like fields on the quantum-to-classical transition process. In particular I will introduce the Bogoliubov coefficients and the squeezing parameters, which are linked to the axion particle number and isocurvature perturbations. I will show that the quantum mechanical particle production and the squeezing of the perturbations are enhanced, if one accounts for anharmonic effects, i.e., the effects of higher order terms in the potential. This effect becomes particularly strong towards the hilltop of the potential.