  Particle production during cosmic expansion can be interpreted as a two-mode
squeezing process of quantum states. The two-mode squeezed states consist of an
infinite number of entangled particles and then enhance the nonclassicality of
particles. There are two methods for estimating the degree of squeezing. One is
to employ instantaneous vacuum states, and the other is to adopt adiabatic
vacuum states. We analytically study the squeezing process of gravitons and
axions by using the two methods. We first consider a cosmological model of
inflation followed by instantaneous reheating leading to a radiation dominated
era. In the case of gravitons, we find no qualitatively difference in the
squeezing between the two methods. However, for the axions, it turns out that
the squeezing in the instantaneous vacuum increases as the mass increases while
the squeezing decreases in the adiabatic vacuum as the mass increases. We then
study the effect of non-instantaneous reheating on the the squeezing and show
that the squeezing is enhanced compared with the instantaneous reheating. We
also illustrate how the squeezed states enhance the violation of Bell
inequality and quantum noise of gravitons and axions.
