Onset of the nonlinear dielectric response of glasses in the two-level system model

We have calculated the real part X’ of the nonlinear dielectric susceptibility of amorphous insulators in the kHz range, by using the two-level system model and a nonperturbative numerical quantum approach. At low temperature T, it is first shown that the standard two-level model should lead to a decrease of X’ when the measuring field E is raised, since raising E increases the population of the upper level and induces Rabi oscillations cancelling the ones induced from the ground level. This predicted E-induced decrease of X’ is at odds with experiments. However, a better, though still not perfect, agreement with low-frequency experimental nonlinear data is recovered if, in our fully quantum simulations, interactions between defects are taken into account by a new relaxation rate whose efficiency increases as √—X, as was proposed recently by Burin et al. [Phys. Rev. Lett. 86, 5616 (2001)]. In this approach, the behavior of X’ at low T is mainly explained by the efficiency of this new relaxation channel. Since a quantitative understanding of glasses is still missing, we finally discuss experiments whose results should yield a refined understanding of this new relaxation mechanism: i) a completely new nonlinear behavior should be found for samples whose thickness is ≃ 10 nm; ii) a decrease of nonequilibrium effects should be found when E is increased.