Theory of nonlinear resonant absorption in dielectric glasses at low temperatures

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Abstract
The saturation of resonant absorption in dielectric glasses at low temperatures is studied. The main specific mechanisms for the relaxation of two-level systems (TLS’s) are spectral diffusion and phonon bottleneck. Spectral diffusion dominates at equilibrium and determines the threshold intensity which appears to be different for high and low frequencies. In the strongly nonlinear case, spectral diffusion determines absorption for low frequencies and sufficiently short pulses. It leads to an absorbed power independent of intensity. The existence of the phonon bottleneck leads to the domination of phonon relaxation for pulses short compared to the equilibrium relaxation time of the TLS’s. For a pulse length typically used in experiments a transient regime is set up when the number of phonons in the resonant region increases due to absorption. The absorption itself appears to be independent of the phonon distribution and so is stationary. The value for the absorption in this case is identical to that obtained before in the stationary regime of TLS relaxation by equilibrium phonons. The results of the present theory are in good agreement with available experimental data on absorption and hole burning.