The nature of dielectric echoes in amorphous solids at low temperatures is investigated. It is shown that at long delay times the echo amplitude is determined by a small subset of two level systems (TLS) having negligible relaxation and decoherence because of their weak coupling to phonons. The echo decay can then be described approximately by power law time dependencies with different powers at times longer and shorter than the typical TLS relaxation time. The theory is applied to recent measurements of two and three pulse dipolar echo in borosilicate glass BK7 and provides a perfect data fit in the broad time and temperature ranges under the assumption that there exist two TLS relaxation mechanisms due to TLS-phonons and TLS-TLS interaction. This interpretation is consistent with the previous experimental and theoretical investigations. Further experiments verifying the theory predictions are suggested.

The properties of amorphous solids below 1 K are dominated by atomic tunneling systems. A basic description is given by the standard tunneling model. Despite its success, the standard tunneling model still remains phenomenological and little is known about the microscopic nature of tunneling systems in amorphous solids. We present dielectric polarization echo experiments on partially deuterated amorphous glycerol. Nuclear quadrupoles, introduced by the deuteration, influence the echo amplitude in a characteristic way and allow us to draw for the first time detailed conclusions about the microscopic nature of the tunneling processes in amorphous glycerol.

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