Low-temperature dipolar echoes in amorphous dielectrics: Significance of relaxation and decoherence free two-level systems

The theoretical model for dielectric echoes in amorphous solids at low temperatures has been developed and applied to the recent two- and three-pulse echo experimental data in borosilicate glass BK7 where the amplitude of dipolar echoes has been observed for unprecedentedly long delay times extending the experimental window for studying the decay by several orders of magnitude. The researchers show that at long delay times the echo amplitude is determined by a small subset of two-level systems (TLS) with negligible relaxation and decoherence because of their weak coupling to phonons. The universal statistics of coupling is obtained by assuming that different TLS elastic tensor components are almost independent. Under this assumption the echo decay can be described approximately by the power law time dependences with different powers at times shorter and longer than the typical TLS relaxation time. These predictions are in a very good agreement with the experimental data and can be used to extract TLS relaxation and decoherence rates from the echo experiments.