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The nature of dielectric echoes in amorphous solids at low temperatures isinvestigated. It is shown that at long delay times the echo amplitude isdetermined by a small subset of two level systems (TLS) having negligiblerelaxation and decoherence because of their weak coupling to phonons. The echodecay can then be described approximately by power law time dependencies withdifferent powers at times longer and shorter than the typical TLS relaxationtime. The theory is applied to recent measurements of two and three pulsedipolar echo in borosilicate glass BK7 and provides a perfect data fit in thebroad time and temperature ranges under the assumption that there exist two TLSrelaxation mechanisms due to TLS-phonons and TLS-TLS interaction. Thisinterpretation is consistent with the previous experimental and theoreticalinvestigations. Further experiments verifying the theory predictions aresuggested.

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