Phonon Echoes in Glass

Abstract

Phonon echoes, the acoustic analog of spin and photon echoes, are observed in fused silica glass at ultralow temperatures. From the phonon echo decay, we infer a homogeneous transverse lifetime of 14\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec and a longitudinal relaxation time of 200\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec for tunneling states at 0.68 GHz at a temperature of 20 mK. The coupling between the two-level systems and phonons is estimated to be 1.6 eV.