The effect of a magnetic field on the dipole echo amplitude in glasses (at temperatures of about 10 mK) induced by the dipole-dipole interaction of nuclear spins has been theoretically studied. It has been shown that a change in the positions of nuclear spins as a result of tunneling and their interaction with the external magnetic field E_H lead to a nonmonotonic magnetic field dependence of the dipole echo amplitude. The approximation that the nuclear dipole-dipole interaction energy E_d is much smaller than the Zeeman energy E_H has been found to be valid in the experimentally important cases. It has been shown that the dipole echo amplitude in this approximation may be described by a simple universal analytic function independent of the microscopic structure of the two-level systems. An excellent agreement of the theory with the experimental data has been obtained without fitting parameters (except for the unknown echo amplitude)
Phonon Echo from Multi-Level Systems and Many-Body Interactions in Low-Temperature Glasses
Key Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology（北京理工大学光电量子架构与测量教育部重点实验室物理学院）；Department of Physics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系）；Department of Physics, University of Michigan（密歇根大学物理系）；School of Physics, Georgia Institute of Technology（佐治亚理工学院物理学院）
