We extended existing theory of the two-pulse electric-dipole echo in glasses in a magnetic field to the three-pulse echo. As is well known, at low temperatures two-level systems (TLS's) are responsible for the echo phenomenon in glasses. Using a diagram technique in the framework of perturbation theory we derived a simple formula for the three-pulse echo amplitude. As in the case of two-pulse echo the magnetic field dependence of the tree-pulse echo amplitude in glasses is related to quadrupole electric moments of TLS's non-spherical nuclei and/or dipole-dipole interaction of their nuclear spins. These two mechanisms are responsible for the fine level splitting of TLS. As a result TLS transforms to multi-level system with the fine level splitting depending on a magnetic field. Due to existence in the theory the additional parameter T - the time interval between the second and the third pulses we have more reach spectrum of echo oscillations in a magnetic field in comparison with the case of the two-pulse echo.
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）
