A theory of the three-pulse electric-dipole echo in glasses in a magnetic field

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 (TLSs) 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 TLS’s quadrupole electric moments of non-spherical nuclei and/or dipole–dipole interaction of their nuclear spins. These two mechanisms are responsible for the additional 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 the existence in the theory the additional parameter TT—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.