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 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.