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

Abstract

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.

Random Nonlinear Infinite-Level-System Model for Amorphous Solid Phonon Echo and Saturation Phenomena

“…Phonon echo can be automatically explained within TTLS model by making analogy to spin echo effect, because both of two-level-system Hamiltonian and the coupling between two-level-system and phonon strain field can be represented by Pauli matrices. D. A. Parshin and his collaborators [22][23][24] has derived a complete theory beyond two-level-system, that for an arbitrary multiple-level-system with randomness and anharmonicity, one can always obtain phonon echo phenomena. In this paper by setting up the coupling btween stress tensor and phonon strain field, we prove that phonon echo essentially comes from off-diagonal matrix elements of stress tensor operators in the basis of glass non-elastic part of Hamiltonian.…”