Oscillations of the Electric-Dipole Echo in Glasses in a Magnetic Field

TL;DR

This paper derives how the electric-dipole echo in glasses with two-level systems oscillates under magnetic fields due to quadrupole interactions, revealing magnetic field-dependent behavior and saturation effects.

Contribution

It introduces a simple diagram technique to derive the electric-dipole echo amplitude considering quadrupole nuclear moments in glasses under magnetic fields.

Findings

Echo amplitude oscillates with weak magnetic fields due to quadrupole interactions.

Increasing magnetic field enhances the average echo amplitude, which saturates at high fields.

The saturation level exceeds the average oscillation level at low magnetic fields.

Abstract

Using a simple diagram technique we derive the electric-dipole echo amplitude from two-level systems with a quadrupole nuclear moment in glasses in an external magnetic field. We show, that due to the quadrupole moment interaction of a tunneling particle with a gradient of an internal electric field, the echo amplitude experiences oscillations in rather weak magnetic fields. With an increase of the magnetic field, when the Zeeman energy becomes larger than the quadrupole energy splitting, the average echo amplitude increases and saturates (for high magnetic fields) at some level which is above the average level of echo oscillations for small magnetic fields.