Effect of a Magnetic Field on the Dipole Echo in Glasses with Nuclear Quadrupole Moments

TL;DR

This paper theoretically investigates how magnetic fields influence the dipole echo in glasses containing nuclei with electric quadrupole moments, revealing oscillatory behavior due to multilevel systems formed from two-level systems at very low temperatures.

Contribution

It introduces a general formula for the dipole echo amplitude in split two-level systems, accounting for magnetic field effects and multilevel structures, supported by analytic and numerical analysis.

Findings

Dipole echo amplitude exhibits oscillations in magnetic field.

Theoretical results align well with experimental data.

Multilevel systems arise from two-level systems due to nuclear quadrupole interactions.

Abstract

The effect of a magnetic field on the dipole echo amplitude in glasses at temperatures of about 10 mK caused by nonspherical nuclei with electric quadrupole moments has been studied theoretically. It has been shown that in this case, the two-level systems (TLS's) that determine the glass properties at low temperatures are transformed into more complicated multilevel systems. These systems have new properties as compared to usual TLS's and, in particular, exhibit oscillations of electric dipole echo amplitude in magnetic field. A general formula that describes the echo amplitude in an arbitrary split TLS has been derived with perturbation theory. Detailed analytic and numerical analysis of the formula has been performed. The theory agrees qualitatively and quantitatively well with experimental data.