Superhyperfine induced photon-echo collapse of erbium in Y$_2$SiO$_5$

TL;DR

This study examines how superhyperfine interactions cause photon-echo decay in erbium-doped Y$_2$SiO$_5$, revealing a unified coherence time and the influence of neighboring nuclei at low magnetic fields.

Contribution

It introduces a detailed model accounting for superhyperfine modulation effects on decoherence without needing spin fluctuation times, and compares exact and approximate approaches.

Findings

Decay curves accurately reproduced by superhyperfine modulation model

Number of involved nuclei increases as magnetic field decreases

Approximate spherical model captures main features of decay near zero-field

Abstract

We investigate the decoherence of Er$^{3+}$ in Y$_2$SiO$_5$ at low magnetic fields using the photon-echo technique. We reproduce accurately a variety of the decay curves with a unique coherence time by considering the so-called superhyperfine modulation induced by a large number of neighbouring spins. There is no need to invoke any characteristic time of the spin fluctuations to reproduce very different decay curves. The number of involved nuclei increases when the magnetic is lowered. The experiment is compared with a model associating 100 surrounding ions with their exact positions in the crystal frame. We also derive an approximate spherical model (angular averaging) to interpret the main feature the observed decay curves close to zero-field.