Scaling of self-stimulated spin echoes

TL;DR

This paper investigates the behavior and amplitude of self-stimulated spin echoes in spin ensembles coupled to superconducting resonators, emphasizing the effects of ensemble cooperativity and anisotropic linewidths.

Contribution

It introduces a method to study echo amplitudes using echo-silencing with a fast tunable resonator and explores the dependence on spin-resonator cooperativity.

Findings

Self-stimulated echoes mainly result from two large control pulses and the preceding echo.

Echo amplitudes depend on the ensemble's cooperativity and linewidth anisotropy.

The study demonstrates the role of control pulses in echo formation.

Abstract

Self-stimulated echoes have recently been reported in the high cooperativity and inhomogeneous coupling regime of spin ensembles with superconducting resonators. In this work, we study their relative amplitudes using echo-silencing made possible by a fast frequency tunable resonator. The highly anisotropic spin linewidth of Er$^{3+}$ electron spins in the CaWO$_4$ crystal also allows to study the dependence on spin-resonator ensemble cooperativity. It is demonstrated that self-stimulated echoes primarily result from a combination of two large control pulses and the echo preceding it.