On the long-time behavior of spin echo and its relation to free induction decay

TL;DR

This paper predicts that spin echoes exhibit two types of long-time decay behaviors and that their decay characteristics are directly related to the free induction decay, with implications for understanding quantum system dynamics.

Contribution

It introduces a theoretical prediction linking long-time decay behaviors of spin echoes to free induction decay, applicable across various quantum systems.

Findings

Spin echoes decay either exponentially or as a superposition of exponential decays.

Long-time decay constants of spin echoes match those of free induction decay.

Supports the eigenvalue-based understanding of quantum system evolution.

Abstract

It is predicted that (i) spin echoes have two kinds of generic long-time decays: either simple exponential, or a superposition of a monotonic and an oscillatory exponential decays; and (ii) the long-time behavior of spin echo and the long-time behavior of the corresponding homogeneous free induction decay are characterized by the same time constants. This prediction extends to various echo problems both within and beyond nuclear magnetic resonance. Experimental confirmation of this prediction would also support the notion of the eigenvalues of time evolution operators in large quantum systems.