# Rephasing efficiency of sequences of phased pulses in spin-echo and light-storage experiments

## TL;DR

This paper studies how the phase accuracy of pulse sequences affects rephasing efficiency in spin echoes and light storage, revealing differences due to spatial coherence effects and confirming findings experimentally.

## Contribution

It introduces a simple model linking pulse phase imperfections to rephasing efficiency and highlights differences between spin echoes and EIT light storage.

## Key findings

- Rephasing efficiency is highly sensitive to pulse phase imperfections.
- Efficiency differs significantly between spin echoes and EIT light storage.
- Experimental validation in Pr$^{3+}$:Y$_{2}$SiO$_{5}$ confirms the model.

## Abstract

We investigate the rephasing efficiency of sequences of phased pulses for spin echoes and light storage by electromagnetically induced transparency (EIT). We derive a simple theoretical model and show that the rephasing efficiency is very sensitive to the phases of the imperfect rephasing pulses. The obtained efficiency differs substantially for spin echoes and EIT light storage, which is due to the spatially retarded coherence phases after EIT light storage. Similar behavior is also expected for other light-storage protocols with spatial retardation or for rephasing of collective quantum states with an unknown or undefined phase, e.g., as relevant in single-photon storage. We confirm the predictions of our theoretical model by experiments in a Pr$^{3+}$:Y$_{2}$SiO$_{5}$ crystal.