Securing coherence rephasing with a pair of adiabatic rapid passages

TL;DR

This paper analyzes how pairs of adiabatic rapid passages (ARPs) can effectively rephase atomic coherences in quantum storage, providing a simple geometric interpretation and experimental validation with rare-earth ion-doped crystals.

Contribution

It offers a comprehensive analysis of ARP-based rephasing, highlighting the importance of phase control and demonstrating the superiority of ARPs over $ ext{pi}$-pulses.

Findings

Double-ARP sequences act as the identity operator under certain conditions.

Phase of ARP fields is crucial for phase preservation.

ARP rephasing outperforms $ ext{pi}$-pulse methods.

Abstract

Coherence rephasing is an essential step in quantum storage protocols that use echo-based strategies. We present a thorough analysis on how two adiabatic rapid passages (ARP) are able to rephase atomic coherences in an inhomogeneously broadened ensemble. We consider both the cases of optical and spin coherences, rephased by optical or radio-frequency (rf) ARPs, respectively. We show how a rephasing sequence consisting of two ARPs in a double-echo scheme is equivalent to the identity operator (any state can be recovered), as long as certain conditions are fulfilled. Our mathematical treatment of the ARPs leads to a very simple geometrical interpretation within the Bloch sphere that permits a visual comprehension of the rephasing process. We also identify the conditions that ensure the rephasing, finding that the phase of the optical or rf ARP fields plays a key role in the capability of the sequence to preserve the phase of the superposition state. This settles a difference between optical and rf ARPs, since field phase control is not readily guaranteed in the former case. We also provide a quantitative comparison between $\pi$-pulse and ARP rephasing efficiencies, showing the superiority of the latter. We experimentally verify the conclusions of our analysis through rf ARP rephasing sequencies performed on the rare-earth ion-doped crystal Tm$^{3+}$:YAG, of interest in quantum memories.