Photon echoes using atomic frequency combs in Pr:YSO -- experiment and semiclassical theory

TL;DR

This paper investigates photon echoes in Pr:YSO using atomic frequency combs with hyperfine structure, combining experimental measurements with semiclassical and rate equation theories to understand broadband quantum memory challenges.

Contribution

It explores the intermediate hyperfine regime with AFCs, providing experimental data and comparing two theoretical models for photon echoes in this complex system.

Findings

Both theoretical models predict photon echoes well but differ in details.

Prepared broadband AFCs with tooth spacings from 1 MHz to 16 MHz.

Measured transmission spectra and photon echoes for each AFC configuration.

Abstract

Photon echoes in rare-earth-doped crystals are studied to understand the challenges of making broadband quantum memories using the atomic frequency comb (AFC) protocol in systems with hyperfine structure. The hyperfine structure of Pr^{3+} poses an obstacle to this goal because frequencies associated with the hyperfine transitions change the simple picture of modulation at an externally imposed frequency. The current work focuses on the intermediate case where the hyperfine spacing is comparable to the comb spacing, a challenging regime that has recently been considered. Operating in this regime may facilitate storing quantum information over a larger spectral range in such systems. In this work, we prepare broadband AFCs using optical combs with tooth spacings ranging from 1 MHz to 16 MHz in fine steps, and measure transmission spectra and photon echoes for each. We predict the spectra and echoes theoretically using the optical combs as input to either a rate equation code or a density matrix code, which calculates the redistribution of populations. We then use the redistributed populations as input to a semiclassical theory using the frequency-dependent dielectric function. The two sets of predictions each give a good, but different account of the photon echoes.