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Frontiers in Optics

Semiclassical Theory of Photon Echoes with Application to Pr:YSO

Zachary H. Levine

Published Jan 1, 2021• 0 citations
Publisher

Abstract

Coherent states are used to prepare a crystal using the Atomic Frequency Comb protocol for quantum memory. Here, semiclassical theory is developed and compared to experimental photon echoes of a coherent pulse.
DOI
10.1364/fio.2021.jw7a.23

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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.
The storage of single photons generated via nondegenerate spontaneous parametric down-conversion in a cavity with a PPKTP crystal in quantum memory based on an atomic frequency comb in a Eu:YSO crystal is demonstrated. A technique for preparing spectral profiles within the absorption line of a doped crystal that are matched to the spectrum of single-photon radiation is developed. For storage times of 250 and 166 ns, quantum memory efficiencies of 3 and 7% have been obtained with signal-to-noise ratios of 1/4 and 1/2, respectively.