Efficient and reversible optical-to-spin conversion for solid-state quantum memories

Long-duration and efficient quantum memories for photons are key components of quantum repeater and network applications. To achieve long duration storage in atomic systems, a short-lived optical coherence can be mapped into a long-lived spin coherence, which is the basis for many quantum memory schemes. In this work, we present modeling and measurements of the back-and-forth, i.e. reversible, optical-to-spin conversion for an atomic frequency comb memory. The AFC memory is implemented in $^{151}\textrm{Eu}^{3+}:\textrm{Y}_2\textrm{SiO}_5$ with an applied magnetic field of 231 mT, which allows lifting Zeeman transition degeneracy which otherwise cause time-domain interference in the optical-to-spin conversion. By optimizing the conversion using the developed simulation tool, we achieve a total efficiency of up to 96%, including the spin echo sequence and spin dephasing, for a storage time of 500 $μ$s. Our methods and results pave the way for long-duration storage of single photon states in 151Eu3+:Y2SiO5 with high signal-to-noise, at the millisecond timescale.

💡 Research Summary

This paper addresses a central challenge in quantum networking: achieving long‑duration, high‑efficiency quantum memories for photons. The authors focus on an atomic‑frequency‑comb (AFC) spin‑wave memory implemented in a 151Eu³⁺:Y₂SiO₅ crystal. In AFC memories, an incoming optical pulse is absorbed by a periodic series of narrow absorption peaks (the “comb”) and re‑emitted after a fixed delay 1/Δ. To obtain on‑demand readout and extend storage beyond the excited‑state lifetime, the optical coherence |g⟩–|e⟩ must be transferred to a long‑lived spin coherence |g⟩–|s⟩. This transfer requires two optical control pulses on the |s⟩–|e⟩ transition and two spin control pulses on the |g⟩–|s⟩ transition, forming a reversible back‑and‑forth mapping.

A major obstacle in Eu³⁺:Y₂SiO₅ is the weak optical and spin transition dipole moments, which make simple π‑pulses inefficient over the full AFC bandwidth and spin inhomogeneous broadening. Moreover, at low magnetic fields the hyperfine structure yields three nearly degenerate Zeeman doublets, causing time‑domain interference that degrades the reversibility of the optical‑to‑spin conversion.

The authors solve both problems by (i) applying a moderate static magnetic field of 231 mT at a precise angle (≈6.9°) in the D₁‑D₂ crystal plane, thereby fully lifting Zeeman degeneracy so that each addressed transition involves a single magnetic sub‑level, and (ii) employing adiabatic, frequency‑chirped “hyperbolic‑square‑hyperbolic” (HSH) pulses for both optical and spin control. An HSH pulse consists of smooth sech‑type rising/falling edges and a flat‑top segment; the frequency chirp follows a tanh profile at the edges and is linear in the middle. Two identical HSH pulses cancel the dynamic phase accumulated during the chirp, effectively implementing an identity operation on the stored coherence while inverting the population over a bandwidth set by the chirp width Γ_HSH.

To predict and optimise performance, a two‑dimensional Bloch‑equation model is developed. The simulation incorporates the Gaussian intensity profile of the crossed‑beam geometry, the full AFC bandwidth, the spin inhomogeneous linewidth, and realistic Rabi frequencies. By scanning pulse durations (T_C, T_sq) and chirp widths, the authors identify a regime where the optical control efficiency η_OC and spin control efficiency η_SC each exceed 0.98. The AFC echo efficiency η_AFC, limited by optical depth and comb finesse, is measured around 0.85. Combining these factors with the spin‑dephasing factor η_spin (≈1 for the 500 µs storage time used) yields a total memory efficiency η_tot = η_AFC·(η_OC)²·(η_SC)²·η_spin of (96 ± 1) %.

Experimentally, the crystal (12.5 mm long) is cooled to 3.3 K, and the magnetic field is generated by permanent NdFeB magnets in a sandwich configuration, with fine adjustment via auxiliary coils to align the field and merge the two magnetic subsites. Raman heterodyne spectroscopy and spectral hole‑burning measurements verify the Zeeman splittings (e.g., 1.76 MHz for the excited‑state |±5/2⟩ doublet), confirming that the bandwidth for a single ion class is limited by this split.

The work demonstrates that, despite the intrinsically weak transition moments of Eu³⁺, near‑unitary reversible optical‑to‑spin conversion is achievable using adiabatic HSH pulses and a properly oriented magnetic field. The methodology is directly transferable to other non‑Kramers rare‑earth systems such as Pr³⁺:Y₂SiO₅, and to protocols requiring broadband population inversion (e.g., noiseless photon‑echo or RASE). Importantly, the high conversion efficiency paves the way for extending spin‑wave storage to the millisecond regime and beyond, especially when combined with dynamical decoupling sequences that can exploit the exceptionally long spin coherence times (up to hours) reported for Eu³⁺ under optimized fields.

In summary, the paper provides a comprehensive theoretical and experimental framework for achieving efficient, reversible optical‑to‑spin mapping in solid‑state quantum memories, delivering a record 96 % total efficiency for 500 µs storage and establishing a clear path toward long‑duration, low‑noise single‑photon storage essential for scalable quantum repeaters and networks.