Hole burning experiments and modeling in erbium-doped silica glass fibers down to millikelvin temperatures: evidence for ultra-long population storage

TL;DR

This work uses spectral hole burning to study spin dynamics of Er$^{3+}$ in Er-doped silica fibers over $T\approx$7 mK–2.4 K and up to $B\approx$0.2 T, revealing two relaxation components at higher temperatures and a third ultra-long-lived component ($T_c$) that yields lifetimes $>\!9$ h near 7 mK. A unified model decomposes $1/T_i$ into three additive mechanisms—Er-Er flip-flop, direct coupling to thermally driven TLS, and Raman-type processes—with shared temperature and field dependencies but component-specific amplitudes $\alpha^i$. The exponents and parameters are fitted to data, showing a transition from Lorentzian to Gaussian spectral holes and a notable emergence of the long-lived ion class, likely linked to isotope/nuclear-spin effects, suggesting EDFs as robust long-term quantum memory candidates. The findings indicate that optimizing the ESR environment and isotope composition could enable stable, long-duration quantum state storage in amorphous Er-doped fibers, with implications for quantum communication networks.

Abstract

We use spectral hole burning to investigate spin dynamics within the electronic Zeeman sublevels of the ground state of the erbium ions in erbium-doped fibers (EDF). Conducted at ultra-low temperatures and under varying magnetic fields, our study reveals distinct changes in spin relaxation dynamics across different conditions. We identified three decay components at approximately 7 mK, with one achieving spin lifetimes of over 9 hours under optimal conditions, while two components were observed at higher temperatures. The fairly stable relative weights of the decay components across conditions suggest distinct ion populations contributing to the observed relaxation dynamics. While earlier studies struggled to account for all decay components at higher temperatures, our approach successfully models spin dynamics across all observed decay components, using a consistent set of underlying mechanisms, including spin flip-flop interactions, direct coupling to two-level systems, and Raman-type processes, and distinguishes the decay components by the strengths with which these mechanisms contribute. These results suggest EDFs' potential as a promising candidate for quantum memory applications, with further room for optimization.

Figures (8)

• Figure 1: Schematic of the experimental setup for spectral hole burning in erbium-doped silica fiber. The continuous-wave external cavity diode laser (ECDL) generates light at a 1532 nm wavelength, monitored by a wavemeter via a 50/50 beamsplitter (BS). A Polarizing Beam Splitter (PBS) controls polarization, while a phase modulator provides spectral resolution by chirping the read pulse, which is generated by a 500 MHz acousto-optic modulator (AOM) for scanning and measuring the spectral hole. The variable attenuator adjusts laser power to optimize hole burning. The erbium-doped silica fiber, mounted in the cryostat, is probed with burn and read pulses. The resulting signal is detected by an InGaAs photodetector.
• Figure 2: Example of spectral hole dynamics at higher temperatures, shown at $T = 180$ mK and $B = 50$ mT. (a) The spectral hole area as a function of waiting time, fitted with two exponential decay components. The data points (blue markers) represent the measured decay of the spectral hole area over time, while the solid red curve represents the fit, with characteristic times $T_a = 8.4 \pm 0.5$ s (62%) and $T_b = 591.4 \pm 32.3$ s (38%), indicating the involvement of two distinct ion classes in the relaxation process. (b) Close-up of the spectral hole 100 ms post-burn, marked by the vertical dashed purple line in (a). A Lorentzian (solid red line) and a Gaussian (dashed yellow line) fit are shown, with the Lorentzian providing a better match. (c) Spectral hole 10 minutes later, where 15% of erbium ions remain, marked by the vertical dashed yellow line in (a); only a Lorentzian fit (solid red line) is shown. In both (b) and (c), experimental results are shown as solid blue lines. The frequency axis is shifted so the spectral hole minimum aligns at 400 MHz. This relative adjustment was applied post-acquisition for visual comparison.
• Figure 3: Spectral hole dynamics at $T = 7$ mK and $B = 50$ mT. (a) The spectral hole area as a function of waiting time, fitted with three exponential decay components. The data points (blue markers) represent the measured decay of the spectral hole area over time. The solid green curve represents the fit, with characteristic times $T_a = 6.3 \pm 0.3$ s (52%), $T_b = 395.7 \pm 17.9$ s (31%), and $T_c = 33961.8 \pm 1364.5$ s (17%), illustrating the presence of an additional ion class at ultra-low temperatures that significantly extends the spin lifetime to over 9 hours. The red dashed curve shows a two-component exponential fit, which inadequately describes the data. (b) Close-up of the spectral hole 100 ms post-burn, marked by the vertical dashed purple line in (a). A Gaussian (solid yellow line) and a Lorentzian (dashed red line) fit are shown, with the Gaussian providing a better match. (c) Spectral hole 7.5 hours later, where 8% of erbium ions remain, marked by the vertical dashed yellow line in (a); only a Gaussian fit (solid yellow line) is shown. In both (b) and (c), experimental results are shown as solid blue lines. The frequency axis is shifted so the spectral hole minimum aligns at 400 MHz. This relative adjustment was applied post-acquisition for visual comparison.
• Figure 4: Weights for two decay components at higher temperatures, with measurements across different conditions fitted to a constant to determine the average weight of each decay component. Panel (a) shows weights at varying temperatures for a fixed magnetic field ($B = 50 \, \text{mT}$), while panels (b) and (c) show weights across different magnetic fields at $T = 800 \, \text{mK}$ and $T = 80 \, \text{mK}$, respectively. The decay component weights $W_a = 0.62$ and $W_b = 0.38$ are shown with shaded regions representing the standard deviation ($\pm 1\sigma$), highlighting the clustering of weights around their means, which suggests the existence of ion classes.
• Figure 5: Weights for three decay components at $T = 7 \, \text{mK}$ across different magnetic fields. The weights were fitted to a constant, yielding average weights $W_a = 0.52$, $W_b = 0.26$, and $W_c = 0.22$. The shaded regions represent the standard deviation ($\pm 1\sigma$) for each decay component weight, illustrating the variability around their means.