Optical investigation of ultra-slow spin relaxation in $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$ single crystals

TL;DR

This study addresses spin-relaxation limits in AFC-based quantum memories realized with $^{171}$Yb:YSO. It develops a theoretical framework that separates spin-lattice relaxation (SLR) and spin-flip-flop (FF) processes and uses optical perturbation with absorption spectroscopy to extract rate parameters, including direct SLR coefficients $A_{ij}$ and Raman terms $c_{ij}$. Experiments on 2 and 10~ppm samples across $T$ from 50 mK to 6 K reveal FF-dominated relaxation at low $T$ and Raman-driven $T^9$ scaling at higher $T$, with population-recovery and SHB analyses yielding consistent Raman coefficients and FF hierarchies. The results imply that AFC lifetimes of hours could be achievable near $1$ K with doping around $2$~ppm, offering practical guidelines for optimizing rare-earth-doped quantum memories and informing doping and temperature choices to balance FF and SLR effects.

Abstract

We present a comprehensive study of spin relaxation dynamics at cryogenic temperatures in a rare-earth-doped crystal used for quantum memory applications: $^{171}$Yb:Y$_2$SiO$_5$. Spin relaxation is indeed a major limiting factor for both the efficiency and storage time of quantum memory protocols based on atomic frequency combs in rare-earth materials. The relaxation dynamics among the four ground-state hyperfine levels were simultaneously investigated by optically perturbing the spin population distribution and monitoring its return to thermal equilibrium through optical absorption spectroscopy. By applying different types of perturbations, we were also able to distinguish between two types of relaxation processes, induced by spin-phonon and spin-spin interactions. Below 1 K, we observed that the re-thermalization of the Yb$^{3+}$ ion population takes several hours, driven solely by direct phonon absorption or emission. However, the effective lifetime of individual spin states is much shorter - on the order of several seconds in low-doped (2 ppm) samples and of milliseconds in 10 ppm samples - due to spin-spin interactions. These findings provide valuable guidelines for optimizing doping levels and operating temperatures in rare-earth-doped crystals for quantum applications. Notably, they suggest that atomic frequency combs with lifetimes of several hours could be realized using $^{171}$Yb:Y$_2$SiO$_5$ crystals with slightly less than 2 ppm doping and operating near 1 K.

Figures (7)

• Figure 1: Evolution of the absorption spectrum of Yb doped YSO at 10 ppm occupying site II recorded at the crystal temperature of 150 mK (a) and 2.0 K (b) and at varying delays after the initialization pulses. The green arrows indicate the spectrum region pumped by the initialization pulses. The black arrows highlight the different recovery behavior of the two absorption peaks at the two temperatures. Portion of the absorption spectrum used to estimate the relative population of levels 4g and 3g (c), and of 1g and 2g (d). The red curves represent the best-fit results using four Lorenztian functions (d) or two Lorentzian functions, and an offset (c). The profile of the single Lorenztians is drawn in green and orange. The absorption spectrum of the 2 ppm sample can be found in Ref. lafitte-houssatOpticalHomogeneousInhomogeneous2022
• Figure 2: Population density recovery of 4g (a) and 2g (b) levels for five temperatures recorded in the 10 ppm sample. The black lines are exponential fits. Population recovery rate estimated through the exponential fits for the 4g (c) and 2g (d) population densities. In black are the results for the 10 ppm sample and in red for the 2 ppm one.
• Figure 3: (Inset) Spectral hole profile at different delay times recorded in the absorption spectrum of the 4g-1e transition of the 2 ppm sample, with Lorentzian fits (black). (Main) Time dependence of the measured hole depth at 1.3 K and 3.3 K. The black lines are the curves obtained from the global fit.
• Figure 4: Spectral hole relaxation rates measured by burning the 4g–1e transition in the 10 ppm (squares) and 2 ppm (circles) samples. The solid lines represent fits to the data using the function $\bar{a} + \bar{c}T^9$, while the dotted lines indicate the $\bar{c}T^9$ contribution alone. For comparison, population recovery rates R$_{1g}$ associated with the 1g level in both samples are also shown in green and orange.
• Figure 5: Population densities and relative fits for two crystal temperatures. Even if the data and prediction for the 3g level population density were not used for the fitting procedure, they are shown as well for completeness. It is clear that the 3g population does not vary significantly and is overestimated by the two-Lorentzian fit (Fig. \ref{['fig:Figure1']}c) for the shortest delays.