Robust Millisecond Coherence Times of Erbium Electron Spins

Erbium-doped solids are prime candidates for quantum memories in optical quantum networks given their telecom-compatible photon emission. An electron spin of erbium with millisecond coherence time is desirable for generating remote entanglement between adjacent quantum network nodes. Here we report GHz-range electron-spin transitions of ${}^{167}{\mathrm{Er}}^{3+}$ in a yttrium oxide (${\mathrm{Y}}_2{\mathrm{O}}_3$) matrix with coherence times that are consistently longer than a millisecond. By polarizing paramagnetic impurity spins we achieve a spin $T_2$ up to 1.46 ms, and up to 7.1 ms after dynamical decoupling. These coherence lifetimes are among the longest found for erbium in crystalline matrices despite the presence of host nuclear spins. We further enhance the coherence time beyond conventional dynamical decoupling, using customized sequences to simultaneously mitigate spectral diffusion and dipolar interactions. Our study not only establishes ${}^{167}{\mathrm{Er}}^{3+}$: ${\mathrm{Y}}_2{\mathrm{O}}_3$ as a significant quantum memory platform but also provides a guideline for engineering long-lived erbium spins in a variety of host materials for quantum technologies.

Figure 1

(a),(c) ${\mathrm{Er}}^{3+}{\text{:Y}}_2{\mathrm{O}}_3$ crystal structure showing the unit cell and ${\mathrm{Er}}^{3+}$ substituting in ${\mathrm{C}}_2$ and ${\mathrm{C}}_{\text{3i}}$ sites, respectively. (b),(d) Zeeman and hyperfine energy levels for ${}^{167}{\mathrm{Er}}^{3+}$ in ${\mathrm{C}}_2$ and ${\mathrm{C}}_{\text{3i}}$ sites, respectively, generated along the eigenaxes of the $g$ tensors with Easyspin [19]. The red lines show the allowed ESR transitions at 5.67-GHz resonance frequency. The spin energy levels and transitions in a magnetic field are discussed in detail in Ref. [20] (e) Millikelvin pulsed ESR setup. (f) Echo detected field sweep of ${}^{167}{\mathrm{Er}}^{3+}$ : ${\mathrm{Y}}_2{\mathrm{O}}_3$ showing predicted transitions as dashes grouped by their $g$ factors. (g) Rabi nutation of echo signal obtained by varying refocusing pulse length for the transition at 259 mT. Sequences above (f),(g) show pulse amplitude in voltage.

Figure 2

Electron spin coherence and relaxation times of ${}^{167}{\mathrm{Er}}^{3+}$: ${\mathrm{Y}}_2{\mathrm{O}}_3$ at millikelvin temperatures. (a) Spin lifetime ($T_1$) (black triangles) is measured using saturation recovery. Spin-coherence time measured with two pulse echo ($T_2$, red dots) and with XY8 dynamical decoupling ($T_2^{\mathrm{XY}8}$, blue triangles) showed coherence times exceeding 1 millisecond spin-coherence time (green dashed line) for lower $g$ transitions. Red and blue boxes highlight the longest XY8 and Hahn-echo coherence times, respectively. (b) Echo decays for the two transitions with longest Hahn echo and XY8 coherence times, as highlighted in (a).

Figure 3

Decoherence mechanisms at sub-Kelvin temperatures for the ${}^{167}{\mathrm{Er}}^{3+}g=1.64$ (259 mT) transition. (a) Temperature dependence of relaxation and decoherence processes: spin lifetime ($T_1$, black dots) fitted with Eq. (2) (black line); coherence time ($T_2$, red dots) fitted with the $T_2$ model described in the text (red line); XY8 dynamical decoupling coherence time ($T_2^{\mathrm{XY}8}$) measured by sending 30 XY8 pulses. Inset shows time-domain Hahn-echo decays for the range of temperatures measured. (b) Spectral diffusion measured with three pulse echoes at a base temperature of 26 mK.

Figure 4

Coherence enhancement with customized dynamical decoupling. (a) Comparison of coherence times under different dynamical decoupling sequences with a common 25-kHz filter center frequency. $T_2$ for Seq.B shown is an estimated upper bound. (b) Noise spectrum computed from CPMG $T_2$ measurement and comparison of the filter functions of all sequences. Filters are normalized in the whole spectrum but only the 0–50 kHz range is shown given the measured noise spectrum range. (c) Customized dynamical decoupling pulse sequences in increasing order of the target ratio of disorder to interaction, along with Seq.B.