Exploration of optimal hyperfine transitions for spin-wave storage in ${}^{167}$Er${}^{3+}$:Y${}_2$SiO${}_5$

Abstract

The dependence of the magnetic fluctuations and the spin coherence time $T_2^{\mathrm{hyp}}$ of the lowest Stark states ${}^4{I}_{15/2}(Z_1)$ in ${}^{167}$Er${}^{3+}$:Y${}_2$SiO${}_5$ under zero magnetic field on Er concentration is numerically investigated in the range of 10 to 100 parts per million (ppm). We investigate two primary sources of magnetic fluctuation limiting spin coherence: a constant contribution from host Y nuclei and a concentration-dependent component from dipole-dipole interactions among Er ions. Due to these two components, the Er-concentration dependence of $T_2^{\mathrm{hyp}}$ at the zero first-order Zeeman (ZEFOZ) points saturates for crystals with Er concentration below 10 ppm and no extension of the $T_2^{\mathrm{hyp}}$ is expected without an external magnetic field. Under a magnetic field, the longest $T_2^{\mathrm{hyp}}$ at a particular ZEFOZ point is expected to be over 170 s (90 s) for site 1 (site 2), which is more than $10^4$ times longer than that at zero field for 10-ppm ${}^{167}$Er${}^{3+}$:Y${}_2$SiO${}_5$. Remarkably, these optimal ZEFOZ points form striking geometric patterns: a line for site 1 and a plane for site 2. This trend, which is favorable for experiments, can be explained by the anisotropy of the effective spin Hamiltonian parameters. Finally, the tolerance of the ZEFOZ point at each site with the longest $T_2^{\mathrm{hyp}}$ against the errors in the applied magnetic field vector is evaluated.

13 pages. 12 figures, 5 tables

References in corpus (8)

• The Quantum Internet
• An Elementary Quantum Network of Single Atoms in Optical Cavities
• Realization of a multi-node quantum network of remote solid-state qubits
• Silicon-Vacancy Spin Qubit in Diamond: A Quantum Memory Exceeding 10 ms with Single-Shot State Readout
• Spin Wave Storage using Chirped Control Fields in Atomic Frequency Comb based Quantum Memory
• Hyperfine interactions of ${\text{Er}}^{3+}$ ions in ${\text{Y}}_2{\text{SiO}}_5$: electron paramagnetic resonance in a tunable microwave cavity
• Prediction of the Optical Polarization and High Field Hyperfine Structure Via a Parametrized Crystal-Field Model for the Low Symmetry Centers in Er${}^{3+}$ Doped Y${}_2$SiO${}_5$
• Demonstration of site-selective angular-resolved absorption spectroscopy of the ${}^4{I}_{15/2}\to$${}^4{I}_{13/2}$ erbium transition in the monoclinic crystal Y${}_2$SiO${}_5$