Effects of magnetic field orientation on optical decoherence in ${\text{Er}}^{3+}:{\text{Y}}_2{\text{SiO}}_5$

The influence of the anisotropic Zeeman effect on optical decoherence was studied for the $1.54\mu \text{m}$ telecom transition in ${\text{Er}}^{3+}:{\text{Y}}_2{\text{SiO}}_5$ using photon echo spectroscopy as a function of applied magnetic field orientation and strength. The decoherence strongly correlates with the Zeeman energy splittings described by the ground- and excited-state $g$ factor variations for all inequivalent ${\text{Er}}^{3+}$ sites, with the observed decoherence times arising from the combined effects of the magnetic dipole-dipole coupling strength and the ground- and excited-state spin-flip rates, along with the natural lifetime of the upper level. The decoherence time was maximized along a preferred magnetic field orientation that minimized the effects of spectral diffusion and that enabled the measurement of an exceptionally narrow optical resonance in a solid—demonstrating a homogeneous linewidth as narrow as 73 Hz.

Figure 1

(Color online) Two-pulse photon echo decoherence time $T_M$ as a function of magnetic field orientation in the ${\mathbf{D}}_1\text{−}{\mathbf{D}}_2$ plane with the laser beam propagating along $b$ for (a) $B=5$, (b) $B=3$, (c) $B=2.25$, and (d) $B=1\text{T}$; the magnetic field angle was measured with respect to ${\mathbf{D}}_1$ in a counterclockwise sense, and the experiment was performed on the $b$ line of the transition as defined in Ref. 14. (e) Corresponding effective $g$ factor variations for site 1 (squares) and site 2 (circles) for the lowest-energy ${{}^{4}I}_{15/2}$ and ${{}^{4}I}_{13/2}$ states of ${\text{Er}}^{3+}:{\text{Y}}_2{\text{SiO}}_5$; ground-state solid symbols, excited-state open symbols. Solid lines are least-squares fits to the data showing excellent agreement.

Figure 2

(Color online) (a) Two-pulse photon echo decoherence time $T_M$ for site 1 as a function of magnetic field orientation in the $\mathbf{b}\text{−}{\mathbf{D}}_2$ plane with the laser beam propagating along ${\mathbf{D}}_1$ for $B=3\text{T}$ at $T=1.6\text{K}$, experiments were performed on the magnetic subclass II of site 1 as defined in Ref. 16. Corresponding effective $g$ factor variations for the lowest-energy ${{}^{4}I}_{15/2}$ and ${{}^{4}I}_{13/2}$ states of ${\text{Er}}^{3+}:{\text{Y}}_2{\text{SiO}}_5$ in the $\mathbf{b}\text{−}{\mathbf{D}}_2$ plane are shown for site 1 in (b) and for site 2 in (c); ground-state solid symbols, excited-state open symbols. Solid lines are least-squares fits to the data showing excellent agreement.

Figure 3

(Color online) (a) Time evolution of the stimulated-photon echo decoherence time $T_M$ for site 2 as a function of magnetic field orientation in the ${\mathbf{D}}_1\text{−}{\mathbf{D}}_2$ plane with the laser beam propagating along $b$ for $B=2\text{T}$ and $T=1.6\text{K}$ for waiting times of $T_W=0$ (two-pulse echo), $10\mu \text{s}$, $100\mu \text{s}$, 1 ms, and 10 ms; the magnetic field angle was measured with respect to ${\mathbf{D}}_1$ in a counterclockwise sense and the experiment was performed on the $b$ line of the transition. (b) Corresponding effective $g$ factor variations for site 1 (squares) and site 2 (circles) for the lowest-energy ${{}^{4}I}_{15/2}$ and ${{}^{4}I}_{13/2}$ states of ${\text{Er}}^{3+}:{\text{Y}}_2{\text{SiO}}_5$; ground-state solid symbols, excited-state open symbols. Solid lines are least-squares fits to the data showing excellent agreement.

Figure 4

(Color online) Two-pulse photon echo decay in 0.0015% ${\text{Er}}^{3+}:{\text{Y}}_2{\text{SiO}}_5$ at $B=7\text{T}$ and $T=1.5\text{K}$. The lasers $k$ vector is along $\mathbf{b}$ and $\mathbf{B}$ is oriented in the ${\mathbf{D}}_1\text{−}{\mathbf{D}}_2$ plane at an angle of $140°$ with respect to the ${\mathbf{D}}_1$ axis. The solid line represents an exponential least square fit to the data yielding a decoherence time of $T_2=4.38\text{ms}$ which corresponds to a homogeneous linewidth of 73 Hz.