Photon echo Measurement of Optical Decoherence in Er$^{3+}$-doped Silicate Fiber

The dephasing time T$_2$ ($\Gamma_h = 1/\pi T_2$ is the homogeneous linewidth) of the $^4$I$_{15/2}$ -- $^4$I$_{13/2}$ transition of Er$^{3+}$ in a silicate optical fiber was measured by two-pulse photon echoes vs. external magnetic field and temperature. A field of 2~T reduces the homogeneous linewidth by 1.8 MHz from its value of 3.2 MHz at zero field, an anomalously large reduction compared to that in oxide crystals with similar Er$^{3+}$ concentration. We propose that the dephasing is caused by two classes of low frequency tunneling modes: elastic ``two-level-systems'' (TLS) responsible for 1.4~MHz and coupled spin-elastic TLS modes for 1.8 MHz. The coupled modes acquire a magnetic character from an elastic Er$^{3+}$ spin-TLS interaction. The temperature dependence of the homogeneous linewidth is linear in the measured range of 1.4 to 4~K. Three- pulse photon echo decays measured from 0.5 $\mu$s to 500 $\mu$s and at a field of 5~T characterized spectral diffusion caused by the distribution of TLS tunneling rates. Our results suggest a potential for application of doped communication fibers in frequency selective optical processing, buffer memories and spatial-spectral holographic devices.