Implementation of an optical quantum memory protocol in the $^{167}$Er$^{3+}$ : Y$_2$SiO$_5$ crystal

A quantum memory protocol has been implemented on the basis of the revival of silenced echo (ROSE) in the $^{167}$Er$^{3+}$ : Y$_2$SiO$_5$ crystal at the telecommunication wavelength for input light fields with a small number of photons. An efficiency of storage of 44% has been reached at a storage time of 40 $\mu$s. The input pulse contains $\sim$ 340 photons on average, the reconstructed echo signal includes 150 photons, and the signal-to-noise ratio is 4. It has been shown that the main source of noise is the spontaneous emission of atoms remaining in the excited state because the parameters of two rephasing pulses are imperfect. Methods of increasing the signal-to-noise ratio for the implementation of the efficient quantum memory for single-photon fields have been discussed.