Optical storage with electromagnetically induced transparency in cold atoms at a high optical depth*

We report experimental demonstration of efficient optical storage with electromagnetically induced transparency (EIT) in a dense cold $^{85}$Rb atomic ensemble trapped in a two-dimensional magneto-optical trap. By varying the optical depth (OD) from 0 to 140, we observe that the optimal storage efficiency for coherent optical pulses has a saturation value of 50{\%} as OD $>$ 50. Our result is consistent with that obtained from hot vapor cell experiments which suggest that a four-wave mixing nonlinear process degrades the EIT storage coherence and efficiency. We apply this EIT quantum memory for narrow-band single photons with controllable waveforms, and obtain an optimal storage efficiency of 49$\pm $3{\%} for single-photon wave packets. This is the highest single-photon storage efficiency reported up to today and brings the EIT atomic quantum memory close to practical application because an efficiency of above 50{\%} is necessary to operate the memory within non-cloning regime and beat the classical limit.