Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay

A high-storage efficiency and long-lived quantum memory for photons is an essential component in long-distance quantum communication and optical quantum computation. Here, we report a 78% storage efficiency of light pulses in a cold atomic medium based on the effect of electromagnetically induced transparency. At 50% storage efficiency, we obtain a fractional delay of 74, which is the best up-to-date record. The classical fidelity of the recalled pulse is better than 90% and nearly independent of the storage time, as confirmed by the direct measurement of phase evolution of the output light pulse with a beat-note interferometer. Such excellent phase coherence between the stored and recalled light pulses suggests that the current result may be readily applied to single photon wave packets. Our work significantly advances the technology of electromagnetically induced transparency–based optical memory and may find practical applications in long-distance quantum communication and optical quantum computation.

Figure 1

Schematic experimental setup. PD1, PD2, and PD3: photodetectors; PMF: polarization-maintained optical fiber; CPL: optical fiber coupler; BS: cubed beam splitter; PBS: cubed polarizing beam splitter; $\lambda /4$: zero-order quarter-wave plate; $L1-L3$: lenses with the focal length $f$ specified in units of millimeters. $M$: mirror; AOM: 80-MHz acoustic optical modulator. Inset: relevant energy levels and laser excitations in the experiment.

Figure 2

(a) Experimental data of the input, slow-light output, and stored and then recalled pulses in the forward configuration are shown by black, red, and blue open circles (located in the left, middle, and right), respectively. Solid lines represent the input pulse used in the calculation and the theoretically predicted outputs. The coupling field employed in the light-storage measurement is shown by the dashed line. $\mathrm{OD}=156$, ${\Omega }_c^{+}=1.1\Gamma$, $\gamma$ (the decoherence rate during pulse propagation) $=5.5\times {10}^{-4}\Gamma$, and ${\tau }_{\mathrm{coh}}$ (the coherence time during light storage) $=98\mu \mathrm{s}$. The storage efficiency (SE) determined from the measurement is 69%. (b) Experimental data and theoretical predictions of SEs as functions of OD are shown in the forward (black squares and blue lines) and backward (red circles and green lines) retrievals. In the forward retrieval, ${\Omega }_c^{+}=0.3\sim 1.1\Gamma$ and increases with OD; $\gamma =2.0\times {10}^{-4}\Gamma$ (upper blue line) or $5.5\times {10}^{-4}\Gamma$ (lower blue line). In the backward retrieval, ${\Omega }_c^{\pm }=1.2\Gamma$ and $\gamma =5.5\times {10}^{-4}\Gamma$.

Figure 3

(a) From left to right, beat notes of the input (black) and slow-light output (red) pluses and the recalled pulses after $7\mu \mathrm{s}$ (cyan) and $55\mu \mathrm{s}$ (blue) storage times. Green dashed lines are the coupling field employed in the light-storage measurement. (b)–(e) Zooming in on the time intervals around the pulse peaks with the same horizontal span of 200 ns. The ratio of the vertical spans in (b)–(e) is $4:2:2:1$. The frequency of beat notes is 80 MHz.

Figure 4

(a) Based on the time-space-reversing method, experimental data and the theoretical predictions of the input pulse and the stored and then backward recalled pulses after 4 and $54\mu \mathrm{s}$ storage times. Green (with the falling edge) and magenta (with the rising edge) dashed lines are the forward and backward coupling fields and other legends are the same as those in Fig. 2a. The input pulse shape is optimized for the maximum SE. $\mathrm{OD}=104$, ${\Omega }_c^{+}={\Omega }_c^{-}=1.2\Gamma$, $\gamma =5.5\times {10}^{-4}\Gamma$, and ${\tau }_{\mathrm{coh}}=104\mu \mathrm{s}$. The storage efficiencies (SE) determined from the measurements are 78% and 56% at 4 and $54\mu \mathrm{s}$ storage time, respectively. The FWHM of the input pulse is about $0.88\mu \mathrm{s}$. (b) SE as a function of storage time. The solid line is the best fit with the Gaussian-decay function, $\exp (-t^2/{\tau }_{\mathrm{coh}}^2)$, which determines ${\tau }_{\mathrm{coh}}$ is $92\mu \mathrm{s}$.