Highly Efficient Coherent Optical Memory Based on Electromagnetically Induced Transparency

Quantum memory is an important component in the long-distance quantum communication based on the quantum repeater protocol. To outperform the direct transmission of photons with quantum repeaters, it is crucial to develop quantum memories with high fidelity, high efficiency and a long storage time. Here, we achieve a storage efficiency of 92.0 (1.5)% for a coherent optical memory based on the electromagnetically induced transparency scheme in optically dense cold atomic media. We also obtain a useful time-bandwidth product of 1200, considering only storage where the retrieval efficiency remains above 50%. Both are the best record to date in all kinds of schemes for the realization of optical memory. Our work significantly advances the pursuit of a high-performance optical memory and should have important applications in quantum information science.

Figure 1

(a) and (b): Relevant energy levels and laser excitations for the $D_2$ and $D_1$ EIT scheme, respectively. (c) Schematic experimental setup. AOM: acousto-optic modulator; APD: avalanche photodetector; $B$: block; BS: beam splitter; FC: fiber coupler; FM: flip mirror; $L$: lens; $M$: mirror; MM fiber: multimode fiber; PD: photodetector; PM fiber: polarization-maintaining fiber; PMT: photomultiplier tube.

Figure 2

(a) ${\gamma }_{21}$ and (b) ac Stark shift versus the control power for both $D_1$ and $D_2$ EIT schemes. The insets are the $y$-scale zoom of the $D_1$ data. In (a), the blue line is a calculation with ${\gamma }_{21}={\gamma }_0+\mathbf{(}(\sqrt{48/7}{\mathrm{\Omega }}_c{)}^2/4{\delta }_s^2\mathbf{)}{\gamma }_{41}$, where ${\gamma }_0=0.0001\mathrm{\Gamma }$, ${\gamma }_{41}=0.8\mathrm{\Gamma }$. In (b), the red (blue) line is a linear fit to the $D_1$ ($D_2$) data. The slope is positive (negative) for the $D_1$ ($D_2$) system because the control field causes an ac Stark shift on state $|1⟩$ ($|2⟩$) due to the red-detuned, off-resonant excitation of the probe ($|2⟩\to |4⟩$) transition.

Figure 3

(a) A representative EIT spectrum. The red line in a fitting curve. (b) Blue, green, and red traces are the input, slow, and stored-and-retrieved pulse, respectively. The dashed black trace is the control intensity. The purple line is a calculated slow light curve. (c) The representative beat note data. (d),(e),(f) Parts of the beat note data around the peaks of the three pulses in (c).

Figure 4

(a) ${\eta }_{\mathrm{tran}}$ versus $T_p$ for the $D_1$ scheme. The blue line is a calculation of Eq. (1) with parameters $\{\zeta ,{\gamma }_{31},{\gamma }_{21}\}$ of $\{2.3,0.8\mathrm{\Gamma },0.0002\mathrm{\Gamma }\}$, respectively. (b) SE versus storage time. The blue line is a fit curve of $A{e}^{-t^2/{\tau }^2}$ with $A=0.90$ and $\tau =325\mu \mathrm{s}$. (c) TBP at 50% SE for the results in (a) and with $\tau =325\mu \mathrm{s}$. (d) SE versus OD for the $D_1$ (circle) and $D_2$ (square) schemes. The line for the $D_1$ scheme is a calculation based on Eq. (1) with parameters $\{T_p,\zeta ,{\gamma }_{21}\}$ of $\{207\mathrm{ns},2.7,0.0001\mathrm{\Gamma }\}$, respectively. The line for the $D_2$ scheme is a calculation of Eq. (1) with parameters $\{T_p,\zeta \}$ of $\{207\mathrm{ns},2.7\}$ and ${\gamma }_{21}={\gamma }_0+((48/7){\mathrm{\Omega }}_c^2/4{\delta }_s^2){\gamma }_{41}$, where ${\gamma }_0=0.0005\mathrm{\Gamma }$ and ${\delta }_s=2\pi \times 251.09\mathrm{MHz}$. The relation between ${\gamma }_{31}$ (or ${\gamma }_{41}$) and OD is mentioned in [37].

Figure 5

(a) Numerical calculations of ${\eta }_{\mathrm{tran}}$ versus OD with(red circle) and without (blue cross) the presence of FWM. Perfect phase matching is assumed and $T_p$ is 200 ns. ${\mathrm{\Omega }}_c$ is adjusted for each OD to keep $\zeta =2.7$. Inset shows the ratio of those two traces, reflecting the FWM gain versus OD. The results in (b) and (c) are based on the steady-state calculation including the phase mismatching. The parameters $\{D,{\mathrm{\Omega }}_c,{\gamma }_{21}\}$ are $\{1000,6.72\mathrm{\Gamma },0.0002\mathrm{\Gamma }\}$, respectively. (b) FWM gain versus ${\delta }_p$ at $\theta =0^0$. (c) Probe transmission versus $\theta$ for ${\delta }_p=0.04\mathrm{\Gamma }$. (d) Peak probe transmission versus the pump detuning for an OD of 603. The pump power is half of the control power. The blue solid curve is a numerical calculation with $D=600$, $\theta ={0.5}^0$, ${\mathrm{\Omega }}_c=6.2\mathrm{\Gamma }$, and ${\gamma }_{21}=0.0005\mathrm{\Gamma }$.