Towards highly multimode optical quantum memory for quantum repeaters

Long-distance quantum communication through optical fibers is currently limited to a few hundreds of kilometres due to fiber losses. Quantum repeaters could extend this limit to continental distances. Most approaches to quantum repeaters require highly multimode quantum memories in order to reach high communication rates. The atomic frequency comb memory scheme can in principle achieve high temporal multimode storage, without sacrificing memory efficiency. However, previous demonstrations have been hampered by the difficulty of creating high-resolution atomic combs, which reduces the efficiency for multimode storage. In this article we present a comb preparation method that allows one to increase the multimode capacity for a fixed memory bandwidth. We apply the method to a ${}^{151}\mathrm{Eu}^{3+}$-doped ${\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal, in which we demonstrate storage of 100 modes for 51 $\mu \mathrm{s}$ using the AFC echo scheme (a delay-line memory) and storage of 50 modes for 0.541 ms using the AFC spin-wave memory (an on-demand memory). We also briefly discuss the ultimate multimode limit imposed by the optical decoherence rate, for a fixed memory bandwidth.

Figure 1

Absorption spectrum of an AFC. Here $d$ is the optical depth of one peak, $\mathrm{\Gamma }$ its width, $\mathrm{\Delta }$ the periodicity, and $B$ the bandwidth of the AFC.

Figure 2

Time sequence of the spin-wave AFC storage. The incoming input pulses are first mapped onto an optical collective excitation which is then transferred back and forth to a spin state using a pair of strong optical control pulses. An RF sequence can be applied during the spin-wave storage to increase the storage time beyond the limit otherwise given by the inhomogeneous spin broadening.

Figure 3

Fourier limitation $1/\tau$ as a function of AFC echo time 1/$\mathrm{\Delta }$, for the serial and parallel sequences discussed in Sec. 3. The target AFC peak width $\mathrm{\Gamma }$ is also plotted to illustrate the condition in Eq. (10).

Figure 4

Comparison of the temporal profiles (left figures) and the corresponding Fourier spectra (right figures) for the serial (a and c) and parallel methods (b and d). Preparation sequences for two different AFC echo times are shown, $1/\mathrm{\Delta }=5\mu \text{s}$ (a and b) and $1/\mathrm{\Delta }=15\mu \text{s}$ (c and d). The vertical axes represent amplitudes in arbitrary units, in both time and frequency domain. Note that for the parallel method the top hat Fourier spectrum is slightly modulated due to the finite pulse width with respect to the total duration $T_{\mathrm{prep}}=2$ ms.

Figure 5

Simplified sketch of the experimental setup for AFC memory experiments. The cavity-stabilized 580 nm light source is sent to two different AOMs: one generates the input pulses to be stored, and one generates the pulses for the AFC preparation and the control field. The crystal is cooled to about 4 K in a cryostat. To increase the memory absorption, a double-pass configuration is realized through the crystal by using a polarizing beam splitter (PBS) and a Faraday rotator (FR). The RF coil placed around the crystal generates the 34.5 MHz field necessary for storage time extension through spin echoes.

Figure 6

AFC echo efficiency versus $1/\mathrm{\Delta }$ using the serial method (red squares) and parallel method with $T_{\mathrm{prep}}=2$ and 6 ms (blue circles and black diamonds). For the parallel method with $T_{\mathrm{prep}}=2$ ms the efficiency is fitted to an exponential decay (blue line) with a time constant of 27.5 $\mu \mathrm{s}$ at $exp(-1)$ of the maximum value. For the case $T_{\mathrm{prep}}$ = 6 ms the decay is nonexponential. The slightly different efficiencies at the shortest $1/\mathrm{\Delta }$ we attribute to different optical depths, due to a slow drift of the frequency-stabilized laser within the inhomogeneous broadening.

Figure 7

AFC echoes of 100 temporal input modes for $1/\mathrm{\Delta }=51\mu \mathrm{s}$. The measured efficiency averaged over the temporal modes is 8.5 $\pm 0.5$%.

Figure 8

Spin-wave storage of 50 temporal modes for 541 $\mu \mathrm{s}$. Here $1/\mathrm{\Delta }=41\mu \mathrm{s}$ and $T_S=0.5$ ms. The efficiency averaged over the temporal modes is 1.6%.