Dependence of retrieval efficiency on waist ratio of read beam to anti-Stokes photon mode in cavity-enhanced quantum memory

Abstract

<sec>Quantum communication is promising for absolutely safe information transmission. However, the direct transmission distance of quantum states is limited by the no-cloning theorem and transmission loss. To solve these problems, Duan et al. proposed a promising quantum repeater scheme, DLCZ protocol (Duan L M, Lukin M D, Cirac J I, Zoller P <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1038/35106500">2001 <i>Nature</i> <b>414</b> 413</ext-link>), in which linear optics and atomic ensembles are used to combine entanglement generation and quantum memory into a single node. A quantum memory with highly retrieval efficiency is beneficial to increasing the rate of entanglement swapping, and also achieving high-speed entanglement distribution. Up to now, high-efficiency quantum memories have been realized by using high-optical-depth atomic ensembles or by coupling atomic ensembles with a medium-finesse optical cavity. However, the effect of the waist ratio of read beam mode and anti-Stokes photon mode on intrinsic retrieval efficiency has not been studied in detail. Here, we study the dependence of intrinsic retrieval efficiency on the waist ratio of read beam mode to anti-Stokes photon mode in cavity-enhanced quantum memory.</sec><sec>In this work, an <sup>87</sup>Rb atomic ensemble, that is placed at the center of a passively stabilized polarization interferometer (BD<sub>1,2</sub>), is used as quantum memory. Firstly, the ensemble is captured through magneto-optical trapping (MOT) and prepared into the Zeeman sub-level of ground state <inline-formula><tex-math id="M4">\begin{document}$ \left| {5{{\text{S}}_{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}},F = 1,m = 0} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M4.png"/></alternatives></inline-formula>. Then, a weak write pulse with frequency red-detuned from the <inline-formula><tex-math id="M5">\begin{document}$ \left| {5{{\text{S}}_{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}},F = 1,m = 0} \right\rangle \to \left| {5{{\text{P}}_{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}},F' = 1,m = 1} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M5.png"/></alternatives></inline-formula> transition by 110 MHz, illuminates the atoms and induces spontaneous Raman scattering out a Stokes photon. In this regime of weak excitation, the detection of a Stokes photon heralds the storage of a single spin wave <inline-formula><tex-math id="M6">\begin{document}$ \left| {5{{\text{S}}_{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}},F = 1,m = 0} \right\rangle \leftrightarrow \left| {5{{\text{S}}_{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}},F = 2,m = 0} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M6.png"/></alternatives></inline-formula> (<inline-formula><tex-math id="M7">\begin{document}$ \left| {5{{\text{S}}_{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}},F = 1,m = 0} \right\rangle \leftrightarrow \left| {5{{\text{S}}_{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}},F = 2,m = 2} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M7.png"/></alternatives></inline-formula>) distributed among the whole ensemble. After a programmable delay, a read pulse that generates a 110 MHz red-detuning from the <inline-formula><tex-math id="M8">\begin{document}$ \left| {5{{\text{S}}_{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}},F = 2,m = 0} \right\rangle \to \left| {5{{\text{P}}_{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}},F' = 2,m = - 1} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M8.png"/></alternatives></inline-formula> transition converts this spin wave into an anti-Stokes photon. We detect the Stokes photons and anti-Stokes photons with polarization <inline-formula><tex-math id="M9">\begin{document}$ {\sigma ^ + } $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M9.png"/></alternatives></inline-formula>, which means that all the spin-waves are stored in a magnetic-field-insensitive state to reduce the decoherence caused by the stray magnetic fields. In order to increase the intrinsic retrieval efficiency, the atomic ensemble is placed in a ring cavity. The cavity length is 4 m, the finesse is measured to be ~15, and the escape efficiency of ring cavity is 52.9%. Both Stokes and anti-Stokes photon qubits are required to resonate with the ring cavity. To meet this requirement, a cavity-locking beam is injected into the cavity to stabilize the cavity length by using a Pound-Drever-Hall locking scheme. Finally, we fix the Stokes (anti-Stokes) photon mode waist and change the waist ratio through changing the write beam (read beam) waist.</sec><sec>The experimental results show that when the waist ratio of read beam mode to anti-Stokes photon mode is 3, the intrinsic retrieval efficiency reaches to <inline-formula><tex-math id="M10">\begin{document}$ 68.9 {\text{%}} \pm 1.6{\text{%}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M10.png"/></alternatives></inline-formula> and normalized cross-correlation function <inline-formula><tex-math id="M11">\begin{document}$ {g^{(2)}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M11.png"/></alternatives></inline-formula> can achieve <inline-formula><tex-math id="M12">\begin{document}$ 26.5 \pm 1.9 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230966_M12.png"/></alternatives></inline-formula>. We build a theoretical model, which shows that the intrinsic retrieval efficiency reaches the peak when the waist ratio is 3, and the intrinsic retrieval efficiency tends to be stable when the waist ratio continues to increase. The experimental results accord with the theoretical results. In the future, we will improve the intrinsic retrieval efficiency by enhancing the fineness of the optical cavity with optimal cavity parameters.</sec>