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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 2001 Nature 414 413 ), 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.In this work, an 87Rb atomic ensemble, that is placed at the center of a passively stabilized polarization interferometer (BD1,2), 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 $ \left| {5{{\text{S}}_{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}},F = 1,m = 0} \right\rangle $ . Then, a weak write pulse with frequency red-detuned from the$ \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 $ 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$ \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 $ ($ \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 $ ) distributed among the whole ensemble. After a programmable delay, a read pulse that generates a 110 MHz red-detuning from the$ \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 $ transition converts this spin wave into an anti-Stokes photon. We detect the Stokes photons and anti-Stokes photons with polarization$ {\sigma ^ + } $ , 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.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 $ 68.9 {\text{%}} \pm 1.6{\text{%}} $ and normalized cross-correlation function$ {g^{(2)}} $ can achieve$ 26.5 \pm 1.9 $ . 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.-
Keywords:
- cold atomic ensemble /
- cavity enhanced quantum memory /
- waist ratio of the read beam mode to anti-Stokes photon mode /
- retrieval efficiency
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图 1 实验能级图 (a)写过程; (b)读过程
Figure 1. Relevant 87Rb atomic levels: (a) Writing process; (b) reading process.
图 2 实验装置图, 其中BD为光移束器, PZT为压电陶瓷, OSFS为光谱滤波器组, SMF为单模光纤, PD为光电探测器, SPD为单光子探测器, OC为输出耦合镜
Figure 2. Experimental setup. BD, the beam displacer; PZT, the piezoelectric transducer; OSFS, optical-spectrum-filter set; SMF, single-mode fiber; PD, photodiode; SPD, singlephoton detector; OC, output coupler.
图 3 实验时序图. 自上而下依次为磁光阱、锁腔过程、态制备过程、写过程、读过程
Figure 3. Time sequence of experiment. From top to bottom, they are magneto-optical trap, the locking cavity process, the state cleaning process, the writing process, the reading procress.
图 4 读光饱和功率密度下, 本质恢复效率随腰斑比的变化. 橙色菱形为理论值, 蓝色方块为实验数据
Figure 4. Intrinsic retrieval efficiency as a function of the waist width ratio under the saturation power density of read. The orange diamond represents the theoretical value and the blue square represents the experimental data.
图 5 腰斑比
$ \alpha = 3 $ 时, 本质恢复效率(蓝色方块)与互关联函数$ {g^{(2)}} $ (红色圆点)随读激光功率的变化Figure 5. Intrinsic retrieval efficiency (the blue square) and the cross-correlation function
$ {g^{(2)}} $ (the red dot) as a function of read power at the waist width ratio$ \alpha = 3 $ . -
[1] Zhao B, Chen Z B, Chen Y A, Schmiedmayer J, Pan J W 2007 Phys. Rev. Lett. 98 240502
Google Scholar
[2] Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413
Google Scholar
[3] Sangouard N, Simon C, de Riedmatten H, Gisin N 2011 Rev. Mod. Phys. 83 33
Google Scholar
[4] Pan J W, Simon C, Brukner Č, Zeilinger A 2001 Nature 410 1067
Google Scholar
[5] Briegel H J, Dür W, Cirac J I, Zoller P 1998 Phys. Rev. Lett. 81 5932
Google Scholar
[6] Pan J W, Gasparoni S, Ursin R, Weihs G, Zeilinger A 2003 Nature 423 417
Google Scholar
[7] Reichle R, Leibfried D, Knill E, et al. 2006 Nature 443 838
Google Scholar
[8] Matsukevich D N, Chanelière T, Bhattacharya M, et al. 2005 Phys. Rev. Lett. 95 040405
Google Scholar
[9] Dudin Y O, Jenkins S D, Zhao R, et al. 2009 Phys. Rev. Lett. 103 020505
Google Scholar
[10] Kuzmich A, Bowen W P, Boozer A D, Boca A, Chou C W, Duan L M, Kimble H J 2003 Nature 423 731
Google Scholar
[11] Simon J, Tanji H, Thompson J K, Vuletić V 2007 Phys. Rev. Lett. 98 183601
Google Scholar
[12] Matsukevich D N, Chanelière T, Jenkins S D, Lan S Y, Kennedy T A B, Kuzmich A 2006 Phys. Rev. Lett. 96 030405
Google Scholar
[13] Yan Z H, Wu L, Jia X J, Liu Y H, Deng R J, Li S J, Wang H 2017 Nat. Commun. 8 718
Google Scholar
[14] Perseguers S, Lapeyre G J, Cavalcanti D, Lewenstein M, Acín A 2013 Rep. Prog. Phys. 76 096001
Google Scholar
[15] Chanelière T, Matsukevich D N, Jenkins S D, Lan S Y, Kennedy T A B, Kuzmich A 2005 Nature 438 833
Google Scholar
[16] Eisaman M D, André A, Massou F, Fleischhauer M, Zibrov A S, Lukin M D 2005 Nature 438 837
Google Scholar
[17] Heinze G, Hubrich C, Halfmann T 2013 Phys. Rev. Lett. 111 033601
Google Scholar
[18] Hsiao Y F, Tsai P J, Chen H S, Lin S X, Hung C C, Lee C H, Chen Y H, Chen Y F, Yu I A, Chen Y C 2018 Phys. Rev. Lett. 120 183602
Google Scholar
[19] Laurat J, de Riedmatten H, Felinto D, Chou C W, Schomburg E W, Kimble H J 2006 Opt. Express 14 6912
Google Scholar
[20] Yang S J, Wang X J, Li J, Rui J, Bao X H, Pan J W 2015 Phys. Rev. Lett. 114 210501
Google Scholar
[21] Ma L X, Lei X, Yan J L, Li R Y, Chai T, Yan Z H, Jia X J, Xie C D, Peng K C 2022 Nat. Commun. 13 2368
Google Scholar
[22] Bao X H, Reingruber A, Dietrich P, Rui J, Dück A, Strassel T, Li L, Liu N L, Zhao B, Pan J W 2012 Nat. Phys. 8 517
Google Scholar
[23] Yang S J, Wang X J, Bao X H, Pan J W 2016 Nat. Photonics 10 381
Google Scholar
[24] Wang X J, Yang S J, Sun P F, Jing B, Li J, Zhou M T, Bao X H, Pan J W 2021 Phys. Rev. Lett. 126 090501
Google Scholar
[25] Wang Y F, Li J F, Zhang S C, Su K Y, Zhou Y R, Liao K Y, Du S W, Yan H, Zhu S L 2019 Nat. Photonics 13 346
Google Scholar
[26] Farrera P, Heinze G, Albrecht B, Ho M, Chávez M, Teo C, Sangouard N, de Riedmatten H 2016 Nat. Commun. 7 13556
Google Scholar
[27] Gorshkov A V, André A, Lukin M D, Sørensen A S 2007 Phys. Rev. A 76 033805
Google Scholar
[28] Nunn J, Walmsley A, Raymer M G, Surmacz K, Waldermann F C, Wang Z, Jaksch D 2007 Phys. Rev. A 75 011401
Google Scholar
[29] Reiserer A, Rempe G 2015 Rev. Mod. Phys. 87 1379
Google Scholar
[30] Surmacz K, Nunn J, Reim K, Lee K. C, Lorenz V. O, Sussman B, Walmsley I. A, Jaksch D 2008 Phys. Rev. A 78 033806
Google Scholar
[31] Gujarati T P, Wu Y K, Duan L M 2018 Phys. Rev. A 97 033826
Google Scholar
[32] Vernaz-Gris P, Huang K, Cao M, Sheremet A S, Laurat J 2018 Nat. Commun. 9 363
Google Scholar
[33] Wang M J, Wang S Z, Ma T F, Li Y, Xie Y, Jiao H L, Liu H L, Li S J, Wang H 2023 Quantum 7 903
Google Scholar
[34] Wang S Z, Wang M J, Wen Y F, Xv Z X, Ma T F, Li S J, Wang H 2021 Commun. Phys. 4 168
Google Scholar
[35] Black D E 2001 Am. J. Phys. 69 79
Google Scholar
[36] Li C, Wang H Y, Artemiy D, Riccard M O, Miao H X, Han S 2021 Results Phys. 30 104835
Google Scholar
[37] Su J, Jiao M X, Jiang F 2018 Optik 168 348
Google Scholar
[38] Stoyanov L, Stefanov A, Dreischuh A, Paulus G G 2023 Opt. express 31 13683
Google Scholar
[39] Hiekkamäki M, Barros R F, Ornigotti M, Fickler R 2022 Nat. Photonics 16 828
Google Scholar
[40] Iulia G 2023 Nat. Rev. Phys. 5 372
Google Scholar
[41] Erpenbeck A, Gull E, Cohen G 2023 Phys. Rev. Lett. 130 186301
Google Scholar
[42] Dum R, Zoller P, Ritsch H 1992 Phys. Rev. A 45 4879
Google Scholar
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