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Quantum memory of light is not only the building block of constructing large-scale quantum computer, but also the kernel component of quantum repeater for quantum networks, which makes long distance quantum communication come true. Due to the inevitable optical losses, squeezed vacuum generated from optical parametric amplifier becomes squeezed thermal state of light, which is no longer the minimum uncertainty state. Therefore quantum memory of squeezed thermal state of optical field is the key step towards the implementation of quantum internet. Atomic ensemble is one of ideal quantum memory media, as a result of high optical depth and good atomic coherence. Electromagnetically induced transparency (EIT) is one of mature approaches to quantum state mapping between non-classical optical fields and atomic spin waves. In atomic ensembles, the EIT can on-demand map quantum state between quadratures of light and spin waves of atomic ensemble, i.e., controlled quantum memory. Here the condition of quantum memory for squeezed thermal state of light is investigated according to the fidelity benchmark of quantum memory. The fidelity benchmark of quantum memory is the maximum fidelity which can be reached by classical methods, and it is quantum memory if the memory fidelity is higher than the fidelity benchmark of quantum memory. By numerically calculating the fidelity benchmark of quantum memory for different kinds of squeezed thermal states of light and the dependence of memory fidelity on the memory efficiency, we obtain the minimum memory efficiency which can realize quantum memory for squeezed thermal state of light. The quantum memory can be easily obtained by increasing squeezing parameter r. The thermal state fluctuation is sensitive to the realization of quantum memory. The required minimum memory efficiency is lower, when smaller thermal state fluctuation is employed in experiment by reducing the optical losses in optical parametric amplifier. On the other hand, quantum memory fidelity benchmark is high for small squeezing parameter and large optical depth, which requires high memory efficiency. And atomic memory efficiency can be increased by utilizing optical cavity to enhance the interaction between light and atom or atomic ensemble with high optical depth. For example, the fidelity benchmark is 0.80, when squeezing parameter r is 0.35 and thermal state fluctuation is 2.38 dB. Thus quantum memory can be realized if the memory efficiency is larger than 4.34%. Our work can provide the direct reference for experimental design of continuous variable quantum memory, quantum repeater, and quantum computer based on atomic ensembles.
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Keywords:
- quantum memory /
- squeezed thermal state of light /
- fidelity
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[21] Meng X D, Tian L, Zhang Z Y, Yan Z H, Li S J, Wang H 2012 Acta Sin. Quantum Opt. 18357(in Chinese)[孟祥栋, 田龙, 张志英, 闫智辉, 李淑静, 王海2012量子光学学报18357]
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[39] Ou Z Y 2008Phys. Rev. A 78 023819
[40] Scutaru H 1998J. Phys. A 31 3659
[41] Bao X H, Reingruber A, Dietrich P, Rui J, Dck A, Strassel T, Li L, Liu N L, Zhao B, Pan J W 2010New J. Phys. 12 093032
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[1] Pan J W, Chen Z B, Lu C Y, Weinfurter H, Zeilinger A, Zukowski M 2012 Rev. Mod. Phys. 84777
[2] Braunstein S L, Loock P 2005 Rev. Mod. Phys. 77513
[3] Wu LA, Kimble H J, Hall J L, Wu H F 1986Phys. Rev. Lett. 57 2520
[4] Sun H X, Liu K, Zhang J X, Gao J R 2015 Acta Phys. Sin. 64234210(in Chinese)[孙恒信, 刘奎, 张俊香, 郜江瑞2015 64234210]
[5] The LIGO Scientific Collaboration 2013 Nature Photon. 7613
[6] Marino A M, Stroud C R 2006Phys. Rev. A 74 022315
[7] Aoki T, Takei N, Yonezawa H, Wakui K, Hiraoka T, Furusawa A 2003Phys. Rev. Lett. 91 080404
[8] Su X L, Zhao Y P, Hao S H, Jia X J, Xie C D, Peng K C 2012Opt. Lett. 37 5178
[9] Su X L, Hao S H, Deng X W, Ma L Y, Wang M H, Jia X J, Xie C D, Peng K C 2013 Nature Commun. 42828
[10] Furusawa A, Sorensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282706
[11] Mehmet M, Ast S, Eberle T, Steinlechner S, Vahlbruch H, Schnabel R 2011 Opt. Express 1925763
[12] Wu Z Q, Zhou H J, Wang Y J, Zheng Y H 2013 Acta Sin. Quantum Opt. 191(in Chinese)[邬志强, 周海军, 王雅君, 郑耀辉2013量子光学学报191]
[13] Sun Z N, Feng J X, Wan Z J, Zhang K S 2016 Acta Phys. Sin. 65044203(in Chinese)[孙志妮, 冯晋霞, 万振菊, 张宽收2016 65044203]
[14] Kimble H J 2008Nature 453 1023
[15] Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414413
[16] Han Y S, Wen X, He J, Yang B D, Wang Y H, Wang J M 2016 Opt. Express 242350
[17] Fleischhauer M, Lukin M D 2000Phys. Rev. Lett. 84 5094
[18] Phillips D F, Fleischhauer A, Mair A, Walsworth R L, Lukin M D 2001Phys. Rev. Lett. 86 783
[19] Liu C, Dutton Z, Behroozi C H, Hau L V 2001 Nature 409490
[20] Reim K F, Nunn J, Lorenz V O, Sussman B J, Lee K C, Langford N K, Jaksch D, Walmsley I A 2010 Nature Photon. 4218
[21] Meng X D, Tian L, Zhang Z Y, Yan Z H, Li S J, Wang H 2012 Acta Sin. Quantum Opt. 18357(in Chinese)[孟祥栋, 田龙, 张志英, 闫智辉, 李淑静, 王海2012量子光学学报18357]
[22] Ding D S, Zhang W, Zhou Z Y, Shi S, Shi B S, Guo G C 2015 Nature Photon. 9332
[23] Yan Y, Li S J, Tian L, Wang H 2016Acta Phys. Sin. 65 014205 (in Chinese)[闫妍, 李淑静, 田龙, 王海2016 65 014205]
[24] Julsgaard B, Sherson J, Cirac J I, Fiurasek J, Polzik E S 2004Nature 432 482
[25] Hosseini M, Sparkes B M, Campbell G, Lam P K, Buchler B C 2011 Nature Commun. 2174
[26] Specht H P, Nolleke C, Reiserer A, Uphoff M, Figueroa E, Ritter S, Rempe G 2011 Nature 473190
[27] Langer C, Ozeri R, Jost J D, Chiaverini J, DeMarco B, Ben-Kish A, Blakestad R B, Britton J, Hume D B, Itano W M, Leibfried D, Reichle R, Rosenband T, Schaetz T, Schmidt P O, Wineland D J 2005Phys. Rev. Lett. 95 060502
[28] Hedges M P, Longdell J J, Li Y M, Sellars M J 2010Nature 465 1052
[29] Flurin E, Roch N, Pillet J D, Mallet F, Huard B 2015Phys. Rev. Lett. 114 090503
[30] Appel J, Figueroa E, Korystov D, Lobino M, Lvovsky A I 2008Phys. Rev. Lett. 100 093602
[31] Honda K, Akamatsu D, Arikawa M, Yokoi Y, Akiba K, Nagatsuka S, Tanimura T, Furusawa A, Kozuma M 2008Phys. Rev. Lett. 100 093601
[32] Jensen K, Wasilewski W, Krauter H, Fernholz T, Nielsen B M, Owari M, Plenio M B, Serafini A, Wolf M M, Polzik E S 2011 Nature Phys. 7 13
[33] Zhang T C, Goh K W, Chou C W, Lodahl P, Kimble H J 2003 Phys. Rev. A 67 033802
[34] Zhang J X, Xie C D, Peng K C 2005Chin. Phys. Lett. 22 3005
[35] Takei N, Aoki T, Koike S, Yoshino K, Wakui K, Yonezawa H, Hiraoka T, Mizuno J, Takeika M, Ban M, Furusawa A 2005Phys. Rev. A 72 042304
[36] Hammerer K, Wolf M M, Polzik E S, Cirac J I 2005Phys. Rev. Lett. 94 150503
[37] Owari M, Plenio M B, Polzik E S, Serafini A, Wolf M M 2008New. J. Phys. 10 113014
[38] Adesso G, Chiribella G 2008Phys. Rev. Lett. 100 170503
[39] Ou Z Y 2008Phys. Rev. A 78 023819
[40] Scutaru H 1998J. Phys. A 31 3659
[41] Bao X H, Reingruber A, Dietrich P, Rui J, Dck A, Strassel T, Li L, Liu N L, Zhao B, Pan J W 2010New J. Phys. 12 093032
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