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Generation and quantum state reconstruction of a squeezed vacuum light field resonant on the rubidium D1 line

Li Shu-Jing Zhang Na-Na Yan Hong-Mei Xu Zhong-Xiao Wang Hai

Generation and quantum state reconstruction of a squeezed vacuum light field resonant on the rubidium D1 line

Li Shu-Jing, Zhang Na-Na, Yan Hong-Mei, Xu Zhong-Xiao, Wang Hai
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  • The squeezed light field is a kind of important continuous variable quantum resource.It has wide applications in precision measurement and quantum information processing.Quantum storage is the foundations of quantum repeater and long distance quantum communication,and alkali metal atoms are an ideal quantum storage medium due to long ground state coherent time. With the rapid development of quantum storage technology in atomic medium,the preparation of the squeezed light which resonates with alkali metal atoms has become one of the research hotspots in the field of quantum information.In this paper,we report the generation of squeezed vacuum at 795 nm (resonant on the rubidium D1 transition line) by using an optical parametric oscillation based on a periodically poled KTiOPO4 crystal. The generated squeezed light field is detected by a balanced homodyne detector,and the squeezing of-3 dB and anti-squeezing of 5.8 dB are observed at a pump power of 45 mW.By using a maximum likelihood estimation,the density matrix of the squeezed light field is reconstructed.The time-domain signals from the balanced homodyne detector are collected to acquire the noise distribution of the squeezed light under different phase angles.The likelihood function is established for the measured quadrature components.An identity matrix is chosen as an initial density matrix,and the density matrix of the squeezed field is obtained through an iterative algorithm.The diagonal elements of the density matrix denote the photon number distribution,which includes not only even photon number states but also odd photon number states.The occurrence of odd photon number states mainly comes from the system losses and the imperfect quantum efficiency of detector.The Wigner function in phase space is calculated through the density matrix,and the maximum value of the Wigner function is 0.309.The standard deviation of the squeezed component is 64.4% of that of the vacuum state,corresponding to the squeezing degree of-3.8 dB.The standard deviation of the anti-squeezing component is 1.64 times that of the vacuum state,corresponding to the anti-squeezing degree of 4.3 dB.We theoretically calculate the photon number distribution and the Wigner function of the vacuum squeezed field,and compare the results obtained by theoretical calculation with those obtained by maximum likelihood reconstruction.The probability of vacuum state|0 obtained by maximum likelihood reconstruction is greater,and the probability of photon number state|n(n=1,2,) is smaller than the corresponding theoretical calculation results.From the theoretical calculation,the maximum value of Wigner function is 0.231,and the short axis and long axis of noise range deduced from the contours of the Wigner function are larger than the results from the maximum likelihood reconstruction.The possible reasons for the discrepancy are as follows. 1) The phase scanning is nonuniform during the measurement of the quadrature components.2) The low-frequency electronic noise is not completely filtered out in the datum acquisition process.3) The datum points of measured quadrature components are not enough.In conclusion,we produce a vacuum squeezed field of 795 nm,and obtain the photon number distribution and the Wigner function in phase space through maximum likelihood estimation and theoretical calculation,respectively.This work will provide an experimental basis for generating the Schrodinger cat state.
      Corresponding author: Wang Hai, wanghai@sxu.edu.cn
    • Funds: Project supported by the Key Project of the Ministry of Science and Technology of China (Grant No. 2016YFA0301402), the National Natural Science Foundation of China (Grant Nos. 11475109, 11274211, 11604191), and the Fund for Shanxi 1331Project Key Subjects Construction, China.
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    Eberle T, Steinlechner S, Bauchrowitz J, Hndchen V, Vahlbruch H, Mehmet M, Mller-Ebhardt H, Schnabel R 2010 Phys. Rev. Lett. 104 251102

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    Pooser R C, Lwrie B 2015 Optica 2 393

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    Furusawa A, Srensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706

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    Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413

    [7]

    Brask J B, Rigas I, Polzik E S, Andersen U L, Srensen A S 2010 Phys. Rev. Lett. 105 160501

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    Fleischhauer M, Lukin M D 2000 Phys. Rev. Lett. 84 5094

    [9]

    Yang S J, Wang X J, Bao X H, Pan J W 2016 Nat. Photon. 10 381

    [10]

    Chen Y H, Lee M J, Wang I C, Du S W, Chen Y F, Chen Y C, Yu I A 2013 Phys. Rev. Lett. 110 083601

    [11]

    Honda K, Akamatsu D, Arikawa M, Yokoi Y, Akiba K, Nagatsuka S, Tanimura T, Furusawa A, Kozuma M 2008 Phys. Rev. Lett. 100 093601

    [12]

    Appel J, Figueroa E, Korystov D, Lobino M, Lvovsky A I 2008 Phys. Rev. Lett. 100 093602

    [13]

    Mehmet M, Ast S, Eberle T, Steinlechner S, Vahlbruch H, Schnabel R 2011 Opt. Express 19 25763

    [14]

    Aoki T, Takahashi G, Furusawa A 2006 Opt. Express 14 6930

    [15]

    Han Y S, Wen X, He J, Yang B D, Wang Y H, Wang J M 2016 Opt. Express 24 2350

    [16]

    Takeno Y, Yukawa M, Yonezawa H, Furusawa A 2007 Opt. Express 15 4321

    [17]

    Burks S, Ortalo J, Chiummo A, Jia X J, Villa F, Bramati A, Laurat J, Giacobino E 2009 Opt. Express 17 3777

    [18]

    Mikhailov E E, Novikova I 2008 Opt. Lett. 33 1213

    [19]

    Ries J, Brezger B, Lvovsky A I 2003 Phys. Rev. A 68 025801

    [20]

    Barreiro S, Valente P, Failache H, Lezama A 2011 Phys. Rev. A 84 033851

    [21]

    Horrom T, Singh R, Dowling J P, Mikhailov E E 2012 Phys. Rev. A 86 023803

    [22]

    Slusher R E, Hollberg L W, Yurke B, Mertz J C, Valleys J F 1985 Phys. Rev. Lett. 55 2409

    [23]

    Swaim J D, Glasser R T 2017 Phys. Rev. A 96 033818

    [24]

    Wen F, Li Z P, Zhang Y Q, Gao H, Che J L, Abdulkhaleq H, Zhang Y P, Wang H X 2016 Sci. Rep. 6 25554

    [25]

    Tanimura T, Akamatsu D, Yokoi Y 2006 Opt. Lett. 31 2344

    [26]

    Htet G, Glckl O, Pilypas K A, Harb C C, Buchler B C, Bachor H A, Lam P K 2007 J. Phys. B: At. Mol. Opt. Phys. 40 221

    [27]

    Vogel K, Risken H 1989 Phys. Rev. A 40 R2847

    [28]

    Beck M, Smithey D T, Raymer M G 1993 Phys. Rev. A 48 R890

    [29]

    Smithey D T, Beck M, Cooper J, Raymer M G 1993 Phys. Rev. A 48 3159

    [30]

    Lvovsky A I, Raymer M G 2009 Rev. Mod. Phys. 81 299

    [31]

    Lvovsky A I 2004 J. Opt. B: Quantum Semiclass. Opt. 6 S556

    [32]

    Drever R W P, Hall J L, Kowaiski F V, Hough J, Ford G M, Munley A J, Ward H 1983 Appl. Phys. B 31 97

    [33]

    Boulanger B, Rousseau I, Fve J P, Maglione M, Mnaert B, Marnier G 1999 IEEE J. Quantum Electron. 35 281

  • [1]

    Taylor M A, Janousek J, Daria V, Knittel J, Hage B, Bachor H A, Bowen W P 2013 Nat. Photon. 7 229

    [2]

    Eberle T, Steinlechner S, Bauchrowitz J, Hndchen V, Vahlbruch H, Mehmet M, Mller-Ebhardt H, Schnabel R 2010 Phys. Rev. Lett. 104 251102

    [3]

    Pooser R C, Lwrie B 2015 Optica 2 393

    [4]

    Braunstein S L, van Loock P 2005 Rev. Mod. Phys. 77 513

    [5]

    Furusawa A, Srensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706

    [6]

    Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413

    [7]

    Brask J B, Rigas I, Polzik E S, Andersen U L, Srensen A S 2010 Phys. Rev. Lett. 105 160501

    [8]

    Fleischhauer M, Lukin M D 2000 Phys. Rev. Lett. 84 5094

    [9]

    Yang S J, Wang X J, Bao X H, Pan J W 2016 Nat. Photon. 10 381

    [10]

    Chen Y H, Lee M J, Wang I C, Du S W, Chen Y F, Chen Y C, Yu I A 2013 Phys. Rev. Lett. 110 083601

    [11]

    Honda K, Akamatsu D, Arikawa M, Yokoi Y, Akiba K, Nagatsuka S, Tanimura T, Furusawa A, Kozuma M 2008 Phys. Rev. Lett. 100 093601

    [12]

    Appel J, Figueroa E, Korystov D, Lobino M, Lvovsky A I 2008 Phys. Rev. Lett. 100 093602

    [13]

    Mehmet M, Ast S, Eberle T, Steinlechner S, Vahlbruch H, Schnabel R 2011 Opt. Express 19 25763

    [14]

    Aoki T, Takahashi G, Furusawa A 2006 Opt. Express 14 6930

    [15]

    Han Y S, Wen X, He J, Yang B D, Wang Y H, Wang J M 2016 Opt. Express 24 2350

    [16]

    Takeno Y, Yukawa M, Yonezawa H, Furusawa A 2007 Opt. Express 15 4321

    [17]

    Burks S, Ortalo J, Chiummo A, Jia X J, Villa F, Bramati A, Laurat J, Giacobino E 2009 Opt. Express 17 3777

    [18]

    Mikhailov E E, Novikova I 2008 Opt. Lett. 33 1213

    [19]

    Ries J, Brezger B, Lvovsky A I 2003 Phys. Rev. A 68 025801

    [20]

    Barreiro S, Valente P, Failache H, Lezama A 2011 Phys. Rev. A 84 033851

    [21]

    Horrom T, Singh R, Dowling J P, Mikhailov E E 2012 Phys. Rev. A 86 023803

    [22]

    Slusher R E, Hollberg L W, Yurke B, Mertz J C, Valleys J F 1985 Phys. Rev. Lett. 55 2409

    [23]

    Swaim J D, Glasser R T 2017 Phys. Rev. A 96 033818

    [24]

    Wen F, Li Z P, Zhang Y Q, Gao H, Che J L, Abdulkhaleq H, Zhang Y P, Wang H X 2016 Sci. Rep. 6 25554

    [25]

    Tanimura T, Akamatsu D, Yokoi Y 2006 Opt. Lett. 31 2344

    [26]

    Htet G, Glckl O, Pilypas K A, Harb C C, Buchler B C, Bachor H A, Lam P K 2007 J. Phys. B: At. Mol. Opt. Phys. 40 221

    [27]

    Vogel K, Risken H 1989 Phys. Rev. A 40 R2847

    [28]

    Beck M, Smithey D T, Raymer M G 1993 Phys. Rev. A 48 R890

    [29]

    Smithey D T, Beck M, Cooper J, Raymer M G 1993 Phys. Rev. A 48 3159

    [30]

    Lvovsky A I, Raymer M G 2009 Rev. Mod. Phys. 81 299

    [31]

    Lvovsky A I 2004 J. Opt. B: Quantum Semiclass. Opt. 6 S556

    [32]

    Drever R W P, Hall J L, Kowaiski F V, Hough J, Ford G M, Munley A J, Ward H 1983 Appl. Phys. B 31 97

    [33]

    Boulanger B, Rousseau I, Fve J P, Maglione M, Mnaert B, Marnier G 1999 IEEE J. Quantum Electron. 35 281

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  • Received Date:  07 November 2017
  • Accepted Date:  10 February 2018
  • Published Online:  05 May 2018

Generation and quantum state reconstruction of a squeezed vacuum light field resonant on the rubidium D1 line

    Corresponding author: Wang Hai, wanghai@sxu.edu.cn
  • 1. State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China;
  • 2. Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
Fund Project:  Project supported by the Key Project of the Ministry of Science and Technology of China (Grant No. 2016YFA0301402), the National Natural Science Foundation of China (Grant Nos. 11475109, 11274211, 11604191), and the Fund for Shanxi 1331Project Key Subjects Construction, China.

Abstract: The squeezed light field is a kind of important continuous variable quantum resource.It has wide applications in precision measurement and quantum information processing.Quantum storage is the foundations of quantum repeater and long distance quantum communication,and alkali metal atoms are an ideal quantum storage medium due to long ground state coherent time. With the rapid development of quantum storage technology in atomic medium,the preparation of the squeezed light which resonates with alkali metal atoms has become one of the research hotspots in the field of quantum information.In this paper,we report the generation of squeezed vacuum at 795 nm (resonant on the rubidium D1 transition line) by using an optical parametric oscillation based on a periodically poled KTiOPO4 crystal. The generated squeezed light field is detected by a balanced homodyne detector,and the squeezing of-3 dB and anti-squeezing of 5.8 dB are observed at a pump power of 45 mW.By using a maximum likelihood estimation,the density matrix of the squeezed light field is reconstructed.The time-domain signals from the balanced homodyne detector are collected to acquire the noise distribution of the squeezed light under different phase angles.The likelihood function is established for the measured quadrature components.An identity matrix is chosen as an initial density matrix,and the density matrix of the squeezed field is obtained through an iterative algorithm.The diagonal elements of the density matrix denote the photon number distribution,which includes not only even photon number states but also odd photon number states.The occurrence of odd photon number states mainly comes from the system losses and the imperfect quantum efficiency of detector.The Wigner function in phase space is calculated through the density matrix,and the maximum value of the Wigner function is 0.309.The standard deviation of the squeezed component is 64.4% of that of the vacuum state,corresponding to the squeezing degree of-3.8 dB.The standard deviation of the anti-squeezing component is 1.64 times that of the vacuum state,corresponding to the anti-squeezing degree of 4.3 dB.We theoretically calculate the photon number distribution and the Wigner function of the vacuum squeezed field,and compare the results obtained by theoretical calculation with those obtained by maximum likelihood reconstruction.The probability of vacuum state|0 obtained by maximum likelihood reconstruction is greater,and the probability of photon number state|n(n=1,2,) is smaller than the corresponding theoretical calculation results.From the theoretical calculation,the maximum value of Wigner function is 0.231,and the short axis and long axis of noise range deduced from the contours of the Wigner function are larger than the results from the maximum likelihood reconstruction.The possible reasons for the discrepancy are as follows. 1) The phase scanning is nonuniform during the measurement of the quadrature components.2) The low-frequency electronic noise is not completely filtered out in the datum acquisition process.3) The datum points of measured quadrature components are not enough.In conclusion,we produce a vacuum squeezed field of 795 nm,and obtain the photon number distribution and the Wigner function in phase space through maximum likelihood estimation and theoretical calculation,respectively.This work will provide an experimental basis for generating the Schrodinger cat state.

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