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Schrödinger cat state is an important non-classical state, and it can be used in quantum teleportation, quantum computation and quantum repeater. Schrödinger cat state is usually obtained experimentally by subtracting one photon from a squeezed-vacuum state. The fidelity between a photon-subtracted squeezed state and a cat state can be very high under suitable parameters. However, the quality of the generated state will be affected by the imperfect experimental conditions. In this paper, the effect of imperfect experimental conditions on the generation of cat state is theoretically calculated and analyzed.
The input squeezed-vacuum field is represented by Weyl characteristic function, which contains the fluctuation variance of the squeezed and amplified noises. The characteristic function of generated state is obtained by using the transmission matrix of beam splitter and the measurement operator of single-photon detector. We acquire the expression of Wigner function of generated state by the Fourier transform of the Weyl characteristic function. The fidelity is calculated by using the formula F=1/π∫d2ζC1(ζ)C|cat->(ζ), where C1(ζ) and C|cat->(ζ) represent Weyl characteristic function of the generated state and the Schrodinger cat state, respectively. The imperfection of the input squeezed state, the imperfection of the single-photon detector and the loss of the balanced homodyne detection are included in our theoretical model. We calculate the Wigner function at the phase-space origin W(0) and the fidelity in terms of different experimental parameters.
The results show that the fidelity and negativity of W(0) decrease with squeezing purity decreasing. A pure squeezed-vacuum state is composed of even photon number states. In the case of impure squeezing, some odd photon number states appear in the photon number distribution. After subtracting one photon from the impure squeezing state, the generated state consists of not only odd photon number state but also even photon states, which degrades the fidelity of the generated state. The lower squeezing purity is required to meet the demand for W(0)<0 under the condition of higher squeezing degree. There is an optimal squeezing degree to maximize the fidelity of generated state with impure squeezing. The use of inefficient on-ff single-photon detector and the loss of the balanced homodyne detection will further reduce the fidelity of the generated state. Under the practical experimental condition:squeezing degree s=-3 dB, the squeezing purity μ=99% and the quantum efficiency of balanced homodyne detection η=98%, the fidelity of generated state can reach 0.88 with using a commercially available on-off single-photon detector. This work can provide theoretical guidance for generating a high-quality Schrödinger cat state.-
Keywords:
- Schrödinger cat state /
- photon subtraction scheme /
- Wigner function /
- fidelity
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[2] Song S, Caves C M, Yurke B 1990 Phys. Rev. A 41 5261
[3] Minganti F, Bartolo N, Lolli J, Casteels W, Ciuti C 2016 Sci. Rep. 6 26987
[4] Johnson K G, Wong-Campos J D, Neyenhuis B, Mizrahi J, Monroe C 2017 Nat. Commun. 8 697
[5] van Enk S J, Hirota O 2001 Phys. Rev. A 64 022313
[6] Ralph T C, Gilchrist A, Milburn G J, Munro W J, Glancy S 2003 Phys. Rev. A 68 042319
[7] Lund A P, Ralph T C, Haselgrove H L 2008 Phys. Rev. Lett. 100 030503
[8] Monroe C, Meekhof D M, King B E, Wineland D J 1996 Science 272 1131
[9] Hofheinz M, Wang H, Ansmann M, Bialczak R C, Lucero E, Neeley M, O'Connell A D, Sank D, Wenner J, Martinis J M, Cleland A N 2009 Nature 459 546
[10] Ourjoumtsev A, Brouri R T, Laurat J, Grangier P 2006 Science 312 83
[11] Takahashi H, Wakui K, Suzuki S, Takeoka M, Hayasaka K, Furusawa A, Sasaki M 2008 Phys. Rev. Lett. 101 233605
[12] Neergaard-Nielsen J S, Nielsen B M, Hettich C, Mølmer K, Polzik E S 2006 Phys. Rev. Lett. 97 083604
[13] Kim M S, Park E, Knight P L, Jeong H 2005 Phys. Rev. A 71 043805
[14] Suzuki S, Tsujino K, Kannari F, Sasaki M 2006 Opt. Commun. 259 758
[15] Wakui K, Takahashi H, Furusawa A, Sasaki M 2007 Opt. Express 15 3568
[16] Dakna M, Anhut T, Opatrny T, Knöll L, Welsch D G 1997 Phys. Rev. A 55 3184
[17] Wenger J, Tualle-Brouri R, Grangier P 2004 Phys. Rev. Lett. 92 153601
[18] W Asavanant, K Nakashima, Y Shiozawa, J Yoshikawa, A Furusawa 2017 Opt. Express 25 32227
[19] Morin O, Liu J, Huang K, Barbosa F, Fabre C, Laurat J 2014 J. Vis. Exp. 87 e51224
[20] Laghaout A, Neergaard-Nielsen J S, Rigas I, Kragh C, Tipsmark A, Andersen U L 2013 Phys. Rev. A 87 043826
[21] Laghaout A, Neergaard-Nielsen J S, Rigas I 2013 Conference on Lasers and Electron-Optics Europe and International Quantum Electronics Conference,IEEE 1 1
[22] Kim M S, Lee J, Munro W J 2002 Phys. Rev. A 66 030301
[23] Hyukjoon K, Hyunseok J 2015 Phys. Rev. A 91 012340
[24] Lee C T 1995 Phys. Rev. A 52 3374
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[1] Yurke B, Schleich W, Walls D F 1990 Phys. Rev. A 42 1703
[2] Song S, Caves C M, Yurke B 1990 Phys. Rev. A 41 5261
[3] Minganti F, Bartolo N, Lolli J, Casteels W, Ciuti C 2016 Sci. Rep. 6 26987
[4] Johnson K G, Wong-Campos J D, Neyenhuis B, Mizrahi J, Monroe C 2017 Nat. Commun. 8 697
[5] van Enk S J, Hirota O 2001 Phys. Rev. A 64 022313
[6] Ralph T C, Gilchrist A, Milburn G J, Munro W J, Glancy S 2003 Phys. Rev. A 68 042319
[7] Lund A P, Ralph T C, Haselgrove H L 2008 Phys. Rev. Lett. 100 030503
[8] Monroe C, Meekhof D M, King B E, Wineland D J 1996 Science 272 1131
[9] Hofheinz M, Wang H, Ansmann M, Bialczak R C, Lucero E, Neeley M, O'Connell A D, Sank D, Wenner J, Martinis J M, Cleland A N 2009 Nature 459 546
[10] Ourjoumtsev A, Brouri R T, Laurat J, Grangier P 2006 Science 312 83
[11] Takahashi H, Wakui K, Suzuki S, Takeoka M, Hayasaka K, Furusawa A, Sasaki M 2008 Phys. Rev. Lett. 101 233605
[12] Neergaard-Nielsen J S, Nielsen B M, Hettich C, Mølmer K, Polzik E S 2006 Phys. Rev. Lett. 97 083604
[13] Kim M S, Park E, Knight P L, Jeong H 2005 Phys. Rev. A 71 043805
[14] Suzuki S, Tsujino K, Kannari F, Sasaki M 2006 Opt. Commun. 259 758
[15] Wakui K, Takahashi H, Furusawa A, Sasaki M 2007 Opt. Express 15 3568
[16] Dakna M, Anhut T, Opatrny T, Knöll L, Welsch D G 1997 Phys. Rev. A 55 3184
[17] Wenger J, Tualle-Brouri R, Grangier P 2004 Phys. Rev. Lett. 92 153601
[18] W Asavanant, K Nakashima, Y Shiozawa, J Yoshikawa, A Furusawa 2017 Opt. Express 25 32227
[19] Morin O, Liu J, Huang K, Barbosa F, Fabre C, Laurat J 2014 J. Vis. Exp. 87 e51224
[20] Laghaout A, Neergaard-Nielsen J S, Rigas I, Kragh C, Tipsmark A, Andersen U L 2013 Phys. Rev. A 87 043826
[21] Laghaout A, Neergaard-Nielsen J S, Rigas I 2013 Conference on Lasers and Electron-Optics Europe and International Quantum Electronics Conference,IEEE 1 1
[22] Kim M S, Lee J, Munro W J 2002 Phys. Rev. A 66 030301
[23] Hyukjoon K, Hyunseok J 2015 Phys. Rev. A 91 012340
[24] Lee C T 1995 Phys. Rev. A 52 3374
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