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One- and two-mode successively squeezed state, obtained through re-squeezing two single mode squeezed states by the two-mode squeezing operator, is studied in terms of the technique of integration within an ordered product (IWOP) of operators. We first derive the normally ordered form of this one- and two-mode successively squeezing operator, and then investigate the quantum statistical properties of the corresponding squeezed state. Particularly, we use the Weyl ordering invariance under a similar transformation to derive the analytical expression of its Wigner function, which seems very easy and concise. Finally, the experimental generation of one- and two-mode successively squeezed state is also proposed simply.
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Keywords:
- one- and two-mode successively squeezing operator /
- squeezing effect /
- Wigner function /
- the IWOP technique
[1] Dodonov V V 2002 J. Opt. B: Quantum Semiclass. Opt. 4 R1
[2] Loudon R, Knight P L 1987 J. Mod. Opt. 34 709
[3] Walls D F 1983 Nature 306 141
[4] Collet M J, Walls D F 1985 Phys. Rev. A 32 2887
[5] Lakshmi P A, Agarwal G S 1984 Phys. Rev. A 29 2260
[6] Milburn G J, Braunstein S L 1999 Phys. Rev. A 60 937
[7] Zhang J, Peng K C 2000 Phys. Rev. A 62 064302
[8] Song T Q 2004 Acta Phys. Sin. 53 3358 (in Chinese) [宋同强 2004 物理学报 53 3358]
[9] Ban M 1999 J. Opt. B: Quantum Semiclass. Opt. 1 L9
[10] He G Q, Yi Z, Zhu J, Zeng G H 2007 Acta Phys. Sin. 56 6427 (in Chinese) [何广强, 易 智, 朱 俊, 曾贵华 2007 物理学报 56 6427]
[11] Yi Z, He G Q, Zeng G H 2007 Acta Phys. Sin. 58 3166 (in Chinese) [易 智, 何广强, 曾 贵华 2009 物理学报 58 3166]
[12] Hu L Y, Fan H Y 2008 J. Opt. Soc. Am. B 25 1955
[13] Sun Z H, Fan H Y 2000 Acta Phys. Sin. 49 74 (in Chinese) [孙治湖, 范洪义 2000 物理学报 49 74]
[14] Fan H Y 1990 Phys. Rev. A 41 1526
[15] Xu X X, Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661 (in Chinese) [徐学翔, 袁洪 春, 胡利云 2010 物理学报 59 4661]
[16] Jiang N Q, Zheng Y Z 2006 Phys. Rev. A 74 012306
[17] Jiang N Q, Jing N Q, Zhang Y, Cai G C 2008 Europhys. Lett. 84 14002
[18] Jiang N Q, Fan H Y 2008 Commun. Theor. Phys. 49 225
[19] Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R147
[20] Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
[21] Fan H Y, VanderLinde J 1989 Phys. Rev. A 39 1552
[22] Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[23] Lai W K, Buek V, Knight P L 1991 Phys. Rev. A 44 6043
[24] Meng X G, Wang J S 2007 Acta Phys. Sin. 56 4578 (in Chinese) [孟祥国, 王继锁 2007 物理学报 56 4578]
[25] Lee C T 1990 Phys. Rev. A 41 1569
[26] Buek V, Barranco A, Knight P L 1992 Phys. Rev. A 45 6570
[27] Zhao J Q, Lu H X 2010 Acta Phys. Sin. 59 7875 (in Chinese) [赵加强, 逯怀新 2010 物理学报 59 7875]
[28] Lee C T 1990 Phys. Rev. A 42 1608
[29] Schleich P W 2001 Quantum Optics in Phase Space (Berlin: Wiley-Vch)
[30] Zhang Z M 2004 Acta Phys. Sin. 53 70 (in Chinese) [ 2004 53 70]
[31] Meng X G, Wang J S, Liang B L 2007 Acta Phys. Sin. 56 2160 (in Chinese) [张智明 2004 物理学报 53 70]
[32] Hu L Y, Fan H Y 2009 Chin. Phys. B 18 4657
[33] Xu X X, Yuan H C, Fan H Y 2011 Chin. Phys. B 20 024203
[34] Fan H Y 2008 Ann. Phys. 323 500
[35] Bachor H A, Ralph T C 2003 A Guide to Experiments in Quantum Optics (Berlin: Wiley-Vch)
[36] Yang Y, Li F L 2009 Phys. Rev. A 80 022315 064205-7
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[1] Dodonov V V 2002 J. Opt. B: Quantum Semiclass. Opt. 4 R1
[2] Loudon R, Knight P L 1987 J. Mod. Opt. 34 709
[3] Walls D F 1983 Nature 306 141
[4] Collet M J, Walls D F 1985 Phys. Rev. A 32 2887
[5] Lakshmi P A, Agarwal G S 1984 Phys. Rev. A 29 2260
[6] Milburn G J, Braunstein S L 1999 Phys. Rev. A 60 937
[7] Zhang J, Peng K C 2000 Phys. Rev. A 62 064302
[8] Song T Q 2004 Acta Phys. Sin. 53 3358 (in Chinese) [宋同强 2004 物理学报 53 3358]
[9] Ban M 1999 J. Opt. B: Quantum Semiclass. Opt. 1 L9
[10] He G Q, Yi Z, Zhu J, Zeng G H 2007 Acta Phys. Sin. 56 6427 (in Chinese) [何广强, 易 智, 朱 俊, 曾贵华 2007 物理学报 56 6427]
[11] Yi Z, He G Q, Zeng G H 2007 Acta Phys. Sin. 58 3166 (in Chinese) [易 智, 何广强, 曾 贵华 2009 物理学报 58 3166]
[12] Hu L Y, Fan H Y 2008 J. Opt. Soc. Am. B 25 1955
[13] Sun Z H, Fan H Y 2000 Acta Phys. Sin. 49 74 (in Chinese) [孙治湖, 范洪义 2000 物理学报 49 74]
[14] Fan H Y 1990 Phys. Rev. A 41 1526
[15] Xu X X, Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661 (in Chinese) [徐学翔, 袁洪 春, 胡利云 2010 物理学报 59 4661]
[16] Jiang N Q, Zheng Y Z 2006 Phys. Rev. A 74 012306
[17] Jiang N Q, Jing N Q, Zhang Y, Cai G C 2008 Europhys. Lett. 84 14002
[18] Jiang N Q, Fan H Y 2008 Commun. Theor. Phys. 49 225
[19] Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R147
[20] Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
[21] Fan H Y, VanderLinde J 1989 Phys. Rev. A 39 1552
[22] Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[23] Lai W K, Buek V, Knight P L 1991 Phys. Rev. A 44 6043
[24] Meng X G, Wang J S 2007 Acta Phys. Sin. 56 4578 (in Chinese) [孟祥国, 王继锁 2007 物理学报 56 4578]
[25] Lee C T 1990 Phys. Rev. A 41 1569
[26] Buek V, Barranco A, Knight P L 1992 Phys. Rev. A 45 6570
[27] Zhao J Q, Lu H X 2010 Acta Phys. Sin. 59 7875 (in Chinese) [赵加强, 逯怀新 2010 物理学报 59 7875]
[28] Lee C T 1990 Phys. Rev. A 42 1608
[29] Schleich P W 2001 Quantum Optics in Phase Space (Berlin: Wiley-Vch)
[30] Zhang Z M 2004 Acta Phys. Sin. 53 70 (in Chinese) [ 2004 53 70]
[31] Meng X G, Wang J S, Liang B L 2007 Acta Phys. Sin. 56 2160 (in Chinese) [张智明 2004 物理学报 53 70]
[32] Hu L Y, Fan H Y 2009 Chin. Phys. B 18 4657
[33] Xu X X, Yuan H C, Fan H Y 2011 Chin. Phys. B 20 024203
[34] Fan H Y 2008 Ann. Phys. 323 500
[35] Bachor H A, Ralph T C 2003 A Guide to Experiments in Quantum Optics (Berlin: Wiley-Vch)
[36] Yang Y, Li F L 2009 Phys. Rev. A 80 022315 064205-7
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