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通过考察耗散光学腔中少光子数叠加态的Wigner函数随时间 的变化行为, 揭示其非经典特性的动力学演化. 结果表明, 初始时Wigner函数为负的少光子数叠加态, 在耗散过程中其负性逐渐减小 直至消失, 并最后达到一个稳定的正值. 但这并不意味着耗散量子态非经典特性的完全消失. 实际上, 作为非经典特性的另一个重要参量, 光子的二阶关联函数g(2)(0) (g(2)(0)g(2A)(0)却是一个随着耗散而改变的物理参量, 从而可以用于描述光学微腔中光量子态的耗散动力学行为. 最后, 我们给出一个在实验上如何制备少光子数叠加态并对其Wigner函数进行探测的方案.Detections and manipulations of quantum optical state at single-photon level have received much attention in the current experiments. Here, by numerically calculating the time-evolved Wigner functions, we investigate the dynamics of the typical non-classical state, i.e., few-photon superposition states in a dissipating optical microcavity. It is shown that the negativity of their Wigner function vanishes with dissipation. But this does not imply that all the non-classical features of the dissipative quantum state disappear. In fact, it is shown that the value of the second-order correlation function g(2)(0) (which serves usually as the standard criterion of a typical non-classical effect, i.e., the anti-bunching of photons, if g(2)(0)g(2A)(0) varies with the cavity dissipation and thus could be used to describe the physical effects of the dissipative cavity. Finally, we discuss the experimental feasibility of our proposal with a practically-existing cavity QED system.
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Keywords:
- few-photon superposition states /
- Wigner function /
- dissipative optical microcavity /
- anti-bunching
[1] Wigner E P 1932 Phys. Rev. 40 749
[2] Buzek V, Knight P L 1995 Progress in Optics in: Wolf E ed Vol. XXXIV, Edited by (Amsterdam: North Holland), and Refs. Therein.
[3] Yang Y, Li F L 2009 J. Opt. Soc. Am. B 26 830
[4] Hillery M, O' Connell R F, Scully M O, Wigner E P 1984 Phys. Rep. 106 121
[5] Wei L F, Wang S J, Jie Q L 1997 Chin. Sci. Bull. 42 1686
[6] Yang Q Y, Sun J W, Wei L F, Ding L E 2005 Acta Phys. Sin. 54 2704 (in Chinese) [杨庆怡, 孙敬文, 韦联福, 丁良恩 2005 54 2704]
[7] Li S B, Zou X B, Guo G C 2007 Phys. Rev. A 75 045801
[8] Zhang M, Jia H Y 2008 Acta Phys. Sin. 57 880 (in Chinese) [张淼, 贾焕玉 2008 57 880]
[9] Hu L Y, Fan H Y 2010 J. Opt. Soc. Am. B 27 286
[10] Lan H J, Pang H F, Wei L F 2009 Acta Phys. Sin. 58 8281 (in Chinese) [蓝海江, 庞华锋, 韦联福 2009 58 8281]
[11] Biswas A, Agarwal G S 2007 Phys. Rev. A 75 032104
[12] Xu X X, Hu L Y, Fan H Y 2010 Opt. Commun. 283 1801
[13] Hu L Y, Xu X X, Wang Z S, Xu X F 2010 Phys. Rev. A 82 043842
[14] de Queiros I P, Cardoso W B, de Alemida N G 2007 J. Phys. B: At. Mol. Opt. Phys. 40 21
[15] Buller G S, Collins R J 2010 Meas. Sci. Technol. 21 012002
[16] Scully M O, Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press)
[17] Fan H Y, Hu L Y 2009 Opt. Commun. 282 4379
[18] Gradshteyn I S, Ryzhik I M 1965 Table of Integrals, Series and Products (New York: Academic)
[19] William L H 1973 Quantum Statistical Properties of Radiation (New York: John Wiley)
[20] Gardiner C W, Zoller P 2000 Quantum Noise (Berlin: Springer)
[21] Puri R R 2001 Mathematical Methods of Quantum Optics (Berlin: Springer-Verlag)
[22] Wüunsche A 2001 J. Comput. Appl. Math. 133 665
[23] Wüunsche A 2000 J. Phys. A: Math. Gen. 33 1603
[24] Dodono'v V V 2002 J. Opt. B: Quantum Semiclass. Opt. 4 R1
[25] Agarwal G S, Tara K 1992 Phys. Rev. A 46 485
[26] Lutterbach L G, Davidovich L 1997 Phys. Rev. Lett. 78 2547
[27] Cahill K E, Glauber R J 1969 Phys. Rev. 177 1882
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[1] Wigner E P 1932 Phys. Rev. 40 749
[2] Buzek V, Knight P L 1995 Progress in Optics in: Wolf E ed Vol. XXXIV, Edited by (Amsterdam: North Holland), and Refs. Therein.
[3] Yang Y, Li F L 2009 J. Opt. Soc. Am. B 26 830
[4] Hillery M, O' Connell R F, Scully M O, Wigner E P 1984 Phys. Rep. 106 121
[5] Wei L F, Wang S J, Jie Q L 1997 Chin. Sci. Bull. 42 1686
[6] Yang Q Y, Sun J W, Wei L F, Ding L E 2005 Acta Phys. Sin. 54 2704 (in Chinese) [杨庆怡, 孙敬文, 韦联福, 丁良恩 2005 54 2704]
[7] Li S B, Zou X B, Guo G C 2007 Phys. Rev. A 75 045801
[8] Zhang M, Jia H Y 2008 Acta Phys. Sin. 57 880 (in Chinese) [张淼, 贾焕玉 2008 57 880]
[9] Hu L Y, Fan H Y 2010 J. Opt. Soc. Am. B 27 286
[10] Lan H J, Pang H F, Wei L F 2009 Acta Phys. Sin. 58 8281 (in Chinese) [蓝海江, 庞华锋, 韦联福 2009 58 8281]
[11] Biswas A, Agarwal G S 2007 Phys. Rev. A 75 032104
[12] Xu X X, Hu L Y, Fan H Y 2010 Opt. Commun. 283 1801
[13] Hu L Y, Xu X X, Wang Z S, Xu X F 2010 Phys. Rev. A 82 043842
[14] de Queiros I P, Cardoso W B, de Alemida N G 2007 J. Phys. B: At. Mol. Opt. Phys. 40 21
[15] Buller G S, Collins R J 2010 Meas. Sci. Technol. 21 012002
[16] Scully M O, Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press)
[17] Fan H Y, Hu L Y 2009 Opt. Commun. 282 4379
[18] Gradshteyn I S, Ryzhik I M 1965 Table of Integrals, Series and Products (New York: Academic)
[19] William L H 1973 Quantum Statistical Properties of Radiation (New York: John Wiley)
[20] Gardiner C W, Zoller P 2000 Quantum Noise (Berlin: Springer)
[21] Puri R R 2001 Mathematical Methods of Quantum Optics (Berlin: Springer-Verlag)
[22] Wüunsche A 2001 J. Comput. Appl. Math. 133 665
[23] Wüunsche A 2000 J. Phys. A: Math. Gen. 33 1603
[24] Dodono'v V V 2002 J. Opt. B: Quantum Semiclass. Opt. 4 R1
[25] Agarwal G S, Tara K 1992 Phys. Rev. A 46 485
[26] Lutterbach L G, Davidovich L 1997 Phys. Rev. Lett. 78 2547
[27] Cahill K E, Glauber R J 1969 Phys. Rev. 177 1882
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