利用Fock态表象下的Wigner函数表达式,重构了湮没算符k次幂本征态的Wigner函数,并依据Wigner函数在相空间的分布规律,讨论了湮没算符k次幂本征态的非经典特性.数值结果表明:湮没算符k次幂本征态Wigner函数的分布与复参数α的取值有关;湮没算符1次幂的本征态(即相干态)为准经典态(其Wigner函数值总是非负的),而湮没算符大于或等于2次幂的本征态则都具有明显的非经典特性(它们的Wigner函数均出现了负值).
Wigner functions for the eigenstates of k-th power annihilation operators are constructed in phase spaces by using their expressions in Fock presentations. Based on the negativities of their relevant Wigner functions, the non-classical properties of these eigenstates are discussed. The numerical results show that,depending on the complex parameters α, the coherent states are quasi-classical (their Wigner functions are always non-negative), but the eigenstates of k-th (k ≥ 2) power annihilation operators are really non-classical (their relevant Wigner functions can be negative in phase spaces).
参考文献
| [1] | Kurtsiefer C,Pfau T,Mlynek J.Measurement of the Wigner function of an ensemble of helium atoms[J].Nature,1997,386:150-153. |
| [2] | Luttervach L G,Davidovich L.Method for direct measurement of the Wigner function in cavity QED and ion traps[J].Phys,Rev,Lett.,1997,78(13):2547-2550. |
| [3] | Zhang Zhiming.Reconstructing the Wigner function of cavity fields with the micromaser[J].Acta Phys.Sin,.(物理学报),2004,53(1):70-74 (in Chinese). |
| [4] | Nogues G,R.auschenbeutel A,Osnaghi S,et al.Measurement of a negative value for the Wigner function of radiation[J].Phys.Rev.A,2000,62(5):054101. |
| [5] | Lvovsky A I,Hansen H,Aichele T,et al.Quantum state reconstruction of the single-photon Fock state[J].Phys.Rev.Lett.,2001,87(5):050402. |
| [6] | Wei Lianfu,Wang Shunjin,Jie Quanlin.Excited states of coherent state and their nonclassical properties[J].Chinese Science Bulletin.,1997,42(20):1686-1688. |
| [7] | Huang Chunqing,Wan Guangren.Nonclassical properties of the excited double-mode SU(2) coherent state[J].Chinese Journal of Quantum Electronics (量子电子学报),2005,22(1):47-51 (in Chinese). |
| [8] | Zhang Kefu,Wang Zhongjie.Excited circular states and their properties[J].Chinese Journal of Quantum Electronics (量子电子学报),2008,25(2):170-176 (in Chinese). |
| [9] | Zhou Yuxin,Xia Qingfeng,Sun Changyong.Quantum entanglement in system of two-mode squeezed vacuum state interacting with Bose-Einstein condensate[J].Chinese Journal of Quantum Etectronics (量子电子学报),2008,25(3):312-316 (in Chinese). |
| [10] | Zhang Xinding.Light-induced spin Hall effects in cold atoms[J].Chinese Journal of Quantum Electronics (量子电子学报),2009,26(2):187-192 (in Chinese). |
| [11] | Clauher R J.The quantum theory of optical coherence[J].Phys.Rev.,1963,130(6):2529-2539. |
| [12] | Hillery M.Amplitude-squared squeezing of the electromagnetic field[J].Phys.Rev.A,1987,36(8):3796-3802. |
| [13] | Peng Shian,Guo Guangcan.Orthonormalized eigenstates of operator αN and their properties[J].Acta Phys.Sin..(物理学报),1990,39(1):51-60 (in Chinese). |
| [14] | Peng Shian,Yan Dinning,Feng Kaiyin.Orthonormalization eigenstates of α4 and their quantum statistical properties[J].Chinese Journal of Quantum Electronics (量子电子学报),1989,6(4):306-311 (in Chinese). |
| [15] | Sun Jinzuo,Wang Jisuo,Wang Chuankui,Orthonormalized eigenstates of cubic and highter powers of the annihilation operator[J].Phys.Rev.A,1991,44(5):3369-3372. |
| [16] | Sun Jinzuo,Wang Jisuo,Wang Chuankui.Generation of orthonomalized eigenstates of the operator αk (for k ≥ 3) from coherent state and higher-order squeezing[J].Phys.Rev.A,1992,46(3):1700-1704. |
| [17] | Ma Aiqun,Chen Lixue,Gu Qiao.Orthonormalization eigenstates of α5 and their quantum statistical characteristics[J].Journal of Harbin Institute of Technology (哈尔滨工业大学学报),1992,12(1):18-26 (in Chinese). |
| [18] | Parigi V,Zavatta A,Kim M S,et al.Probing quantum commutation rules by addition and subtraction of single photons to/from a light field[J].Science,2007,317:1890-1893. |
| [19] | Ozdemir S K,Miranowicz A,Koashi M,et al.Quantum-scissors device for optical state truncation:a proposal for practical realization[J].Phys.Rev.A,2001,64(6):063818. |
- 下载量()
- 访问量()
- 您的评分：
-
10%
-
20%
-
30%
-
40%
-
50%