Wigner functions for the eigenstates of k-th power annihilation operators and their non-classical properties

Abstract

Abstract:

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 (defining the phase space), 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).

Key words: quantum optics, annihilation operators, eigenstates, Wigner functions, non-classical property

LAN Hai-Jiang, WEI Lian-Fu. Wigner functions for the eigenstates of k-th power annihilation operators and their non-classical properties[J]. J4, 2010, 27(2): 187-192.

References

[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, Rauschenbeutel 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 Electronics (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 aN 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 a4 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 ak(for k≥3) from coherent state and higher-oeder squeezing

[J]. Phys. Rev. A, 1992, 46(3): 1700-1704.

[17] Ma Aiqun, Chen Lixue, Gu Qiao. Orthonormalization Eigenstates of a5 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] Özdemir ? 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.