From the Weyl quantization of a particle on the circle to number-phase Wigner functions

被引：10
作者：
Przanowski, Maciej [1 ]
Brzykcy, Przemyslaw [1 ]
Tosiek, Jaromir [1 ]
机构：
[1] Tech Univ Lodz, Inst Phys, PL-90924 Lodz, Poland
来源：
ANNALS OF PHYSICS | 2014年 / 351卷
关键词：
Quantum phase; Number-phase Wigner function; QUANTUM-MECHANICS; ANGLE VARIABLES; HILBERT-SPACE; POV MEASURES; OPERATORS; FORMALISM; DISCRETE; FIELD; RADIATION; CYLINDER;
D O I：
10.1016/j.aop.2014.10.011
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
A generalized Weyl quantization formalism for a particle on the circle is shown to supply an effective method for defining the number-phase Wigner function in quantum optics. A Wigner function for the state (Q) over cap and the kernel K for a particle on the circle is defined and its properties are analysed. Then it is shown how this Wigner function can be easily modified to give the number-phase Wigner function in quantum optics. Some examples of such number-phase Wigner functions are considered. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：919 / 934
页数：16
相关论文
共 63 条
  • [1] The Wigner function for general Lie groups and the wavelet transform
    Ali, ST
    Atakishiyev, NM
    Chumakov, SM
    Wolf, KB
    [J]. ANNALES HENRI POINCARE, 2000, 1 (04): : 685 - 714
  • [2] PHASE IN QUANTUM OPTICS
    BARNETT, SM
    PEGG, DT
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1986, 19 (18): : 3849 - 3862
  • [3] ON THE HERMITIAN OPTICAL-PHASE OPERATOR
    BARNETT, SM
    PEGG, DT
    [J]. JOURNAL OF MODERN OPTICS, 1989, 36 (01) : 7 - 19
  • [4] QUANTUM-THEORY OF ROTATION ANGLES
    BARNETT, SM
    PEGG, DT
    [J]. PHYSICAL REVIEW A, 1990, 41 (07): : 3427 - 3435
  • [5] BEALS R, 1971, TOPICS OPERATOR THEO
  • [6] SEMICLASSICAL MECHANICS IN PHASE SPACE - STUDY OF WIGNERS FUNCTION
    BERRY, MV
    [J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1977, 287 (1343): : 237 - 271
  • [7] Bialynicka-Birula Z., 1995, J APPL PHYS B, V60, P275
  • [8] On alias-free discrete time Wigner distributions for time-frequency analysis of fusion plasma signals: application to JET magnetic activity data
    Bizarro, J. P. S.
    Figueiredo, A. C. A.
    [J]. NUCLEAR FUSION, 2006, 46 (05) : 645 - 666
  • [9] Comment on 'Wigner function for a particle in an infinite lattice'
    Bizarro, Joao P. S.
    [J]. NEW JOURNAL OF PHYSICS, 2013, 15
  • [10] Comment on "Full quantum reconstruction of vortex states"
    Bizarro, Joao P. S.
    [J]. PHYSICAL REVIEW A, 2010, 81 (01):
1234567