Phase operator for two-state systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 57, Issue 2, 1998, Pages 731-736

  Muller A ^a  

^a UNIVERSITY OF KIEL   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039075890     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.57.731     Document Type: Article

References (26)

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7. Topological Phases in Quantum Theory, edited by B. L. Markovski and S. I. Vinitsky (World Scientific, Singapore, 1989);
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11. A. Messiah, Quantenmechanik II (Walter de Gruyter, Berlin, 1985).
12. When it is necessary to distinguish Bloch and phase vectors or other quantities for different states in general and states with different phases in particular, these are indexed by the state they refer to [e.g., (Formula presented) in Eq. (2.8) and (Formula presented) in Sec. III A].
13. See, e.g., J. Anandan, Nature (London) 360, 307 (1992); NATUAS
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18. See, e.g., M. do Carmo, Differential Geometry of Curves and Surfaces (Prentice Hall, Englewood Cliffs, NJ, 1976).
19. The Pancharatnam phase is a generalization of geometric phases to noncyclic states, see, e.g., J. Samuel and R. Bhandari, Phys. Rev. Lett. 23, 2339 (1988). The application of phase vectors to this case, however possible, will not be considered here, in order to avoid unnecessary complications of the principal line of reasoning.PRLTAO
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25. D. T. Pegg and S. M. Barnett, Phys. Rev. A 39, 1665 (1989).PLRAAN
26. Remember, that according to their definitions, the Bloch and phase vector (b and c) are twice the Pauli vectors (w and x) of the statistical and phase operator, respectively.