Local sampling of phase-space distributions by cascaded optical homodyning

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 59, Issue 1, 1999, Pages R39-R42

  Kis, Z ^a   Kiss, T ^a   Janszky, J ^a   Adam, P ^a   Wallentowitz, S ^b   Vogel, W ^b  

^a WIGNER RESEARCH CENTRE FOR PHYSICS   (Hungary)

^b UNIVERSITY OF ROSTOCK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002171168     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.59.R39     Document Type: Article

References (22)

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18. We use the recursion relations (Formula presented) and (Formula presented) for the regular and irregular harmonic-oscillator eigenfunctions (Formula presented)
19. (Formula presented) since in Eq. (11) (Formula presented) because for all (Formula presented) either the regular or the irregular eigenfunctions are antisymmetric in (Formula presented) i.e., (Formula presented) or (Formula presented)
20. The regular and irregular ground states read (Formula presented) and (Formula presented) with (Formula presented) being Dawson’s integral 18.
21. Note that in this way we derived also the generating function (Formula presented) of the pattern functions, (Formula presented) as (Formula presented)
22. For an efficient numerical calculation of Dawson’s integral, (Formula presented) see Chap. 6.10 of W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1995).