High-order nonlinearities in the motion of a trapped atom

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 59, Issue 1, 1999, Pages 531-538

  Wallentowitz, S ^a   Vogel, W ^a   Knight, P L ^b  

^a UNIVERSITY OF ROSTOCK   (Germany)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

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Indexed keywords

EID: 0000721595     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.59.531     Document Type: Article

References (26)

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24. For (Formula presented) one obtains a zero quantum coupling, where no vibrational quanta are created or annihilated in the motion of the trapped atom. For this case only the excitation-dependent operator function (Formula presented) acts on the motional degree of freedom and leads to phase-shift and dispersive effects; for more details see Ref. 15. We exclude this case here, since we are mainly interested in the particular situation for (Formula presented)
25. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965). (a) For the relation between Laguerre polynomials and the confluent hypergeometric function see Chap. 13, Eq. (13.6.9). (b) For the asymptotic expansion of the confluent hypergeometric function, see Chap. 13, Eq. (13.5.14).
26. For a more detailed discussion of these phase-locking effects in the case of nonlinear squeezing (Formula presented) cf. Ref. 19.