Anatolii A Karatsuba and Ekatherina A Karatsuba 2009 J. Phys. A: Math. Theor. 42 195304 doi:10.1088/1751-8113/42/19/195304
A resummation formula for collapse and revival in the Jaynes–Cummings model
Anatolii A Karatsuba1 and Ekatherina A Karatsuba2
Show affiliationsWe present a new approach to the study of the function of atomic inversion in the model of interaction of a single two-level atom with a single mode of the quantized electromagnetic field in the coherent state in an ideal resonator. The approach suggested is based on an application of certain number-theoretic results to the approximation of the trigonometric sums of a special form, in particular of the functional equation of the Jacobi theta function. New asymptotic formulae for the atomic inversion are found. The asymptotics that we obtain make it possible to predetermine the details of the behavior of the inversion on various time intervals depending on the parameters of the system.
- PACS
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42.50.Ar Photon statistics and coherence theory
- MSC
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81R30 Coherent states (See also 22E45); squeezed states (See also 81V80)
- Subjects
- Dates
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Issue 19 (15 May 2009)
Received 18 June 2008, in final form 23 February 2009
Published 27 April 2009
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A resummation formula for collapse and revival in the Jaynes–Cummings model
Anatolii A Karatsuba and Ekatherina A Karatsuba 2009 J. Phys. A: Math. Theor. 42 195304
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