This article is cited in 5 papers

Quantum revivals of non Rabi type in Jaynes-Cummings model

Yu. I. Ozhigov^ab, N. A. Skovoroda^a, N. B. Viktorova<sup>c

a</sup> Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia
^b Institute of Physics and Technology, RAS, Moscow, Russia
^c Russian State University for the Humanities, Moscow, Russia

Abstract: We studied full revivals of quantum states in the Jaynes-Cummings model. It is proved that in the case of zero detuning in subspaces generated by two adjacent pairs of energy levels, full revival of the subspace does not exist for any values of the parameters. In the case of non-zero detuning on the contrary, the set of parameters that allows full revival of such subspaces is dense as the subset of all parameters. The nature of these revivals differs from Rabi oscillations in subspaces of a single pair of energy. In more complex subspaces the presence of full revival is reduced to particular cases of 10-th Hilbert problem for rational solutions of systems of nonlinear algebraic equations, which has no algorithmic solution in general case.

Keywords: quantum dynamics, quantum revivals, model jf Jaynes-Cummings.

PACS: 03.65

MSC: 81V80

Received: 08.05.2015
Revised: 01.12.2015

DOI: 10.4213/tmf8963

 English version: Theoretical and Mathematical Physics, 2016, 189:2, 1673–1679

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