Quantum revivals of a non-Rabi type in a Jaynes–Cummings model
Y. Ozhigov, N. Skovoroda, N. Victorova
Feb 11, 2015
Citations
3
Citations
Journal
Theoretical and Mathematical Physics
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Key Takeaway Key Takeaway: Full revival of quantum states in the Jaynes-Cummings model with the rotating wave approximation is impossible for zero detuning, but exists for nonzero detuning, and partial revivals occur when the rotating wave approximation is rejected.
Abstract
We study full revivals (e.g., the reappearance in the unitary evolution) of quantum states in the Jaynes–Cummings model with the rotating wave approximation. We prove that in the case of a zero detuning in subspaces generated by two adjacent pairs of energy levels, full revival does not exist for any values of the parameters. In contrast, the set of parameters that allows full revival is everywhere dense in the set of all parameters in the case of a nonzero detuning. The nature of these revivals differs from Rabi oscillations for a single pair of energy levels. In more complex subspaces, the presence of full revival reduces to particular cases of the tenth Hilbert problem for rational solutions of systems of nonlinear algebraic equations, which has no algorithmic solution in the general case. Non-Rabi revivals become partial revivals in the case where the rotating wave approximation is rejected.