Quantum revivals of non Rabi type in Jaynes-Cummings model

TL;DR

This paper investigates quantum state revivals in the Jaynes-Cummings model, revealing conditions for their existence and highlighting differences from Rabi oscillations, with implications for complex quantum systems.

Contribution

It provides a detailed analysis of full quantum revivals in the Jaynes-Cummings model, especially under zero and non-zero detuning, and connects revival phenomena to the 10th Hilbert problem.

Findings

Full revivals do not occur at zero detuning.

Full revivals are dense in parameter space at non-zero detuning.

Revival phenomena relate to solutions of nonlinear algebraic systems.

Abstract

We studied full revivals of quantum states in the Jaynes-Cannings 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.