Integrable nonlinear evolution of the qubit

F.M. Ciaglia, F. Di Cosmo, A. Figueroa +5 more

George Vahala, Efstratios Koukoutsis, Min Soe +4 more

In the simplest problems of closed quantum systems, the time evolution of the wave function of the system is given by the Schrodinger equation. This formally integrates into the unitary evolution Ψ...

Rahul Gupta, Manan Jain, Sudhir R. Jain

Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix Hamiltonian. The dynamics is shown to evolve on two coupled potential energy surfaces (PESs): one of them is binding, while the other one is scattering type. The dynamics is shown to be quasi-integrable with nonlinear resonances. The bounded dynamics with intermittent scattering at random moments presents a scenario reminiscent of Anderson and dynamical localization. We believe that a careful analytical investigation of a multi-component system that is classically non-integrable is relevant to many other fields, including quantum computation with multi-qubit systems.

Yong Zhang

Jakub Rembieliński, Paweł Caban

This paper proposes a general rule that allows to distinguish acceptable and non-acceptable nonlinear quantum evolutions. Convex quasi-linear evolutions are free from problems with superluminal signaling. The explicit model of nonlinear but convex quasi-linear evolution of a qubit is constructed.