Quasi-integrability and nonlinear resonances in cold atoms under modulation

TL;DR

This paper analyzes the quantum dynamics of cold atoms under phase modulation, revealing quasi-integrable behavior with nonlinear resonances and phenomena similar to Anderson localization, with implications for quantum computation.

Contribution

It provides an exact analytical study of a modulated two-level atomic system, highlighting quasi-integrability and nonlinear resonances in a classically non-integrable quantum system.

Findings

Dynamics evolve on coupled potential energy surfaces.

System exhibits quasi-integrability with nonlinear resonances.

Behavior resembles Anderson and dynamical localization.

Abstract

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, one of them binding while the other one scattering type. The dynamics is shown to be quasi-integrable with nonlinear resonances. The bounded dynamics with intermittent scattering at random moments presents the scenario reminiscent to Anderson and dynamical localization. We believe that a careful analytical investigation of a multi-component system which is classically non-integrable is relevant to many other fields, including quantum computation with multi-qubit system.