# Quasi-integrability and nonlinear resonances in cold atoms under modulation

## TL;DR

This paper studies the quantum behavior of cold atoms under phase modulation, revealing quasi-integrable dynamics and nonlinear resonances.

## Contribution

The paper provides an exact analysis of a two-level system under time-dependent Hamiltonian, revealing quasi-integrability and nonlinear resonances.

## Key findings

- The system evolves on two coupled potential energy surfaces, one binding and one scattering.
- The dynamics exhibit quasi-integrability with nonlinear resonances and intermittent scattering.
- The behavior resembles Anderson and dynamical localization phenomena.

## 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 (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.