Stability analysis of a magnetic waveguide with self-generated offset field

TL;DR

This paper analyzes the stability of a self-generated magnetic waveguide for 87Rb atoms, revealing conditions for stable guiding without external offset fields through eigenvalue analysis and Lyapunov transformations.

Contribution

It introduces a novel stability analysis method for a time-modulated magnetic guide without external offset fields, including a threshold frequency criterion.

Findings

Identified a threshold modulation frequency for stability.

Derived an upper bound for stability domains.

Validated stable guiding with experimental parameters.

Abstract

The unexpected emerging stability of a time-modulated magnetic guide, realized without external offset fields, is demonstrated. We found a steady periodic solution around which the nonlinear dynamics is linearized. To investigate the orbital stability of the guiding, a formal criterion based on the analysis of the eigenvalues of the monodromy matrix of the system dynamics is used. To circumvent the difficulty in finding an analytical expression for these eigenvalues, a Lyapunov transformation of the system variables is proposed. From this transformation, an equation of state for the system parameters is derived, and it allows one to estimate an upper bound for the computed stability domains. In particular, we found a general expression for the threshold modulation frequency below which the guiding is unstable. Using experimentally accessible parameters, the stable guiding of 87Rb atoms is investigated.