Generalized parametric resonance in a spin-1 Bose-Einstein condensate

TL;DR

This paper introduces a generalized Mathieu equation to describe the dynamics of spin-1 Bose-Einstein condensates, explaining experimental results and predicting behaviors under various driving strengths, with implications for experimental tuning.

Contribution

It proposes a new generalized Mathieu equation model for spin-1 BECs, extending understanding of parametric resonance beyond traditional Mathieu dynamics.

Findings

Explains experimental results in nematic space with small driving strength.

Predicts behavior in large driving strength regimes.

Provides a tunable model suitable for experimental implementation.

Abstract

We propose a generalized Mathieu equation (GME) which describes well the dynamics for two different models in spin-1 Bose-Einstein condensates. The stability chart of this GME differs significantly from that of Mathieu's equation and the unstable dynamics under this GME is called generalized parametric resonance. A typical region of $\epsilon \gtrsim 1$ and $\delta \approx 0.25$ can be used to distinguish these two equations. The GME we propose not only explains the experimental results of Hoang et al. [Nat. Commun. 7, 11233 (2016)] in nematic space with a small driving strength, but predicts the behavior in the regime of large driving strength. In addition, the model in spin space we propose, whose dynamics also obeys this GME, can be well-tuned such that it is easily implemented in experiments.