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

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 greater than or similar to 1 and delta approximate to 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.

Automated summary

A generalized Mathieu equation (GME) is proposed to describe the dynamics of two different models in spin-1 Bose-Einstein condensates, showing significant differences from Mathieu's equation and allowing the description of generalized parametric resonance. The GME can distinguish between the two equations when epsilon is greater than or equal to 1 and delta is approximately 0.25, explaining experimental results, predicting behavior, and easily implemented in experiments for both nematic and spin space models.