2021/08/27 by Peng Xu, Wenxian Zhang
Mathematics · Physics and Astronomy · #Bose–Einstein condensate #Chart #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Dynamics (music) #Geometry #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Parameter space #Parametric oscillator #Parametric statistics #Physics #Quantum mechanics #Resonance (particle physics) #Space (punctuation) #Spin (aerodynamics) #Stability (learning theory) #Statistics #Strong Light-Matter Interactions #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.104.023324
published as Phys. Rev. A 104, 023324 (2021) · 10 pages, 7 figures
openalex publication_date 2021/08/27 · arxiv created 2021/08/30 · arxiv updated 2022/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 ε\gtrsim 1 and δ≈ 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.