We investigate the stability and dynamics of the orbital angular momentum modes of a repulsive Bose-Einstein condensate trapped in two tunnel-coupled rings in a stack configuration. Within mean-field theory, we derive a two-state model for the system in the case in which we populate equally both rings with a single orbital angular momentum mode and include small perturbations in other modes. Analyzing the fixed point solutions of the model and the associated classical Hamiltonian, we characterize the destabilization of the stationary states and the subsequent dynamics. By populating a single orbital angular momentum mode with an arbitrary population imbalance between the rings, we derive analytically the boundary between the regimes of Josephson oscillations and macroscopic quantum self-trapping and study numerically the stability of these solutions.

中文翻译：

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困在两个堆叠环中的玻色-爱因斯坦凝聚物的轨道角动量动力学

我们研究了在堆叠结构中被困在两个隧道耦合环中的排斥性玻色-爱因斯坦凝结水的轨道角动量模式的稳定性和动力学。在均场理论内，我们推导了系统的二态模型，在这种情况下，我们用单个轨道角动量模式均等地填充了两个环，并在其他模式中包括了小扰动。分析模型的定点解和相关的经典哈密顿量，我们描述了稳态的不稳定性以及随后的动力学。通过在环之间具有任意人口不平衡的情况下填充单个轨道角动量模式，