We provide a complete study of the phase diagram characterising the distinct dynamical regimes emerging in a three-dimensional Josephson junction in an ultracold quantum gas. Considering trapped ultracold superfluids separated into two reservoirs by a barrier of variable height and width, we analyse the population imbalance dynamics following a variable initial population mismatch. We demonstrate that as the chemical potential difference is increased, the system transitions from Josephson plasma oscillations to either a dissipative (in the limit of low and narrow barriers) or a self-trapped regime (for large and wider barriers), with a crossover between the dissipative and the self-trapping regimes which we explore and characterize for the first time. This work, which extends beyond the validity of the standard two-mode model, connects the role of the barrier width, vortex rings and associated acoustic emission with different regimes of the superfluid dynamics across the junction, establishing a framework for its experimental observation, which is found to be within current experimental reach.

中文翻译：

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超冷约瑟夫森结的动力学相图

我们对表征超冷量子气体中三维约瑟夫森结中出现的不同动力学状态的相图进行了完整研究。考虑到被困超冷超流体被可变高度和宽度的屏障分成两个水库，我们分析了可变初始种群失配后的种群失衡动态。我们证明，随着化学势差的增加，系统从约瑟夫森等离子体振荡转变为耗散（在低和窄势垒的限制下）或自陷状态（对于大和更宽的势垒），在我们第一次探索和表征的耗散和自陷机制。这项工作超出了标准双模模型的有效性，