We explore the role of atomic correlations in a harmonically trapped Bose-Einstein condensate coupled to a dissipative cavity where both the atoms and the cavity are blue-detuned from the external pumping laser. Using a genuine beyond-mean-field many-body approach, we extract density distributions and many-body correlations to unveil a pathway to chaos at large pump power through a hierarchical self-organization of the atoms where the atoms transition from a single-well optical lattice to a double-well optical lattice. Correlated states of the atoms emerge and are characterized by local superfluid correlations in phases which are globally superfluid or Mott insulating. Local superfluid-Mott transitions are precluded by a dynamical instability to chaos which occurs via quasiperiodic attractors. Our results explain the mechanism behind the dynamical instabilities observed in experiments.

中文翻译：

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蓝色失谐空腔-BEC系统中通过分层超流动实现混沌的途径

我们探讨了原子相关性在谐波俘获的玻色-爱因斯坦冷凝物中耦合到耗散腔的作用，在该耗散腔中，原子和腔均从外部泵浦激光中失谐。使用真正的平均外场多体方法，我们提取了密度分布和多体相关性，从而揭示了通过原子的分层自组织（其中原子从单井跃迁）而在大泵浦功率下实现混沌的途径。光学晶格到双阱光学晶格。原子的相关状态出现并以局部超流体相关性为特征，这些相在整体上是超流体或莫特绝缘的。局部超流体-莫特跃迁被通过拟周期吸引子发生的动力学不稳定所阻止。