We apply the theory of the inhomogeneous Kibble-Zurek mechanism to understand the quench dynamics in the transition from a Mott insulator to a superfluid in a cold Bose gas confined in both a two-dimensional optical lattice and a harmonic trap. The local quench time and the resulting Kibble-Zurek diabatic-adiabatic boundary take a nontrivial positional dependence due to the Mott-lobe structure of the ground-state phase diagram of the Bose-Hubbard model. We demonstrate the quench dynamics through the time-dependent Gutzwiller simulations, revealing inhomogeneous properties of the growth of the superfluid order parameter. The inhomogeneous Kibble-Zurek theory is applicable to the shallow harmonic trap.

中文翻译：

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非均质Kibble-Zurek机理在有限系统中从Mott绝缘子到超流体过渡的淬灭动力学中的应用

我们应用非均质Kibble-Zurek机理的理论来理解在二维光学晶格和谐波陷阱中均处于冷态的玻色气体中，从Mott绝缘体到超流体的跃迁动力学。由于Bose-Hubbard模型基态相图的Mott-lobe结构，局部淬火时间和由此产生的Kibble-Zurek非绝热-绝热边界具有非平凡的位置依赖性。我们通过与时间有关的Gutzwiller模拟证明了淬灭动力学，揭示了超流体有序参数增长的不均匀特性。不均匀的Kibble-Zurek理论适用于浅谐波陷阱。