We present a cluster mean-field study for ground-state phase diagram and many-body dynamics of spin-1 bosons confined in a two-chain Bose–Hubbard ladder (BHL). For unbiased BHL, we find superfluid (SF) phase and integer filling Mott insulator (IntMI) phase. For biased BHL, in addition to the SF and IntMI phases, there appears half-integer filling Mott insulator (HIntMI) phase. The phase transition between the SF and IntMI phases can be first order at a part of phase boundaries, while the phase transition between the SF and HIntMI phases is always second order. By tuning the bias energy, we report on the change of the nature of SF–MI phase transitions. Furthermore, we study the effect of the spin-dependent interaction on the many-body population dynamics. The spin-dependent interaction can lead to rich dynamical behaviors, but does not influence the particle transfer efficiency. Our results indicate a way to tune the nature of the SF–MI phase transition and open a new avenue to study the many-body dynamics of spinor bosons in optical lattices.

我们针对限制在双链 Bose-Hubbard 阶梯 (BHL) 中的自旋 1 玻色子的基态相图和多体动力学提出了集群平均场研究。对于无偏 BHL，我们发现了超流体 (SF) 相和整数填充莫特绝缘体 (IntMI) 相。对于偏置 BHL，除了 SF 和 IntMI 相外，还出现了半整数填充莫特绝缘体（HIntMI）相。SF 和 IntMI 相之间的相变在部分相边界处可以是一阶的，而 SF 和 HIntMI 相之间的相变总是二阶的。通过调整偏置能量，我们报告了 SF-MI 相变性质的变化。此外，我们研究了自旋相关相互作用对多体动力学的影响。自旋相关的相互作用可以导致丰富的动力学行为，但不影响粒子传输效率。我们的结果表明了一种调整 SF-MI 相变性质的方法，并开辟了研究光学晶格中自旋玻色子多体动力学的新途径。