论文标题
单粒子损失的Bose-Hubbard链中的Bloch振荡
Bloch oscillations in a Bose-Hubbard chain with single-particle losses
论文作者
论文摘要
从理论上讲，我们研究了一维玻色扣链中的Bloch振荡，其中Lindblad方程描述的奇数晶格位点的单粒子损失。对于单个粒子，状态的时间演变完全由非炎性有效的哈密顿量确定。我们分析了该哈密顿量的光谱特性，以提供无限的晶格，并将光谱的特征与可观察的动力学效应（例如呼吸模式中的频率加倍）分析。我们进一步考虑了许多粒子在平均场极限中的情况，导致复杂的非线性Schrödinger动力学。分析表达式是针对广义的非线性固定态和非线性BLOCH带得出的。非线性和粒子损失的相互作用导致非线性Bloch带中的特征，例如消失溶液的消失和形成其他特殊点。固定状态的稳定性是通过Bogoliubov-DE Gennes方程确定的，并显示出强烈影响平均场动力学。值得注意的是，即使远离平均场极限，非线性Bloch频段的稳定性似乎会影响量子动力学。这是两个粒子系统的数值证明。
We theoretically investigate Bloch oscillations in a one-dimensional Bose-Hubbard chain, with single-particle losses from the odd lattice sites described by the Lindblad equation. For a single particle the time evolution of the state is completely determined by a non-Hermitian effective Hamiltonian. We analyse the spectral properties of this Hamiltonian for an infinite lattice and link features of the spectrum to observable dynamical effects, such as frequency doubling in breathing modes. We further consider the case of many particles in the mean-field limit leading to complex nonlinear Schrödinger dynamics. Analytic expressions are derived for the generalised nonlinear stationary states and the nonlinear Bloch bands. The interplay of nonlinearity and particle losses leads to peculiar features in the nonlinear Bloch bands, such as the vanishing of solutions and the formation of additional exceptional points. The stability of the stationary states is determined via the Bogoliubov-de Gennes equation and is shown to strongly influence the mean-field dynamics. Remarkably, even far from the mean-field limit, the stability of the nonlinear Bloch bands appears to affect the quantum dynamics. This is demonstrated numerically for a two-particle system.
