论文标题
通过淬灭动力学直接测量拓扑数
Direct Measurement of Topological Number by Quench Dynamics
论文作者
论文摘要
拓扑数的测量对于拓扑系统的研究至关重要。最近，建立了拓扑数和动力学之间的关系。但是，仍然缺乏通过动力学读取拓扑编号的直接方法。在这项工作中，我们提出了一种新的动态协议，以直接测量未知系统的拓扑数。不同于常见的淬火操作，我们将未知系统的哈密顿量更改为具有已知拓扑特性的另一个系统。淬火后，不同的初始状态在淬灭后最终Bloch带上导致不同的粒子数分布。这样的分布取决于初始bloch状态和最终Bloch状态之间的波函数重叠，这是一个复杂的数字，具体取决于动量。我们证明一个定理是，当动量变化$2π$时，波函数重叠的阶段会变化$Δnπ$，其中$Δn$是初始bloch频段和最终Bloch频段之间的拓扑数差异。基于此和最终BLOCH频段的已知拓扑数，我们可以直接从粒子数分布中推断出初始状态的拓扑数，也不需要跟踪系统的演变或测量自旋纹理。还提出了两个实验方案。这些方案提供了一种方便，可靠的测量方法，并加深对拓扑与动态之间关系的理解。
The measurement of topological number is crucial in the research of topological systems. Recently, the relations between the topological number and the dynamics are built. But a direct method to read out the topological number via the dynamics is still lacking. In this work, we propose a new dynamical protocol to directly measure the topological number of an unknown system. Different from common quench operations, we change the Hamiltonian of the unknown system to another one with known topological properties. After the quench, different initial states result in different particle number distributions on the post-quench final Bloch bands. Such distributions depend on the wavefunction overlap between the initial Bloch state and the final Bloch state, which is a complex number depending on the momentum. We prove a theorem that when the momentum varies by $2π$, the phase of the wavefunction overlap change by $Δnπ$ where $Δn$ is the topological number difference between the initial Bloch band and the final Bloch band. Based on this and the known topological number of the final Bloch band, we can directly deduce the topological number of the initial state from the particle number distribution and need not track the evolution of the system nor measure the spin texture. Two experimental schemes are also proposed as well. These schemes provide a convenient and robust measurement method and also deepens the understanding of the relation between topology and dynamics.
