Ramasesh V V, Flurin E, Rudner M, Siddiqi I, Yao N Y
Department of Physics, University of California, Berkeley California 94720, USA.
Niels Bohr International Academy and Center for Quantum Devices, University of Copenhagen, 2100 Copenhagen, Denmark.
Phys Rev Lett. 2017 Mar 31;118(13):130501. doi: 10.1103/PhysRevLett.118.130501. Epub 2017 Mar 27.
The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a simple time-dependent, Bloch-oscillating quantum walk enables the direct measurement of topological invariants. We consider two classes of one-dimensional quantum walks and connect the global phase imprinted on the walker with its refocusing behavior. By disentangling the dynamical and geometric contributions to this phase, we describe a general strategy to measure the topological invariant in these quantum walks. As an example, we propose an experimental protocol in a circuit QED architecture where a superconducting transmon qubit plays the role of the coin, while the quantum walk takes place in the phase space of a cavity.
单粒子能带结构的拓扑结构在理解众多物理现象中起着基础性作用。受量子行走与这种拓扑能带结构之间联系的启发，我们证明了一种简单的含时布洛赫振荡量子行走能够直接测量拓扑不变量。我们考虑两类一维量子行走，并将施加在行走者上的全局相位与其重聚焦行为联系起来。通过解开对该相位的动力学和几何贡献，我们描述了一种在这些量子行走中测量拓扑不变量的通用策略。作为一个例子，我们提出了一种在电路量子电动力学架构中的实验方案，其中一个超导传输子量子比特充当硬币的角色，而量子行走发生在一个腔的相空间中。
