Measuring Hopf links and Hopf invariants in a quenched topological Raman lattice

Jinlong Yu
Phys. Rev. A 99, 043619 – Published 17 April 2019

Abstract

In a recent experimental work [Z. Wu et al., Science 354, 83 (2016)], the PKU-USTC group realized a two-dimensional two-band quantum anomalous Hall model on a square Raman lattice. By quenching the atom-laser detuning of such a Raman lattice, the time-dependent Bloch vectors for each quasimomentum points define a Hopf mapping from quasimomentum-time space (kx,ky,t)T3 to the Bloch sphere S2. The Hopf links between the preimages of any two Bloch vectors on S2 can be measured experimentally through Bloch-state tomography using spin-resolved time-of-flight measurement together with suitable radio-frequency manipulations. The dynamical Hopf invariants, which are quasimomentum-time integrations of Chern-Simons densities, can also be extracted experimentally through certain quench processes. As the Hopf invariant equals the Chern number of the postquench Hamiltonian, the measurements of Hopf links and Hopf invariants provide an alternative way of understanding the topological phase diagram of the equilibrium system.

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  • Received 17 October 2018

DOI:https://doi.org/10.1103/PhysRevA.99.043619

©2019 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

Jinlong Yu

  • Institute for Advanced Study, Tsinghua University, Beijing 100084, China; Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria; and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria

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Vol. 99, Iss. 4 — April 2019

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