Measuring topology from dynamics by obtaining the Chern number from a linking number

• Published in: Nature communications Vol. 10; no. 1; p. 1728
• Main Authors: Tarnowski, Matthias, Ünal, F. Nur, Fläschner, Nick, Rem, Benno S., Eckardt, André, Sengstock, Klaus, Weitenberg, Christof
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 15.04.2019; Nature Publishing Group; Nature Portfolio
• Subjects: 639/624/400/482; 639/766/119/2792/4128; 639/766/483/3926; Equilibrium; Humanities and Social Sciences; multidisciplinary; Optical lattices; Phase diagrams; Physical properties; Quantum theory; Science; Science (multidisciplinary); Topology; Vortices
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-019-09668-y

Integer-valued topological indices, characterizing nonlocal properties of quantum states of matter, are known to directly predict robust physical properties of equilibrium systems. The Chern number, e.g., determines the quantized Hall conductivity of an insulator. Using non-interacting fermionic atoms in a periodically driven optical lattice, here we demonstrate experimentally that the Chern number determines also the far-from-equilibrium dynamics of a quantum system. Extending a respective proposal to Floquet systems, we measure the linking number that characterizes the trajectories of momentum-space vortices emerging after a strong quench. We observe that it directly corresponds to the ground-state Chern number. This one-to-one relation between a dynamical and a static topological index allows us to experimentally map out the phase diagram of our system. Furthermore, we measure the instantaneous Chern number and show that it remains zero under the unitary dynamics. The connection between the topological properties of the ground state and non-equilibrium dynamics remains obscure. Here, Tarnowski et al. define and measure a linking number between static and dynamical vortices, which directly corresponds to the ground-state Chern number.