Laboratoire de Physique Théorique

de la Matière Condensée

Topological phases of quantum walks and how they can be detected

Janos Asboth (Wigner Research Centre for Physics & Budapest University, Hungary)

Quantum walks are versatile toy models for periodically driven systems in the nonperturbative regime of low-frequency and high-intensity drive. In this regime, systems can have "hidden" topological invariants: they can host topologically protected edge states even if their effective Hamiltonian is topologically trivial. I will discuss schemes we developed [1,2] to measure the bulk topological invariants, including the "hidden" ones, directly, which also work in the case with spatial disorder, and which have recently been measured in quantum walk experiments[3,4].

[1]: T Rakovszky, JK Asbóth, A Alberti: Detecting topological invariants in chiral symmetric insulators via losses, Phys Rev B 95 (20), 201407

[2]: B Tarasinski, JK Asbóth, JP Dahlhaus: Scattering theory of topological phases in discrete-time quantum walks, Phys Rev A 89 (4), 042327

[3]: Zhan, X., Xiao, L., Bian, Z., Wang, K., Qiu, X., Sanders, B.C., Yi, W. and Xue, P.: Detecting topological invariants in nonunitary discrete-time quantum walks. Phys Rev Lett, 119(13), 130501

[4]: S Barkhofen, T Nitsche, F Elster, L Lorz, A Gábris, I Jex, C Silberhorn: Measuring topological invariants in disordered discrete-time quantum walks, Phys Rev A 96 (3), 033846