Suchergebnisse

The topology of one-dimensional chiral systems is captured by the winding number of the Hamiltonian eigenstates. Here we show that this invariant can be read out by measuring the mean chiral displacement of a single-particle wave function that is connected to a fully localized one via a unitary and translation-invariant map. Remarkably, this implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases. We confirm experimentally these results in a quantum walk of structured light. ; A.D'E., R.B., L.M., and F.C. acknowledge financial support from the European Union Horizon 2020 program, under European Research Council (ERC) Grant No. 694683 (PHOSPhOR). A.D. and M.L. acknowledge financial support from the Spanish Ministry MINECO (National Plan 15 FISICATEAMO Grant No. FIS2016-79508-P and SEVERO OCHOA Grant No. SEV-2015-0522, FPI), European Social Fund, Fundació Cellex, Generalitat de Catalunya (AGAUR Grant No. 2017 SGR 1341 and CERCA/Program), ERC AdG NOQIA, and the National Science Centre, Poland-Symfonia Grant No. 2016/20/W/ST4/00314. A.D. is financed by a Juan de la Cierva fellowship (No. IJCI-2017-33180). P.M. acknowledges support by the "Ramón y Cajal" program and by the Spanish MINECO (Grant No. FIS2017-84114-C2-1-P). A.D., M.L., and P.M. acknowledge support from EU FEDER Quantumcat. ; Postprint (published version)

Quantum walks are powerful tools for quantum applications and for designing topological systems. Although they are simulated in a variety of platforms, genuine two-dimensional realizations are still challenging. Here we present an innovative approach to the photonic simulation of a quantum walk in two dimensions, where walker positions are encoded in the transverse wavevector components of a single light beam. The desired dynamics is obtained by means of a sequence of liquid-crystal devices, which apply polarization-dependent transverse "kicks" to the photons in the beam. We engineer our quantum walk so that it realizes a periodically-driven Chern insulator, and we probe its topological features by detecting the anomalous displacement of the photonic wavepacket under the effect of a constant force. Our compact, versatile platform offers exciting prospects for the photonic simulation of two-dimensional quantum dynamics and topological systems. ; AD'E, FC, RB and LM acknowledge financial support from the European Union Horizon 2020 program, under European Research Council (ERC) grant no. 694683 (PHOSPhOR). ADa, MM, PM and ML acknowledge Spanish MINECO (Severo Ochoa SEV-2015-0522, FisicaTeAMO FIS2016-79508-P, and SWUQM FIS2017- 84114-C2-1-P), the Generalitat de Catalunya (SGR874 and CERCA), the EU (ERC AdG OSYRIS 339106, H2020-FETProAct QUIC 641122), the Fundaci´o Privada Cellex, a Cellex-ICFO-MPQ fellowship, the "Juan de la Cierva" program (IJCI-2017-33180) and the "Ramon y Cajal" program ; Postprint (updated version)