EL SOKHEN Rabih : Topological photonics in coupled ber rings

Résumé de thèse :

Periodically driven lattices exhibit a spectrum of modes that is both periodic in space and quasienergy. This phenomenon allows the emergence of bands featuring topological chiral edge states traversing the gap, even while exhibiting trivial Chern indices [1]. Such phases are referred to as anomalous topological phases. In cases where the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the existence of a bulk invariant, known as the winding number. However, recent theoretical works show that 2D lattices subject to periodic discrete step walks result in a richer topological phase diagram, where the existence of chiral edge states does not only depend on the bulk invariant but also on an invariant associated with the specific edge termination. In this work, we experimentally validate this finding and present a simultaneous measurement of both edge states and bulk invariants in anomalous topological phases.

To achieve this, we use a 1D+1 discrete step walks synthetic photonic lattice made of two optical fiber rings, characterized by a minor disparity in length and coupled with a variable beamsplitter (VBS). The time evolution of light pulses in the rings can be mapped into a one-dimensional lattice subject to a coherent step walk. The time step corresponds to each round trip of light in the rings and the split walk can be designed to have a time periodicity of two or four round trips. A second parametric synthetic dimension appears in the system when one of the rings incorporates an external phase modulator (PM), introducing a phase φ to the light pulses [2]. By employing a heterodyne detection technique [3], we measure the eigenvectors, extract the Berry curvature, and deduce the Chern number associated with the bands. Alternating the amplitude of the coupling ratio θ at the beam splitter connecting the two rings between two values θ1 and θ2 at odd and even time steps allow us to construct a phase diagram that includes trivial and anomalous phases with zero Chern number.

Furthermore, we formulate an expression for the winding number and demonstrate that the emergence of edge states is tied to the specific geometrical boundaries. This means that the system can exhibit topological behavior across all values of θ, with the ability to add or remove edge states by setting the beamsplitter to full reflectance at a chosen lattice site. The topological phase in discrete step walks opens a fully new playground to study in different dimensions, with implications still to be understood when spin-orbit coupling, particle interactions, or non-Hermitian effects are considered

[1] M. S. Rudner, N. H. Lindner, E. Berg, and M. Levin, Phys. Rev. X 3, 31005 (2013)

[2] M. Wimmer, H. M. Price, I. Carusotto, and U. Peschel, Nat.Phys. 13, 545 (2017).

[3] C. Lechevalier, C. Evain, P. Suret, F. Copie, A. Amo, and S. Randoux, Commun. Phys. 4, 243 (2021).

Doctorant : EL SOKHEN Rabih

Directeur(s) de thèse : Stéphane RANDOUX, Alberto AMO