Simulation of time-periodic and topological tight-binding systems with plasmonic waveguide arrays

Abstract

Floquet engineering, the control by external time-periodic forcing, is a powerful tool to manipulate different quantum systems. The underlying principle is that driving a system periodically with frequency w induces hybridization of the eigenstates of a static system separated in energy by a multiple of hw. By choosing a proper driving scheme one can thus take an advantage of this hybridization to create new synthetically designed properties, that would be inaccessible in equilibrium.<br /> In this thesis Floquet engineering is utilized to tailor topological and transport properties of surface plasmon polaritons propagating in arrays of coupled waveguides. Evanescently coupled waveguides is a widely used experimental platform to study various coherent quantum phenomena encountered in atomic and condensed matter physics. Such experiments are based on the mathematical analogy between the paraxial Helmholtz equation for the electromagnetic field propagating in arrays of coupled waveguides and the Schrödinger equation that describes temporal evolution of a single particle wavefunction in tight-binding atomic lattices. Within this quantum-optical analogy the time axis of a quantum system is directly mapped into the propagation distance of surface plasmon polaritons. Therefore, periodically modulating the waveguide geometry along the propagation distance enables us to mimic the effect of external time-periodic field.<br /> Under the scope of this thesis we investigate three periodically-driven one-dimensional tight-binding systems that illuminate different applications of the Floquet engineering. In order to make predictions about the dynamics of each system we perform numerical calculations based on the Floquet theory. The obtained theoretical findings are used to design the plasmonic structures, which are then fabricated by negative-tone electron beam lithography. The propagation of surface plasmon polaritons in the fabricated samples is monitored by real- and Fourier space leakage radiation microscopy.<br /> As the first system, we consider a one-dimensional prototype of a topological insulator described by the Su-Schriefer-Heeger model. This model supports two topologically distinct phases that, when interfaced, give rise to a topologically protected edge state localized at the boundary. This is the manifestation of the so-called bulk boundary correspondence principle. The question we address here is what happens with the topological edge state if the boundary between the two phases is subject to local time-periodic perturbations while the bulk is kept static?<br /> In the second project we deal with the topological transport quantization that emerges in the slowly driven Rice-Mele model. This phenomenon, known as the Thouless pumping, breaks down at the non-adiabatic conditions, which is the major limitation for the experimental realization of this effect. The reason is that finite driving frequencies induce coupling between the forward and backward propagating Floquet states. As a result, the system becomes topologically trivial and the transport deviates from perfect quantization. We are aimed to show that using sufficiently strong time-periodic losses the Thouless pumping can be restored at an arbitrary large driving frequency.<br /> Inspired by the previously obtained results, in the third part of this thesis we demonstrate another application of time-periodic losses. In contrast to the previous example where losses were applied globally, here, they are confined only to the few lattice sites and serve as a directional filter for a Hamiltonian, i.e. lossless, quantum ratchet. Ratchet is a system where broken space and time inversion symmetry gives rise to a directional transport without a bias force. As a ratchet system we consider a periodically-driven Su-Schrieffer-Heeger model, which for certain resonant driving frequencies supports directional current once the relevant symmetries are broken by initial conditions. On the example of this system we want to show that properly chosen time-periodic losses can transmit the current in one direction but strongly suppress it in the opposite direction.