Abstract

Recent technological advances in quantum simulators have proven that synthetic materials are very well suited to study and realise many condensed matter models. However, many of these synthetic systems are characterized by neutral particles that do not couple to real gauge fields. In order to simulate interesting electromagnetic phenomena, such as the topological insulators, or the Landau levels, there is the need for the implementation of artificial gauge fields. In particular, the topological insulators are very interesting both from the point of view of fundamental physics and concrete applications. They are bulk insulating materials that carry a certain number of edge states which are topologically protected against small perturbations of the system. An example of a topological insulator is the integer quantum Hall effect. While there have been many works studying topological physics with quantum artificial systems, little attention was dedicated to the interplay of topology and the purely classical world. Only in the last couple of years, pioneering efforts to encode a non-trivial topology in the dynamical matrix or into the Hamiltonian of a system have proven that the hallmarks of a topological insulator are not the prerogative of quantum mechanics, but can be also observed with a classical system governed by Newton’s equations. The first part of this thesis is therefore based on our studies dedicated to the implementation of a classical analogue of the integer quantum Hall system, by realizing the Harper-Hofstadter model for classical frequency-modulated coupled harmonic oscillators. The achievement of an artificial gauge field allows also for the deeper study of magnetic effects such as Landau levels. In graphene, an inhomogeneous strain of the lattice is equivalent to an artificial pseudo-magnetic field, and the low-energy spectrum shows the formation of relativistic pseudo-Landau levels. The second part of the thesis is therefore focussed on the photonics honeycomb lattice geometry and our theoretical proposal for a configuration based on an intrinsically driven-dissipative system in which to probe the physics of the Landau levels, and especially the spatial structure of their wavefunctions. Finally, we have also studied spin-orbit coupling in a mechanical system of masses and springs induced by pre-tensioned springs that split the longitudinal and transverse couplings in the honeycomb geometry. We have presented the experimental results of a simple mechanical benzene composed of six pendula connected with pre-tensioned springs, to verify that the eigenmodes of this system are well described by our theory in the presence of spin-orbit coupling.