We examine the Goos-Hänchen (G-H) shift of a Gaussian beam reflected on a thin slab of Ag/TiO₂ hyperbolic multilayer metamaterial (HMM). The HMM is modeled using the effective medium theory which yields the anisotropic dielectric functions of the HMM. The G-H shifts can be very large on the surface of the HMM. It can be about 40 µm which are far bigger than the G-H shifts on the usual materials like metals and dielectrics. The enhancement is due to the excitation of the Brewster modes in HMM. Such Brewster modes in HMM have a well-defined frequency-dependent line shape. We relate the the half width at half maximum of the G-H shift to the imaginary part of the complex frequency of the Brewster mode. Moreover, we also present results for the Imbert-Fedorov shifts as well as the spin Hall effect of light on the surface of a thin HMM slab. We show that the spin Hall effect on the HMM slab is much more pronounced than that on the surface of metal. Thus a thin HMM slab can be used to enhance the lateral displacements, which can have many interesting applications for optical devices.

Recently considerable effort is devoted to the realization of the strong coupling regime of the radiation matter interaction in the context of emitter at a meta surface. The strong interaction is well realized in cavity quantum electrodynamics which also shows that the strong coupling is much easier to realize using a collection of emitters. Keeping this in mind we study if emitters on a hyperbolic meta materials can yield strong coupling regime. We show that the strong coupling can be realized for densities of emitters exceeding a critical value. A way to detect the strong coupling between emitters and a hyperbolic metamaterials is to use the Kretschman-Raether configuration.The strong coupling appears as the splitting of the reflectivity dip. In the weak coupling regime the dip position shifts. The shift and splitting can be used to sense active molecules at surfaces.

Topologically protected states are important in realizing robust excitation transfer between distant sites in photonic lattices. Here, we propose an efficient gap-protected transfer of photons in a scalable one-dimensional waveguide array by transporting the topological defect state of a Su–Schrieffer–Heeger model. The separation between neighboring waveguides is designed according to the Jaynes–Cummings model. As a result, the zero-energy eigenstate is topologically protected from the extended states by a constant energy gap, which leads to a fast and robust excitation transfer. We also show that the transport can be further sped up by the quasi-periodic oscillation induced by the non-adiabatic effect. This scheme has potential applications in scalable quantum information processing.

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Cold atoms provide a flexible platform for synthesizing and characterizing topological matter, where geometric phases play a central role. However, cold atoms are intrinsically prone to thermal noise, which can overwhelm the topological response and hamper promised applications. On the other hand, geometric phases also determine the energy spectra of particles subjected to a static force, based on the polarization relation between Wannier-Stark ladders and geometric Zak phases. By exploiting this relation, we develop a method to extract geometric phases from energy spectra of room-temperature superradiance lattices, which are momentum-space lattices of timed Dicke states. In such momentum-space lattices the thermal motion of atoms, instead of being a source of noise, provides effective forces which lead to spectroscopic signatures of the Zak phases. We measure Zak phases directly from the anti-crossings between Wannier-Stark ladders in the Doppler-broadened absorption spectra of superradiance lattices. Our approach paves the way of measuring topological invariants and developing their applications in room-temperature atoms.