Steffen Weimann

Observation of Localized States in Lieb Photonic Lattices.

We present the first experimental demonstration of a new type of localized state in the continuum, namely, compacton-like linear states in flat-band lattices. To this end, we employ photonic Lieb lattices, which exhibit three tight-binding bands, with one being perfectly flat. Discrete predictions are confirmed by realistic continuous numerical simulations as well as by direct experiments. Our results could be of great importance for fundamental physics as well as for various applications where light needs to be conducted in a diffractionless and localized manner over long distances.

Topologically protected bound states in photonic parity–time-symmetric crystals

Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.

Experimental observation of bulk and edge transport in photonic Lieb lattices

We analyze the transport of light in the bulk and at the edge of photonic Lieb lattices, whose unique feature is the existence of a flat band representing stationary states in the middle of the band structure that can form localized bulk states. We find that transport in bulk Lieb lattices is significantly affected by the particular excitation site within the unit cell, due to overlap with the flat band states. Additionally, we demonstrate the existence of new edge states in anisotropic Lieb lattices. These states arise due to a virtual defect at the lattice edges and are not described by the standard tight-binding model.

Compact surface Fano states embedded in the continuum of waveguide arrays.

We describe theoretically and observe experimentally the formation of a surface state in a semi-infinite waveguide array with a side-coupled waveguide, designed to simultaneously achieve Fano and Fabry-Perot resonances. We demonstrate that the surface mode is compact, with all energy concentrated in a few waveguides at the edge and no field penetration beyond the side-coupled waveguide position. Furthermore, we show that by broadening the spectral band in the rest of the waveguide array it is possible to suppress exponentially localized modes, while the Fano state having the eigenvalue embedded in the continuum is preserved.

Mobility transition from ballistic to diffusive transport in non-Hermitian lattices

Within all physical disciplines, it is accepted that wave transport is predetermined by the existence of disorder. In this vein, it is known that ballistic transport is possible only when a structure is ordered, and that disorder is crucial for diffusion or (Anderson-)localization to occur. As this commonly accepted picture is based on the very foundations of quantum mechanics where Hermiticity of the Hamiltonian is naturally assumed, the question arises whether these concepts of transport hold true within the more general context of non-Hermitian systems. Here we demonstrate theoretically and experimentally that in ordered time-independent -symmetric systems, which are symmetric under space-time reflection, wave transport can undergo a sudden change from ballistic to diffusive after a specific point in time. This transition as well as the diffusive transport in general is impossible in Hermitian systems in the absence of disorder. In contrast, we find that this transition depends only on the degree of dissipation.

Implementation of quantum and classical discrete fractional Fourier transforms

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

Impact of loss on the wave dynamics in photonic waveguide lattices.

We analyze the impact of loss in lattices of coupled optical waveguides and find that, in such a case, the hopping between adjacent waveguides is necessarily complex. This results not only in a transition of the light spreading from ballistic to diffusive, but also in a new kind of diffraction that is caused by loss dispersion. We prove our theoretical results with experimental observations.

Transport in Sawtooth photonic lattices.

We investigate, theoretically and experimentally, a photonic realization of a Sawtooth lattice. This special lattice exhibits two spectral bands, with one of them experiencing a complete collapse to a highly degenerate flat band for a special set of inter-site coupling constants. We report the observation of different transport regimes, including strong transport inhibition due to the appearance of the non-diffractive flat band. Moreover, we excite localized Shockley surface states residing in the gap between the two linear bands.

Radiation-loss management in modulated waveguides

In this work, we discuss the management of radiation loss in photonic waveguides. As an experimental basis, we introduce a new technique of fabricating waveguides with tunable loss, which is particularly useful when implementing non-Hermitian (PT-symmetric) systems. To this end, we employ laser-written waveguides with a transverse sinusoidal modulation, which causes well-controllable radiation losses of almost arbitrary amount. Numerical simulations support our experimental findings. Our study shows that the radiation loss not only depends on the local waveguide curvature but also is influenced by interference effects. As a consequence, the loss is a nonmonotonous function of the bending parameters, such as period length.

Measuring the Aharonov-Anandan phase in multiport photonic systems.

Beyond the adiabatic limit, the Aharonov-Anandan phase is a generalized description of Berrys phase. In this regime, systems with time-independent Hamiltonians may also acquire observable geometric phases. Here we report on a measurement of the Aharonov-Anandan phase in photonics. Different from previous optical experiments on geometric phases, the implementation is based on light modes confined in evanescently coupled waveguides rather than polarization-like systems, thereby physical models in more than two-dimensional Hilbert spaces are achievable. In a tailored photonic lattice, we realize time-independent quantum-driven harmonic oscillators initially prepared in the vacuum state and achieve a measurement of the Aharonov-Anandan phase via integrated interferometry.