Simon Stützer

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.

Observation of supersymmetric scattering in photonic lattices

Supersymmetric (SUSY) optical structures display a number of intriguing properties that can lead to a variety of potential applications, ranging from perfect global phase matching to highly efficient mode conversion and novel multiplexing schemes. Here, we experimentally investigate the scattering characteristics of SUSY photonic lattices. We directly observe the light dynamics in such systems and compare the reflection/transmission properties of SUSY partner structures. In doing so, we demonstrate that discrete settings constitute a promising testbed for studying the different facets of optical supersymmetry.

Experimental observation of superdiffusive transport in random dimer lattices

We experimentally observe anomalous wavepacket evolution in a realization of a one-dimensional finite binary Anderson model in the presence of short-range correlations. To this end, we employ weakly-coupled optical waveguides with propagation constants e1 and e2. The correlations enforce the creation of dimers, i.e. two adjacent waveguides with the same e, randomly placed along the lattice. A transition from a ballistic to a superdiffusive wavepacket expansion and, eventually, to localization is observed as the contrast between the two propagation constants increases.

Anderson cross-localization

We report Anderson localization in two-dimensional optical waveguide arrays with disorder in waveguide separation introduced along one axis of the array, in an uncorrelated fashion for each waveguide row. We show that the anisotropic nature of such disorder induces a strong localization along both array axes. The degree of localization in the cross-axis remains weaker than that in the direction in which disorder is introduced. This effect is illustrated both theoretically and experimentally.

Optical simulation of charge conservation violation and Majorana dynamics

Unphysical solutions are ruled out in physical equations, as they lead to behavior that violates fundamental physical laws. One of the celebrated equations that allows unphysical solutions is the relativistic Majorana equation, thought to describe neutrinos and other exotic particles predicted in theories beyond the standard model. The neutrally charged Majorana fermion is the equation’s physical solution, whereas the charged version is, due to charge nonconservation, unphysical and cannot exist. Here, we present an experimental scheme simulating the dynamics of a charged Majorana particle by light propagation in a tailored waveguide chip. Specifically, we simulate the free-particle evolution as well as the unphysical operation of charge conjugation. We do this by exploiting the fact that the wave function is not a directly observable physical quantity and by decomposing the unphysical solution to observable entities. Our results illustrate the potential of investigating theories beyond the standard model in a compact laboratory setting.

Hybrid Bloch-Anderson localization of light.

We investigate the interplay of two qualitatively different localization mechanisms: Bloch oscillations and Anderson localization in a system of weakly-coupled optical waveguides.

Enhanced distribution of a wave-packet in lattices with disorder and nonlinearity

We show, numerically and experimentally, that the presence of weak disorder results in an enhanced energy distribution of an initially localized wave-packet, in one- and two-dimensional finite lattices. The addition of a focusing nonlinearity facilitates the spreading effect even further by increasing the wave-packet effective size. We find a clear transition between the regions of enhanced spreading (weak disorder) and localization (strong disorder).

Anderson localization in a periodic photonic lattice with a disordered boundary

We investigate experimentally the light evolution inside a two-dimensional finite periodic array of weakly coupled optical waveguides with a disordered boundary. For a completely localized initial condition away from the surface, we find that the disordered boundary induces an asymptotic localization in the bulk, centered around the initial position of the input beam.

Superballistic growth of the variance of optical wave packets.

We experimentally demonstrate that hybrid ordered-disordered photonic lattices can generate faster than the ballistic growth of the second moment of a spreading wave packet for parametrically large time intervals.

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.