A random walk is a stochastic process in which particles or waves travel along random trajectories. The first application of a random walk was in the description of particle motion in a fluid (brownian motion); now it is a central concept in statistical physics, describing transport phenomena such as heat, sound and light diffusion. Lévy flights are a particular class of generalized random walk in which the step lengths during the walk are described by a 'heavy-tailed' probability distribution. They can describe all stochastic processes that are scale invariant. Lévy flights have accordingly turned out to be applicable to a diverse range of fields, describing animal foraging patterns, the distribution of human travel and even some aspects of earthquake behaviour. Transport based on Lévy flights has been extensively studied numerically, but experimental work has been limited and, to date, it has not seemed possible to observe and study Lévy transport in actual materials. For example, experimental work on heat, sound, and light diffusion is generally limited to normal, brownian, diffusion. Here we show that it is possible to engineer an optical material in which light waves perform a Lévy flight. The key parameters that determine the transport behaviour can be easily tuned, making this an ideal experimental system in which to study Lévy flights in a controlled way. The development of a material in which the diffusive transport of light is governed by Lévy statistics might even permit the development of new optical functionalities that go beyond normal light diffusion.

Controlling long-distance quantum correlations is central to quantum computation and simulation. In quantum dot arrays, experiments so far rely on nearest-neighbour couplings only, and inducing long-distance correlations requires sequential local operations. Here, we show that two distant sites can be tunnel-coupled directly. The coupling is mediated by virtual occupation of an intermediate site, with a strength that is controlled via the energy detuning of this site. It permits a single charge to oscillate coherently between the outer sites of a triple dot array without passing through the middle, as demonstrated through the observation of Landau-Zener-Stückelberg interference. The long-distance coupling significantly improves the prospects of fault-tolerant quantum computation using quantum dot arrays, and opens up new avenues for performing quantum simulations in nanoscale devices.

The ability to mold the flow of light at the wavelength scale has been largely investigated in photonic-crystal-based devices, a class of materials in which the propagation of light is driven by interferences between multiply Bragg scattered waves and whose energy dispersion is described by a photonic band diagram [1]. Light propagation in such structures is defined by Bloch modes, which can be engineered by varying the structural parameters of the material [2][3][4]. In disordered media, both the direction and phase of the propagating waves are randomized in a complex manner, making any attempt to control light propagation particularly challenging. Disordered media are currently investigated in several contexts, ranging from the study of collective multiple scattering phenomena [5,6] to cavity quantum electrodynamics and random lasing [7,8], to the possibility to provide efficient solutions in renewable energy [9], imaging [10], and spectroscopy-based applications [11]. Transport in such systems can be described in terms of photonic modes, or quasi-modes, which exhibit characteristic spatial profiles and spectra [12,13]. In diffusive systems, these modes are spatially and spectrally overlapping while in the regime of Anderson localization, they become spatially and spectrally-isolated [14]. Unlike Bloch modes in periodic systems, the precise formation of photonic modes in a single realization of the disorder is unpredictable.Control over light transport can be obtained by shaping the incident wave to excite only a specific part of the modes available in a given system [15][16][17][18]. For fully exploiting the potential of disordered systems, however, a mode control is needed. It was shown 3 theoretically that isolated modes could be selectively tuned and possibly coupled to each other by a local fine modification of the dielectric structure [19,20].In this Article, we demonstrate experimentally the ability to fully control the spectral properties of an individual photonic mode in a two-dimensional disordered photonic structure [21], in a wavelength range that is relevant for photonic research driven applications. A statistical analysis of individual spatially-isolated random photonic modes is performed by multi-dimensional near-field imaging, leading to a detailed determination of intensity fluctuations, decay lengths and mode volumes. We then demonstrate that individual modes can be fine-tuned either by near-field tip perturbation or by local sub-micrometer-scale oxidation of the semiconductor slab [22]. The resonant frequency of a selected mode is gradually shifted until it is in perfect spectral superposition with the frequency of other two modes, located a few micrometers apart and spatially overlapping with the tuned mode. On spectral resonance, we observe frequency crossing and anti-crossing behaviours, respectively, the latter indicating mode interaction. This provides the experimental proof-of- (e) and (f), respectively). The main difference between the two spectra normalized to the average intensity i...