Memristive cells based on different physical effects, that is, phase change, valence change, and electrochemical processes, are discussed with respect to their potential to overcome the voltage–time dilemma that is crucial for an application in storage devices. Strongly non‐linear switching kinetics are required, spanning more than 15 orders of magnitude in time. Temperature‐driven and field‐driven crystallization, threshold switching, ion migration, as well as redox reactions at interfaces are identified as relevant mechanisms. In phase change materials the combination of a reversible threshold switching and extremely large crystal growth velocities at high voltages enables ultra‐fast resistive switching whereas lower voltages will not be sufficient to overcome the energy barrier for crystallization. In electrochemical cells it depends on the voltage regime, which mechanism is the rate‐determining one for switching. While electro‐crystallization dominates at low voltages, electron transfer in the medium voltage range and a mixture of electron transfer and ion migration at high voltages. In valence change materials, ion migration is found to be accelerated by a combined effect of electric field and local temperature increase due to Joule heating. All discussed types of resistive switches can provide sufficient non‐linearity of switching kinetics for overcoming the voltage time dilemma.

Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated.

The geometric properties of energy bands underlie fascinating phenomena in many systems, including solid-state, ultracold gases and photonics. The local geometric characteristics such as the Berry curvature 1 can be related to global topological invariants such as those classifying the quantum Hall states or topological insulators. Regardless of the band topology, however, any non-zero Berry curvature can have important consequences, such as in the semi-classical evolution of a coherent wavepacket. Here, we experimentally demonstrate that the wavepacket dynamics can be used to directly map out the Berry curvature. To this end, we use optical pulses in two coupled fibre loops to study the discrete time evolution of a wavepacket in a one-dimensional geometric 'charge' pump, where the Berry curvature leads to an anomalous displacement of the wavepacket. This is both the first direct observation of Berry curvature e ects in an optical system, and a proof-ofprinciple demonstration that wavepacket dynamics can serve as a high-resolution tool for mapping out geometric properties.The Berry curvature is a geometrical property of an energy band, which plays a key role in many physical phenomena as it encodes how eigenstates evolve as a local function of parameters 1 . In a twodimensional (2D) quantum Hall system, for example, the integral of the Berry curvature over the 2D Brillouin zone determines the Chern number: a global topological invariant that underlies the quantization of Hall transport for a 2D filled energy band 2 . As first explained by Thouless 3 , there can be an analogous topological quantization of particle transport in a 1D band insulator, when the lattice potential is 'pumped' , that is, is slowly and periodically modulated in time. Also in this case, the geometrical and topological properties are defined for an effective 2D parameter space, but now one spanned by the 1D Bloch momentum and the external periodic pumping parameter.A local non-zero Berry curvature can have striking physical effects in both 2D systems and 1D pumps, regardless of whether the global topological Chern number is non-trivial. In the simplest case, a semi-classical wavepacket moves as a coherent object governed by classical equations of motion with an additional 'anomalous' Hall velocity due to the geometrical Berry curvature at its centre-ofmass, as an external force is applied or as the control parameter is pumped 1,4 . As highlighted further below, this anomalous transport can be understood physically as the Berry curvature acting like a magnetic field in parameter space [5][6][7] .In recent years, there have been many landmark experiments to engineer and study geometrical and topological energy bands in ultracold gases and photonics . In photonics, for example, topological edge states have been studied in a wide variety of (effectively) 1D set-ups, such as quantum walks 14 and pumping in optical quasicrystals 13,29,30 , as well as in 2D quantum Hall-like systems of photonic crystals 9-11 , propagating waveguides 12 and silico...

Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals exhibit unusual properties like secondary emissions and resonant restoration of PT symmetry. In addition, we present a versatile method for reconstructing the real and imaginary components of the band structure by directly monitoring the light evolution during a cycle of these oscillations.

Time-resolved threshold switching characteristics including transient parameters such as delay time and holding voltage are reported for a nanoscale GeTe6 Ovonic threshold switching (OTS) device. The voltage dependence of the threshold switching process has been studied, revealing switching in less than 5 ns in the fastest case. A constant holding voltage is observed for the different voltage pulses applied, which is an indicative for a stable on state in the amorphous phase. In addition, the potential of GeTe6 devices as OTS selectors is validated.