Davide Pierangeli

Italian National Research Council | CNR · Institute for Complex Systems ISC

One of the most controversial phenomena in nonlinear dynamics is the reappearance of initial conditions. Celebrated as the Fermi-Pasta-Ulam-Tsingou problem, the attempt to understand how these recurrences form during the complex evolution that leads to equilibrium has deeply influenced the entire development of nonlinear science. The enigma is rend...

Quantum and classical physics can be used for mathematical computations that are hard to tackle by conventional electronics. Very recently, optical Ising machines have been demonstrated for computing the minima of spin Hamiltonians, paving the way to new ultrafast hardware for machine learning. However, the proposed systems are either tricky to sca...

From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, transitions between extreme waves are allowed. However, these have never been experimentally observed because control strategies are still missing. We introduce the new concept of topological control based on the one-to-one correspondence...

Many developments in science and engineering depend on tackling complex optimizations on large scales. The challenge motivates an intense search for specific computing hardware that takes advantage of quantum features, nonlinear dynamics, or photonics. A paradigmatic optimization problem is to find low-energy states in classical spin systems with f...

Modern machine-learning applications require huge artificial networks demanding computational power and memory. Light-based platforms promise ultrafast and energy-efficient hardware, which may help realize next-generation data processing devices. However, current photonic networks are limited by the number of input-output nodes that can be processe...

States of light encoding multiple polarizations - vector beams - offer unique capabilities in metrology and communication. However, their practical application is limited by the lack of methods for measuring many polarizations in a scalable and compact way. Here we demonstrate polarimetry of vector beams in a single shot without any polarization op...

Modern machine learning applications require huge artificial networks demanding in computational power and memory. Light-based platforms promise ultra-fast and energy-efficient hardware, which may help in realizing next-generation data processing devices. However, current photonic networks are limited by the number of input-output nodes that can be...

We experimentally and numerically explore the role of dimensionality in multiple (three or more) soliton fusion supported by nonreciprocal energy exchange. Three-soliton fusion into an intense wave is found when an extra dimension, with no broken inversion symmetry, is involved. The phenomenon is observed for 2+1D spatial waves in photorefractive c...

The race to heuristically solve nondeterministic polynomial-time (NP) problems through efficient methods is ongoing. Recently, optics was demonstrated as a promising tool to find the ground state of a spin-glass Ising Hamiltonian, which represents an archetypal NP problem. However, achieving completely programmable spin couplings in these large-sca...

We propose an all-optical spatial coherent Ising machine with a parametric cavity and spatial light modulator (SLM). We discuss how different SLM configurations realize different couplings, and then study the performance of the proposed machine.

The race to heuristically solve non-deterministic polynomial-time (NP) problems through efficient methods is ongoing. Recently, optics was demonstrated as a promising tool to find the ground state of a spin-glass Ising Hamiltonian, which represents an archetypal NP problem. However, achieving completely programmable spin couplings in these large-sc...

Networks of optical oscillators simulating coupled Ising spins have been recently proposed as a heuristic platform to solve hard optimization problems. These networks, called coherent Ising machines (CIMs), exploit the fact that the collective nonlinear dynamics of coupled oscillators can drive the system close to the global minimum of the classica...

Networks of optical oscillators simulating coupled Ising spins have been recently proposed as a heuristic platform to solve hard optimization problems. These networks, called coherent Ising machines (CIMs), exploit the fact that the collective nonlinear dynamics of coupled oscillators can drive the system close to the global minimum of the classica...

We observe chaotic optical wave dynamics characterized by erratic energy transfer and soliton annihilation and creation in the aftermath of a three-soliton collision in a photorefractive crystal. Irregular dynamics are found to be mediated by the nonlinear Raman effect, a coherent interaction that leads to nonreciprocal soliton energy exchange. Res...

We experimentally demonstrate an optical machine learning scheme that uses spatial dispersive shock waves for performing classification and regression tasks. The non-linear optical device is easy-to-train and reaches accuracies comparable to digital reservoir machines.

Photonic brain-inspired platforms are emerging as novel analog computing devices, enabling fast and energy-efficient operations for machine learning. These artificial neural networks generally require tailored optical elements, such as integrated photonic circuits, engineered diffractive layers, nanophotonic materials, or time-delay schemes, which...

Photonic brain-inspired platforms are emerging as novel analog computing devices, enabling fast and energyefficient operations for machine learning. These artificial neural networks generally require tailored optical elements, such as integrated photonic circuits, engineered diffractive layers, nanophotonic materials, or time-delay schemes, which a...

We perform real-time stereoscopic wide-area imaging of a ferroelectric phase-transition in KTN:Li. Spontaneous polarization is observed to form a thermally hysteretic 3D lattice of mutually interlinked closed-flux patterns that spans the entire sample. Results are compatible with a supercrystal of $N=4$ topological texture defects arising as the th...

We perform percolation analysis of crossed-polarizer transmission images in a biased nanodisordered bulk KTN:Li perovskite. Two distinct percolative transitions are identified at two electric field thresholds. The low-field transition involves a directional fractal chain of dimension D=1.65, while the high-field transition has a dimension D>2. Dire...

We study theoretically neural networks embedding a nonlinear wave as a computing reservoir. We demonstrate interpolation of large datasets and Boolean logic. We discuss the existence of a critical nonlinearity for learning.

Dispersive shock waves in thermal optical media are nonlinear phenomena whose intrinsic irreversibility is described by time asymmetric quantum mechanics. Recent studies demonstrated that the nonlocal wave breaking evolves in an exponentially decaying dynamics ruled by the reversed harmonic oscillator, namely, the simplest irreversible quantum syst...

Dispersive waves (DWs) radiation in optical fibers allow to excite frequencies in spectral regions that are otherwise difficult to access. However, the resonant emission is weak and phase matching inhibits its shaping, making it ineffective in many applications. Here, we numerically investigated that DWs generated from high-energy pulses propagatin...

Combinatorial optimization problems are crucial for widespread applications but remain difficult to solve on a large scale with conventional hardware. Novel optical platforms, known as coherent or photonic Ising machines, are attracting considerable attention as accelerators on optimization tasks formulable as Ising models. Annealing is a well-know...

Nonlinear response in a material increases with its index of refraction as n⁴. Commonly, n~1 so that diffraction, dispersion, and chromatic walk-off limit nonlinear scattering. Ferroelectric crystals with a periodic 3D polarization structure overcome some of these constraints through versatile Cherenkov and quasi-phase-matching mechanisms. Three-di...

Optical neural networks process information at the speed of light and are energetically efficient. Photonic artificial intelligence allows speech recognition, image classification, and Ising machines. Modern machine learning paradigms, as extreme learning machines, reveal that disordered and biological materials may realize optical neural networks...

We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layered model, with an encoding input layer, a wave layer, and a decoding readout, behaves as a conventional neural network in approximati...

Many developments in science and engineering depend on tackling complex optimizations on large scales. The challenge motivates intense search for specific computing hardware that takes advantage from quantum features [1, 2], stochastic elements [3], nonlinear dissipative dynamics [4-8], in-memory operations [9, 10], or photonics [11-14]. A paradigm...

Ising machines are novel computing devices for the energy minimization of Ising models. These combinatorial optimization problems are of paramount importance for science and technology, but remain difficult to tackle on large scale by conventional electronics. Recently, various photonics-based Ising machines demonstrated fast computing of a Ising g...

Combinatorial optimization problems are crucial for widespread applications but remain difficult to solve on a large scale with conventional hardware. Novel optical platforms, known as coherent or photonic Ising machines, are attracting considerable attention as accelerators on optimization tasks formulable as Ising models. Annealing is a well-know...

Novel machine learning computational tools open new perspectives for quantum information systems. Here we adopt the open-source programming library TensorFlow to design multi-level quantum gates, including a computing reservoir represented by a random unitary matrix. In optics, the reservoir is a disordered medium or a multi-modal fiber. We show th...

Ising machines are novel computing devices for the energy minimization of Ising models. These combinatorial optimization problems are of paramount importance for science and technology, but remain difficult to tackle on large scale by conventional electronics. Recently, various photonics-based Ising machines demonstrated ultra-fast computing of Isi...

Diffraction, dispersion, chromatic walk-off, and an index of refraction $n \sim$ 1 impose strong constraints on nonlinear optical processes. Nanodisordered ferroelectric perovskites manifest a super-crystal phase with a giant broadband index of refraction $n \gg 1$. Here nonlinear response is strongly enhanced while all light waves are forced to co...

We demonstrate experimentally in biased photorefractive crystals that collisions between random-amplitude optical spatial solitons produce long-tailed statistics from input Gaussian fluctuations. The effect is mediated by Raman nonlocal corrections to Kerr self-focusing that turn soliton-soliton interaction into a Maxwell demon for the output wave...

We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layer model, with an encoding input layer, a wave layer, and a decoding readout, behaves as a conventional neural network in approximating...

We report the observation of strong nonreciprocal soliton amplification mediated by a Raman-scattering-like effect in single isolated collisions. A pump soliton is found to lose the greater part of its energy to a signal soliton, irrespective of the pump-signal relative amplitude. The result is an efficient rectifying mechanism able to accumulate e...

We investigate the mutual interaction of two spatially-separated Airy beams in the nonlinear Schrödinger equation with the fractional Laplacian. Depending on the beam separation (d), relative phase and Lévy index (α), we observed an anomalous attraction or repulsion between the Airy beams. Anomalous attraction leads to a single breather soliton wit...

Dispersive shock waves in thermal optical media belong to the third-order nonlinear phenomena, whose intrinsic irreversibility is described by time asymmetric quantum mechanics. Recent studies demonstrated that nonlocal wave breaking evolves in an exponentially decaying dynamics ruled by the reversed harmonic oscillator, namely, the simplest irreve...

From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed because of the lack of control strategies. We introduce a new concept of nonlinear wave topological control, bas...

Dispersive shock waves are fascinating phenomena occurring when nonlinearity overwhelms linear effects, such as dispersion and diffraction. Many features of shock waves are still under investigation, as the interplay with noninstantaneity in temporal pulses transmission and nonlocality in spatial beams propagation. Despite the rich and vast literat...

In principle, materials with a broadband giant index of refraction (n > 10) overcome chromatic aberration and shrink the diffraction limit down to the nanoscale, allowing new opportunities for nanoscopic imaging. They also open alternative avenues for the management of light to improve the performance of photovoltaic cells. Recent advances have dem...

Quantum and classical physics can be used for mathematical computations that are hard to tackle by conventional electronics. Very recently, optical Ising machines have been demonstrated for computing the minima of spin Hamiltonians, paving the way to new ultra-fast hardware for machine learning. However, the proposed systems are either tricky to sc...

Novel computational tools in machine learning open new perspectives in quantum information systems. Here we adopt the open-source programming library Tensorflow to design multi-level quantum gates including a computing reservoir represented by a random unitary matrix. In optics, the reservoir is a disordered medium or a multimodal fiber. We show th...

Recently P.G. Grinevich and P.M. Santini suggested simple approximate formulas for solving periodic Cauchy problem for the focusing Nonlnear Schrodinger Equation (NLS) under assumption that one starts from a small perturbation of the unstable condensate and the number of unstable modes is not too large. With the help of these results, optical exper...

Optical fabrication of waveguides in a volume is limited by diffraction in the writing beams. We demonstrate the use of nondiffracting waves in the form of Bessel beams to fabricate scalable optical wiring through direct writing in a photosensitive volume. Experiments are performed in paraelectric potassium-lithium-tantalate-niobate (KLTN), where w...

We propose and experimentally demonstrate the use of spatial light modulation for calculating the ground state of an Ising Hamiltonian. We realize configurations with thousands of interacting spins that settle in a low-temperature ferromagnetic-like phase.

We introduce the topological control, based on correspondences between phases and genus of toroidal surfaces associated with nonlinear Schroedinger equation. We prove it experimentally and report observations of controlled transitions from shock to rogue waves.

We report the observation of more than three Fermi-Pasta-Ulam-Tsingou recurrences in nonlinear optical wave propagation and experimentally demonstrate that the recurrent behavior is governed by the exact solution of the nonlinear Schrodinger integrable dynamics.

We employ living three-dimensional tumour brain models to demonstrate a bio-inspired optical neural network trained via image transmission to detect cancer mor-phodynamics inaccessible by optical imaging.

Dispersive shock waves are fascinating phenomena occurring when nonlinearity overwhelms linear effects, such as dispersion and diffraction. Many features of shock waves are still under investigation, as the interplay with noninstantaneity in temporal pulses transmission and nonlocality in spatial beams propagation. Despite the rich and vast literat...

We investigate Airy-soliton interaction in a nonlinear fiber with Raman effect. We find that Airy solitons may fuse upon interaction at a position that can be controlled by a proper engineering of the Airy tail direction. This control allows us to generate Airy solitons with varying deceleration. At variance with the case of two solitons interactio...

The new era of artificial intelligence demands large-scale ultrafast hardware for machine learning. Optical artificial neural networks process classical and quantum information at the speed of light, and are compatible with silicon technology, but lack scalability and need expensive manufacturing of many computational layers. New paradigms, as rese...

In principle, materials with a broadband giant index of refraction (n > 10) overcome chromatic aberration and shrink the diffraction limit down to the nanoscale, allowing new opportunities for nanoscopic imaging¹. They also open alternative avenues for the management of light to improve the performance of photovoltaic cells². Recent advances have d...

We predict and observe Bessel-beam optical self-trapping in a strongly self-focusing medium. Nonlinearity leads to solutions with a signature pulsing along the propagation direction, a breather that we observe in a photorefractive potassium-lithium-tantalate-niobate crystal. The nonlinear construct is formed as an interference pattern locks togethe...

Solitons and nonlinear waves emit resonant radiation in the presence of perturbations. This effect is relevant for nonlinear fiber optics, supercontinuum generation, rogue waves, and complex nonlinear dynamics. However, resonant radiation is narrowband, and the challenge is finding novel ways to generate and tailor broadband spectra. We theoretical...

We report the observation of replica symmetry breaking in optical wave propagation, a phenomenon that emerges from the interplay of disorder and nonlinearity and demonstrates a spin-glass phase for light.

We have demonstrated experimentally and numerically that a Bessel-Beam propagating in a strongly self-focusing medium undergoes relevant dynamics along the propagation axis that ultimately cause it to self-trap into a periodic breather.

A landmark of statistical mechanics, spin-glass theory describes critical phenomena in disordered systems that range from condensed matter to biophysics and social dynamics. The most fascinating concept is the breaking of replica symmetry: identical copies of the randomly interacting system that manifest completely different dynamics. Replica symme...

In this chapter, we discuss rogue waves emerging as light beams that undergo highly-nonlinear regimes of propagation in photorefractive ferroelectric crystals. The interplay between unstable nonlinear wave dynamics and hosting disorder gives rise to a strong turbulent scenario characterized by localized spatial waves of extreme intensity populating...