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Theories on the bosonic nature of dark matter are a promising alternative to the cold dark matter model. Here we consider a dark matter halo in the state of a Bose-Einstein condensate, subject to the gravitation of a black hole. In the low energy limit, we bring together the general relativity in the Schwarzschild metric and the quantum description of the Bose-Einstein condensate. The model is solvable in the Fermi normal coordinates with the so called highly nonlocal approximation and describes tidal deformations in the condensate wave function. The black hole deforms the localized condensate until the attraction of the compact object overcomes the self-gravitation and destabilizes the solitonic dark matter. Moreover, the model can be implemented as a gravitational analog in the laboratory; the time-dependent potential generated by the galactic black hole can be mimicked by an optical trap acting on a conventional condensate. The results open the way to new laboratory simulators for quantum gravitational effects.

In this work, we present a method to characterise the transmission matrices of complex scattering media using a physics-informed, multi-plane neural network (MPNN) without the requirement of a known optical reference field. We use this method to accurately measure the transmission matrix of a commercial multi-mode fiber without the problems of output-phase ambiguity and dark spots, leading to upto 58% improvement in focusing efficiency compared with phase-stepping holography. We demonstrate how our method is significantly more noise-robust than phase-stepping holography and show how it can be generalised to characterise a cascade of transmission matrices, allowing one to control the propagation of light between independent scattering media. This work presents an essential tool for accurate light control through complex media, with applications ranging from classical optical networks, biomedical imaging, to quantum information processing.

In this chapter we report on the measurements of the overlap distribution of the replica symmetry breaking solution in complex disordered systems. After a general introduction to the problem of the experimental validation of the Parisi order parameter, we focus on the systems where the measurement has been possible for the first time: random lasers. Starting from first principles of light-matter interaction we sketch the main steps leading to the construction of the statistical mechanical model for the dynamics of light modes in a random laser, a spherical multi-p-spin model with complex spins. A new overlap is introduced, the intensity fluctuation overlap, whose probability distribution, under specific assumptions, is equivalent to the Parisi overlap distribution. The experimental protocol for measuring this overlap is based on the possibility of experimentally realizing real replicas. After a description of the first experiment on the random laser made of T5CO$_x$ grains we review and discuss various experiments measuring the overlap distribution, as well as the possible connection with Levy-like distribution of the intensity of the light modes around the laser threshold, the connection with turbulence in fiber lasers and the role of spatial etherogeneities of light modes in random media., Comment: Contribution to the edited volume "Spin Glass Theory and Far Beyond - Replica Symmetry Breaking after 40 years", World Scientific. 30 pages, 16 figures

Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional self-localized solitary waves, are marginally explored for what concerns quantum features. We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schroedinger-Newton equation. We theoretically investigate the quantum diffusion of the soliton center of mass and other parameters, varying the interaction length. 3D+1 simulations of the Ito partial differential equations arising from the positive P-representation of the density matrix validate the theoretical analysis. The numerical results unveil the onset of non-Gaussian statistics of the soliton, which may signal quantum-gravitational effects and be a resource for quantum computing. The non-Gaussianity arises from the interplay between the soliton parameter quantum diffusion and stable invariant propagation. The fluctuations and the non-Gaussianity are universal effects expected for any nonlocality and dimensionality., Second revised and extended version, 14 pages, 3 figures

The ability to create and manipulate strongly correlated quantum many-body states is of central importance to the study of collective phenomena in several condensed-matter systems. In the last decades, a great amount of work has been focused on ultracold atoms in optical lattices, which provide a flexible platform to simulate peculiar phases of matter both for fermionic and bosonic particles. The recent experimental demonstration of Bose-Einstein condensation (BEC) of light in dye-filled microcavities has opened the intriguing possibility to build photonic simulators of solid-state systems, with potential advantages over their atomic counterpart. A distinctive feature of photon BEC is the thermo-optical nature of the effective photon-photon interaction, which is intrinsically nonlocal and can thus induce interactions of arbitrary range. This offers the opportunity to systematically study the collective behaviour of many-body systems with tunable interaction range. In this paper, we theoretically study the effect of nonlocal interactions in photon BEC. We first present numerical results of BEC in a double-well potential, and then extend our analysis to a short one-dimensional lattice with open boundaries. By resorting to a numerical procedure inspired by the Newton-Raphson method, we simulate the time-independent Gross-Pitaevskii equation and provide evidence of surface localization induced by nonlocality, where the condensate density is localized at the boundaries of the potential. Our work paves the way towards the realization of synthetic matter with photons, where the interplay between long-range interactions and low dimensionality can lead to the emergence of unexplored nontrivial collective phenomena., 13 pages, 6 figures. Updated version after publication in Phys. Rev. A

We propose a straightforward and effective approach to design, by strain-engineering, photonic topological insulators supporting high quality factors edge states. Chiral strain-engineering creates opposite synthetic gauge fields in two domains resulting in Landau levels with the same energy spacing but different topological numbers. The boundary of the two topological domains hosts robust time-reversal and spin-momentum-locked edge states, exhibiting high quality factors due to continuous strain modulation. By shaping the synthetic gauge field, we obtain a remarkable field confinement and tunability, with the strain strongly affecting the degree of localization of the edge states. Notably the two-domain design stabilizes the strain-induced topological edge state. The large potential bandwidth of the strain-engineering and the opportunity to induce the mechanical stress at the fabrication stage enables large scalability for many potential applications in photonics, such as tunable microcavities, new lasers and information processing devices, including the quantum regime., 31 pages, 10 figures

In the context of quantum information, highly nonlinear regimes, such as those supporting solitons, are marginally investigated. We miss general methods for quantum solitons, although they can act as entanglement generators or as self-organized quantum processors. We develop a computational approach that uses a neural network as a variational ansatz for quantum solitons in an array of waveguides. By training the resulting phase-space quantum machine learning model, we find different soliton solutions varying the number of particles and interaction strength. We consider Gaussian states that enable measuring the degree of entanglement and sampling the probability distribution of many-particle events. We also determine the probability of generating particle pairs and unveil that soliton bound states emit correlated pairs. These results may have a role in boson sampling with nonlinear systems and in quantum processors for entangled nonlinear waves., Comment: Minor changes. 21 figures and 20 pages

We use neural networks to represent the characteristic function of many-body Gaussian states in the quantum phase space. By a pullback mechanism, we model transformations due to unitary operators as linear layers that can be cascaded to simulate complex multi-particle processes. We use the layered neural networks for non-classical light propagation in random interferometers, and compute boson pattern probabilities by automatic differentiation. We also demonstrate that multi-particle events in Gaussian boson sampling can be optimized by a proper design and training of the neural network weights. The results are potentially useful to the creation of new sources and complex circuits for quantum technologies., Comment: Extended version, with correct figure 4, code available in github

Spin and angular momenta of light are important degrees of freedom in nanophotonics which control light propagation, optical forces and information encoding. Typically, optical angular momentum is generated using q-plates or spatial light modulators. Here, we show that graphene-supported plasmonic nanostructures with broken rotational symmetry provide a surprising spin to orbital angular momentum conversion, which can be continuously controlled by changing the electrochemical potential of graphene. Upon resonant illumination by a circularly polarized plane wave, a polygonal array of indium-tin-oxide nanoparticles on a graphene sheet generates scattered field carrying electrically-tunable orbital angular momentum. This unique photonic spin-orbit coupling occurs due to the strong coupling of graphene plasmon polaritons and localised surface plasmons of the nanoparticles and leads to the controlled directional excitation of graphene plasmons. The tuneable spin-orbit conversion pave the way to high-rate information encoding in optical communications, electric steering functionalities in optical tweezers, and nanorouting of higher-dimensional entangled photon states.

By considering a cigar-shaped trapping potential elongated in a proper curvilinear coordinate, we discover a new form of wave localization which arises from the interplay of geometry and topological protection. The potential is modulated in its shape such that local curvature introduces a trapping potential. The curvature varies along the trap curvilinear axis encodes a topological Harper modulation. The varying geometry maps our system in a one-dimensional Andre-Aubry-Harper grating. We show that a mobility edge exists and topologically protected states arises. These states are extremely robust with respect to disorder in shape of the string. The results may be relevant for localization phenomena in Bose-Einstein condensates, optical fibers and waveguides, and new laser devices, but also for fundamental studies on string theory. Taking into account that the one-dimensional modulation mimic the existence of a additional dimensions, our system is the first example of physically realizable five-dimensional string., 10 pages, 6 figures

In any form of wave propagation, strong spatiotemporal coupling appears when non-elementary, three-dimensional wave-packets are composed by superimposing pure plane waves, or spontaneously generated by light-matter interaction and nonlinear processes. Ultrashort pulses with orbital angular momentum (OAM), or ultrashort vortices, furnish a critical paradigm in which the analysis of the spatiotemporal coupling in the form of temporal-OAM coupling can be carried out accurately by analytical tools. By generalizing and unifying previously reported results, we show that universal and spatially heterogeneous space-time correlations occur in propagation-invariant temporal pulses carrying OAM. In regions with high intensity, the pulse duration has a lower bound fixed by the topological charge of the vortex and such that the duration must increase with the topological charge. In regions with low intensity in the vicinity of the vortex, a large blue-shift of the carrier oscillations and an increase of the number of them is predicted for strongly twisted beams. We think that these very general findings highlight the existence of a structural coupling between space and time. These results have also applications in free-space communications, spectroscopy, and high-harmonic generation., Comment: 6 figures, 8 pages

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 that trainable operators at the input and the readout enable one to realize multi-level gates. We study various qudit gates, including the scaling properties of the algorithms with the size of the reservoir. Despite an initial low slop learning stage, TensorFlow turns out to be an extremely versatile resource for designing gates with complex media, including different models that use spatial light modulators with quantized modulation levels., Comment: Added a new section and a new figure about implementation of the gates by a single spatial light modulator. 9 pages and 4 figures

Modified uncertainty principle and non-commutative variables may phenomenologically account for quantum gravity effects, independently of the considered theory of quantum gravity. We show that quantum fluids enable experimental analogs and direct tests of the modified uncertainty principle expected to be valid at the Planck scale. We consider a quantum clock realized by a long-lasting quantum fluid wave-packet orbiting in a trapping potential. We investigate the hydrodynamics of the Schr\"odinger equation encompassing kinetic terms due to Planck-scale effects. We study the resulting generalized mechanics and validate the predictions by quantum simulations. Wave-packet orbiting generates a continuous amplification of the quantum gravity effects. The non-commutative variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is strongly resembling the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton's theory. In our case, the corrections are due to the modified uncertainty principle. The results can be employed to emulate quantum gravity in the laboratory, or to realize human-scale experiments to determine bounds for the most studied quantum-gravity models and probe Planckian physics., Comment: 7 pages, 4 figures, revised version with suggested experiments

We explore the nonlinear response of plasmonic materials driven by ultrashort pulses of electromagnetic radiation with temporal duration of few femtoseconds and high peak intensity. By developing the Fokker-Planck-Landau theory of electron collisions, we solve analytically the collisional integral and derive a novel set of hydrodynamical equations accounting for plasma dynamics at ultrashort time scales. While in the limit of small light intensities we recover the well established Drude model of plasmas, in the high intensity limit we observe nonlinear quenching of collision-induced damping leading to absorption saturation. Our results provide a general background to understand electron dynamics in plasmonic materials with promising photonic applications in the manipulation of plasma waves with reduced absorption at the femtosecond time scale.

A dynamical system defined by a metriplectic structure is a dissipative model characterized by a specific pair of tensors, which defines the Leibniz brackets. Generally, these tensors are Poisson brackets tensor and a symmetric metric tensor that models purely dissipative dynamics. In this paper, the metriplectic system describing a simplified two-photon absorption by a two-level atom is disclosed. The Hamiltonian component describes the free electromagnetic radiation. The metric component encodes the radiation-matter coupling, driving the system to an asymptotically stable state in which the excited level of the atom is populated due to absorption. This work is intended as a first result to pave the way to apply the metriplectic formalism to many other irreversible processes in nonlinear optics., Comment: 7 pages, 1 figure

Many theories of quantum gravity, as string theory, loop quantum gravity, and doubly special relativity, predict the existence of a minimal length scale and outline the need to generalize the uncertainty principle. This generalized uncertainty principle relies on modified commutation relations that - if applied to the second quantization - imply an excess energy of the electromagnetic quanta with respect to $\hbar \omega$. Here we show that this "dark energy of the photon" is amplified during nonlinear optical process. Therefore, if one accepts the minimal length scenario, one must expect to observe specific optical frequencies in optical harmonic generation by intense laser fields. Other processes as four-wave mixing and supercontinuum generation may also contain similar spectral features of quantum-gravity. Nonlinear optics may hence be helpful to falsify some of the most investigated approaches to the unification of quantum mechanics and general relativity., Comment: 12 pages, 1 figure, updated references

Rainbow gravity modifies general relativity by introducing an energy dependent metric, which is expected to have a role in the quantum theory of black holes and in quantum gravity at Planck energy scale. We show that rainbow gravity can be simulated in the laboratory by nonlinear waves in nonlocal media, as those occurring in Bose-condensed gases and nonlinear optics. We reveal that at a classical level, a nonlocal nonlinear Schr\"odinger equation may emulate the curved space time in proximity of a rotating black hole as dictated by the rainbow gravity scenario. We also demonstrate that a fully quantized analysis is possible. By the positive $\mathcal{P}$-representation, we study superradiance and show that the instability of a black-hole and the existence of an event horizon are inhibited by an energy dependent metric. Our results open the way to a number of fascinating experimental tests of quantum gravity theories and quantum field theory in curved manifolds, and also demonstrate that these theories may be novel tools for open problems in nonlinear quantum physics., Comment: 8 pages, 4 figures

We have very little experience of the quantum dynamics of the ubiquitous nonlinear waves. Observed phenomena in high energy physics are perturbations to linear waves, and classical nonlinear waves, like solitons, are barely affected by quantum effects. We know that solitons, immutable in classical physics, exhibit collapse and revivals according to quantum mechanics. However this effect is very weak and has never been observed experimentally. By predicting black hole evaporation Hawking first introduced a distinctly quantum effect in nonlinear gravitational physics.Here we show the existence of a general and universal quantum process whereby a soliton emits quantum radiation with a specific frequency content, and a temperature given by the number of quanta, the soliton Schwarzschild radius, and the amount of nonlinearity, in a precise and surprisingly simple way. This result may ultimately lead to the first experimental evidence of genuine quantum black hole evaporation. In addition, our results show that black hole radiation occurs in a fully quantised theory, at variance with the common approach based on quantum field theory in a curved background; this may provide insights into quantum gravity theories. Our findings also have relevance to the entire field of nonlinear waves, including cold atomic gases and extreme phenomena such as shocks and rogue-waves. Finally, the predicted effect may potentially be exploited for novel tunable quantum light sources., 5 pages, 3 figures, minor changes to text and references

The use of virtually lossless topologically isolated edge states may lead to a novel class of thresholdless lasers operating without inversion. One needs however to understand if topological states may be coupled to external radiation and act as active cavities. We study a two-level topological insulator and show that self-induced transparency pulses can directly excite edge states. We simulate laser emission by a suitable designed topological cavity, and show that it can emit tunable radiation. For a configuration of sites following the off-diagonal Aubry-Andre-Harper model we solve the Maxwell-Bloch equations in the time domain and provide a first principle confirmation of topological lasers. Our results open the road to a new class of light emitters with topological protection for applications ranging from low-cost energetically-effective integrated lasers sources, also including silicon photonics, to strong coupling devices for studying ultrafast quantum processes with engineered vacuum.

The description of shock waves beyond the shock point is a challenge in nonlinear physics. Finding solutions to the global dynamics of dispersive shock waves is not always possible due to the lack of integrability. Here we propose a new method based on the eigenstates (Gamow vectors) of a reversed harmonic oscillator in a rigged Hilbert space. These vectors allow analytical formulation for the development of undular bores of shock waves in a nonlinear nonlocal medium. Experiments by a photothermal induced nonlinearity confirm theoretical predictions: as the undulation period as a function of power and the characteristic quantized decays of Gamow vectors. Our results demonstrate that Gamow vector are a novel and effective paradigm for describing extreme nonlinear phenomena., 5 pages, 3 figures

We present a theoretical analysis for the \GH and \IF shifts experienced by an X-wave upon reflection from a dielectric interface. We show that the temporal chirp, as well as the bandwidth of the X-wave directly affect the spatial shifts in a way that can be experimentally observed, while the angular shifts do not depend on the spectral features of the X-Wave. A dependence of the spatial shifts on the spatial structure of the X-wave is also discussed.

We investigate the dynamics of a Bose-Einstein condensate in a progressively bended three dimensional cigar shaped potential. The interplay between geometry and nonlinearity is considered. At high curvature, topological localization occurs and becomes frustrated by the generation of curved dispersive shock-waves when the strength of nonlinearity is increased. The analysis is supported by four-dimensional parallel simulations., Comment: 5 pages, 4 figures, minor corrections

Localized surface plasmon resonances have recently attracted considerable attention due to their ability to dramatically enhance near-field optical intensities and boost nanoscale light-matter interactions. Here we demonstrate unambiguously that polyhedral silver nanoparticles can be tailored to promote enhanced coherent emission from organic dye dispersions in a cavity. In particular, we observe that nanoparticles supporting resonances close to the absorption peak of the dye yield to more efficient lasing, up to one order of magnitude, which is also evidenced by the narrowing of the emission spectral line down to 3 nm. Moreover we observe emission saturation and energy dependent spectral shifts associated with Kerr effects, which demonstrate the general relevance of non-resonant nonlinearities in plasmonic enhanced laser emissions. Works in this area will contribute to the design of novel kind of laser sources providing ultra-short pulsed operation and structural tunability.

We have evaluated the nonmesonic weak decay spectra within the independent-particle shell-model, and compared them with the recent measurements of: i) the single and double coincidence nucleon spectra in ${\mathrm{^{12}_{\Lambda}C}}$ performed at KEK, and ii) proton kinetic energy spectra in ${\mathrm{^{5}_{\Lambda}He}}$, ${\mathrm{^{7}_{\Lambda}Li}}$, ${\mathrm{^{9}_{\Lambda}Be}}$, ${\mathrm{^{11}_{\Lambda}B}}$, ${\mathrm{^{12}_{\Lambda}C}}$, ${\mathrm{^{13}_{\Lambda}C}}$, ${\mathrm{^{15}_{\Lambda}N}}$ and ${\mathrm{^{16}_{\Lambda}O}}$ done by FINUDA. Based on this comparison we argue that the extraction from the data of the three-body $\Lambda NN \rightarrow nNN$ induced decay rate, as done in these works, could be questionable., Comment: 15 pages, 8 figures

Self-induced transparency pulses propagating in a random medium embedded in a two-level system can transfer energy to localized Anderson states. This allows the onset of two-level laser-like action., Comment: 5 pages, 5 figures, revised version

The nonlinear propagation of light pulses in liquid-filled photonic crystal fibers is considered. Due to the slow reorientational nonlinearity of some molecular liquids, the nonlinear modes propagating inside such structures can be approximated, for pulse durations much shorter than the molecular relaxation time, by temporally highly-nonlocal solitons, analytical solutions of a linear Schroedinger equation. The physical relevance of these novel solitary structures, which may have a broad range of applications, is discussed and supported by detailed numerical simulations., 4 pages, 3 figures

We investigate a special class of cellular automata (CA) evolving in a environment filled by an electromagnetic wave. The rules of the Conway's Game of Life are modified to account for the ability to retrieve life-sustenance from the field energy. Light-induced self-structuring and self-healing abilities and various dynamic phases are displayed by the CA. Photo-driven genetic selection and the nonlinear feedback of the CA on the electromagnetic field are included in the model, and there are evidences of self-organized light-localization processes. The evolution of the electromagnetic field is based on the Finite Difference Time Domain (FDTD) approach. Applications are envisaged in evolutionary biology, artificial life, DNA replication, swarming, optical tweezing and field-driven soft-matter., Comment: Revised and enlarged version. Added genetic selection and nonlinear feedback of the CA on the electromagnetic field. 12 pages, 13 figures. To appear in the book Game of Life Cellular Automata (Springer 2010, Andy Adamtzky ed.).

The WorldWide Web is one of the most important communication systems we use in our everyday life. Despite its central role, the growth and the development of the WWW is not controlled by any central authority. This situation has created a huge ensemble of connections whose complexity can be fruitfully described and quantified by network theory. One important application that allows to sort out the information present in these connections is given by the PageRank alghorithm. Computation of this quantity is usually made iteratively with a large use of computational time. In this paper we show that the PageRank can be expressed in terms of a wave function obeying a Schroedinger-like equation. In particular the topological disorder given by the unbalance of outgoing and ingoing links between pages, induces wave function and potential structuring. This allows to directly localize the pages with the largest score. Through this new representation we can now compute the PageRank without iterative techniques. For most of the cases of interest our method is faster than the original one. Our results also clarify the role of topology in the diffusion of information within complex networks. The whole approach opens the possibility to novel techniques inspired by quantum physics for the analysis of the WWW properties., Comment: 5 pages

We present a comparison between the random motion of an adiabatic and a diathermal piston sliding in a perfect gas. In particular, their dynamical behaviour, if investigated by means of Langevin's approach, shows the amplitude of the adiabatic-piston random displacements around the equilibrium position to be much larger (by a factor (M/m)^(1/2), where M and m are the piston mass and the mass of the single gas molecule) than that of the diathermal piston. The origin of this intriguing difference, which is accounted for in the frame of Langevin's approach, is also explored in terms of a space-phase analysis., Comment: 12 pages, 1 figure

Using a 3D Finite-Difference Time-Domain parallel code, we report on the linear and nonlinear propagation of light pulses in a disordered assembly of scatterers, whose spatial distribution is generated by a Molecular Dynamics code; refractive index dispersion is also taken into account. We calculate the static and dynamical diffusion constant of light, while considering a pulsed excitation. Our results are in quantitative agreement with reported experiments, also furnishing evidence of a non-exponential decay of the transmitted pulse in the linear regime and in the presence of localized modes. By using an high power excitation, we numerically demonstrate the ``modulational instability random laser'': at high peak input powers energy is transferred to localized states from the input pulse, via third-order nonlinearity and optical parametric amplification, and this process is signed by a power-dependent non-exponential time-decay of the transmitted pulse., Comment: 5 pages, 4 figures. Revised version with new figure 4 with localized states

Using Z-scan and dynamic light scattering measurements we investigate the nonlinear optics response of a colloidal solution undergoing dynamics slowing down with age. We study the high optical nonlinearity of an organic dye (Rhodamine B) dispersed in a water-clay (Laponite) solution, at different clay concentrations (2.0 wt% - 2.6 wt%), experiencing the gelation process. We determine the clay platelets self diffusion coefficient and, by its comparison with the structural relaxation time, we conclude that the gelation process proceeds through the structuring of interconnecting clay platelets network rather than through clusters growth and aggregation., Comment: 4 figures, 4 pages

We predict that spatial self-trapping of light can occur in soft matter encompassing a wide class of new materials such as colloids, foams, gels, fractal aggregates etc. We develop a general nonlocal theory that allows to relate the properties of the trapped state of Maxwell equations to the measurable static structure factor of the specific material. We give numerical evidence for stable trapping in fractal aggregates and suggest also the possibility of soliton spectroscopy of soft-matter., 5 pages, 3 figures

We investigate optical parametric oscillations through four-wave mixing in resonant cavities and photonic crystals. The theoretical analysis underlines the relevant features of the phenomenon and the role of the density of states. Using fully vectorial 3D time-domain simulations, including both dispersion and nonlinear polarization, for the first time we address this process in a face centered cubic lattice and in a photonic crystal slab. The results lead the way to the development of novel parametric sources in isotropic media., 5 pages, 3 figures

The limits of the Second Law of Thermodynamics, which reigns undisputed in the macroscopic world, are investigated at the mesoscopic level, corresponding to spatial dimensions of a few microns. An extremely simple isolated system, modeled after Callen's adiabatic piston, [1] can, under appropriate conditions, be described as a self-organizing Brownian motor and shown to exhibit a perpetuum mobile behavior., Comment: 17 pages, 4 figures. Revised version

A quantum theory of 3D X-shaped optical bullets in Kerr media is presented. The existence of progressive undistorted squeezed vacuum is predicted. Applications to quantum non-demolition experiments, entanglement and interferometers for gravitational waves detection are envisaged., Comment: 4 pages, 2 figures

The generation of finite energy packets of X-waves is analysed in normally dispersive cubic media by using an X-wave expansion. The 3D nonlinear Schroedinger model is reduced to a 1D equation with anomalous dispersion. Pulse splitting and beam replenishment as observed in experiments with water and Kerr media are explained in terms of a higher order breathing soliton. The results presented also hold in periodic media and Bose-condensed gases., Comment: 18 pages, 6 figures, corrected version to be published in Physical Review E

In the framework of the paraxial and of the slowly varying envelope approximations, with reference to a normally dispersive medium or to vacuum, the electromagnetic field is given as a continuous quantum superposition of non-dispersive and non-diffracting wave-packets (namely X-waves). Entangled states as pairs of elementary excitations traveling at (approximately) the same velocity are found in optical parametric amplification., 7 pages, revised version

We predict that an ultra-cold Bose gas in an optical lattice can give rise to a new form of condensation, namely matter X waves. These are non-spreading 3D wave-packets which reflect the symmetry of the Laplacian with a negative effective mass along the lattice direction, and are allowed to exist in the absence of any trapping potential even in the limit of non-interacting atoms. This result has also strong implications for optical propagation in periodic structures, Comment: 5 pages, 2 figures

Using a 3D fully-vectorial nonlinear time-domain analysis we numerically investigate the generation of terahertz radiation by pumping a photonic crystal microcavity out of resonance. High quality factors and a quadratic susceptibility lead to few-cycle terahertz pulses via optical rectification. Material dispersion as well as linear and nonlinear anisotropy is fully accounted for., 3 pages, 4 figures