Theory and application of cavity solitons in photonic devices.

Driven optical cavities containing a nonlinear medium support stable dissipative solitons, cavity solitons, in the form of bright or dark spots of light on a uniformly-lit background. Broadening effects due to diffraction or group velocity dispersion are balanced by the nonlinear interaction with the medium while cavity losses balance the input energy. The history, properties, physical interpretation and wide application of cavity solitons are reviewed.

Frequency comb enhancement via the self-crystallization of vectorial cavity solitons.

Long-range interactions between dark vectorial temporal cavity solitons are induced by the formation of patterns via spontaneous symmetry breaking of orthogonally polarized fields in ring resonators. Turing patterns of alternating polarizations form between adjacent solitons, pushing them apart so that a random distribution of solitons along the cavity length spontaneously reaches equal equilibrium distances, the soliton crystal, without any mode crossing or external modulation. Enhancement of the frequency comb is achieved through the spontaneous formation of regularly spaced soliton crystals, 'self-crystallization', with greater power and spacing of the spectral lines for increasing soliton numbers.

Cavity soliton inhibition of extreme events in lasers with injection.

Vortex mediated turbulence can be the key element in the generation of extreme events in spatially extended lasers with optical injection. Here, we study the interplay of vortex mediated turbulence and cavity solitons on the onset of extreme events in semiconductor lasers with injection. We first analyze and characterize these two features separately, spatiotemporal chaotic optical vortices for low values of the injection intensity and cavity solitons above the locking regime.

Nonlinear topological symmetry protection in a dissipative system.

We investigate experimentally and theoretically a system ruled by an intricate interplay between topology, nonlinearity, and spontaneous symmetry breaking. The experiment is based on a two-mode coherently-driven optical resonator where photons interact through the Kerr nonlinearity. In presence of a phase defect, the modal structure acquires a synthetic Möbius topology enabling the realization of spontaneous symmetry breaking in inherently bias-free conditions without fine tuning of parameters.

Generating Multiparticle Entangled States by Self-Organization of Driven Ultracold Atoms.

We describe a mechanism for guiding the dynamical evolution of ultracold atomic motional degrees of freedom toward multiparticle entangled Dicke-squeezed states, via nonlinear self-organization under external driving. Two examples of many-body models are investigated. In the first model, the external drive is a temporally oscillating magnetic field leading to self-organization by interatomic scattering.

Control of Light-Atom Solitons and Atomic Transport by Optical Vortex Beams Propagating through a Bose-Einstein Condensate.

We model propagation of far-red-detuned optical vortex beams through a Bose-Einstein condensate using nonlinear Schrödinger and Gross-Pitaevskii equations. We show the formation of coupled light-atomic solitons that rotate azimuthally before moving off tangentially, carrying angular momentum. The number, and velocity, of solitons, depends on the orbital angular momentum of the optical field.

Self-emergence of robust solitons in a microcavity.

In many disciplines, states that emerge in open systems far from equilibrium are determined by a few global parameters. These states can often mimic thermodynamic equilibrium, a classic example being the oscillation threshold of a laser that resembles a phase transition in condensed matter. However, many classes of states cannot form spontaneously in dissipative systems, and this is the case for cavity solitons that generally need to be induced by external perturbations, as in the case of optical memories.

Breathing dynamics of symmetry-broken temporal cavity solitons in Kerr ring resonators.

We investigate theoretically and experimentally the instabilities of symmetry-broken, vectorial, bright cavity solitons (CSs) of two-mode nonlinear passive Kerr resonators. Through comprehensive theoretical analyses of coupled Lugiato-Lefever equations, we identify two different breathing regimes where the two components of the vectorial CSs breathe respectively in-phase and out-of-phase. Moreover, we find that deep out-of-phase breathing can lead to intermittent self-switching of the two components, spontaneously transforming a soliton into its mirror-symmetric state.

A Kerr polarization controller.

Kerr-effect-induced changes of the polarization state of light are well known in pulsed laser systems. An example is nonlinear polarization rotation, which is critical to the operation of many types of mode-locked lasers. Here, we demonstrate that the Kerr effect in a high-finesse Fabry-Pérot resonator can be utilized to control the polarization of a continuous wave laser.

Spontaneous symmetry breaking of dissipative optical solitons in a two-component Kerr resonator.

Dissipative solitons are self-localized structures that can persist indefinitely in open systems driven out of equilibrium. They play a key role in photonics, underpinning technologies from mode-locked lasers to microresonator optical frequency combs. Here we report on experimental observations of spontaneous symmetry breaking of dissipative optical solitons.

Multiple Self-Organized Phases and Spatial Solitons in Cold Atoms Mediated by Optical Feedback.

We study the transverse self-structuring of cold atomic clouds with effective atomic interactions mediated by a coherent driving beam retroreflected by means of a single mirror. The resulting self-structuring due to optomechanical forces is much richer than that of an effective-Kerr medium, displaying hexagonal, stripe and honeycomb phases depending on the interaction strength parametrized by the linear susceptibility. Phase domains are described by Ginzburg-Landau amplitude equations with real coefficients.

Temporal cavity solitons in a laser-based microcomb: a path to a self-starting pulsed laser without saturable absorption.

We theoretically present a design of self-starting operation of microcombs based on laser-cavity solitons in a system composed of a micro-resonator nested in and coupled to an amplifying laser cavity. We demonstrate that it is possible to engineer the modulational-instability gain of the system's zero state to allow the start-up with a well-defined number of robust solitons. The approach can be implemented by using the system parameters, such as the cavity length mismatch and the gain shape, to control the number and repetition rate of the generated solitons.

Thermal, Quantum Antibunching and Lasing Thresholds from Single Emitters to Macroscopic Devices.

Starting from a fully quantized Hamiltonian for an ensemble of identical emitters coupled to the modes of an optical cavity, we determine analytically regimes of thermal, collective anti-bunching and laser emission that depend explicitly on the number of emitters. The lasing regime is reached for a number of emitters above a critical number-which depends on the light-matter coupling, detuning, and the dissipation rates-via a universal transition from thermal emission to collective anti-bunching to lasing as the pump increases. Cases where the second order intensity correlation fails to predict laser action are also presented.

Self-Switching Kerr Oscillations of Counterpropagating Light in Microresonators.

We report the experimental and numerical observation of oscillatory antiphase switching between counterpropagating light beams in Kerr ring microresonators, where dominance between the intensities of the two beams is periodically or chaotically exchanged. Self-switching occurs in balanced regimes of operation and is well captured by a simple coupled dynamical system featuring only the self- and cross-phase Kerr nonlinearities. Switching phenomena are due to temporal instabilities of symmetry-broken states combined with attractor merging, which restores the broken symmetry on average.

Dissipative Polarization Domain Walls in a Passive Coherently Driven Kerr Resonator.

Using a passive, coherently driven nonlinear optical fiber ring resonator, we report the experimental realization of dissipative polarization domain walls. The domain walls arise through a symmetry breaking bifurcation and consist of temporally localized structures where the amplitudes of the two polarization modes of the resonator interchange, segregating domains of orthogonal polarization states. We show that dissipative polarization domain walls can persist in the resonator without changing shape.

Collisionally Inhomogeneous Bose-Einstein Condensates with a Linear Interaction Gradient.

We study the evolution of a collisionally inhomogeneous matter wave in a spatial gradient of the interaction strength. Starting with a Bose-Einstein condensate with weak repulsive interactions in quasi-one-dimensional geometry, we monitor the evolution of a matter wave that simultaneously extends into spatial regions with attractive and repulsive interactions. We observe the formation and the decay of solitonlike density peaks, counterpropagating self-interfering wave packets, and the creation of cascades of solitons.

Polarization modulation instability in a nonlinear fiber Kerr resonator.

We report on the experimental and numerical observation of polarization modulation instability (PMI) in a nonlinear fiber Kerr resonator. This phenomenon is phased-matched through the relative phase detuning between the intracavity fields associated with the two principal polarization modes of the cavity. Our experimental investigation is based on a 12 m long fiber ring resonator in which a polarization controller is inserted to finely control the level of intracavity birefringence.

Control of spatially rotating structures in diffractive Kerr cavities.

Turing patterns in self-focussing nonlinear optical cavities pumped by beams carrying orbital angular momentum (OAM) are shown to rotate with an angular velocity =2/ on rings of radii . We verify this prediction in 1D models on a ring and for 2D Laguerre-Gaussian and top-hat pumps with OAM. Full control over the angular velocity of the pattern in the range -2/ ≤≤2/ is obtained by using cylindrical vector beam pumps that consist of orthogonally polarized eigenmodes with equal and opposite OAM.

Excitation Modes of Bright Matter-Wave Solitons.

We experimentally study the excitation modes of bright matter-wave solitons in a quasi-one-dimensional geometry. The solitons are created by quenching the interactions of a Bose-Einstein condensate of cesium atoms from repulsive to attractive in combination with a rapid reduction of the longitudinal confinement. A deliberate mismatch of quench parameters allows for the excitation of breathing modes of the emerging soliton and for the determination of its breathing frequency as a function of atom number and confinement.

Multiple-time-scale analysis for pinned breathers in Bose-Hubbard chains.

Localized and pinned discrete breathers in Bose-Einstein condensates in optical lattices or in arrays of optical waveguides oscillate with frequencies which are much higher than those present in the spectrum of the background. Hence, the interaction between localized breathers and their surroundings is extremely weak leading to a multiple-time-scale perturbation expansion. We identify the leading order in the asymptotic expansion of the breather amplitude which does not average to zero after one full oscillation.

Dynamical Freezing of Relaxation to Equilibrium.

We provide evidence of an extremely slow thermalization occurring in the discrete nonlinear Schrödinger model. At variance with many similar processes encountered in statistical mechanics-typically ascribed to the presence of (free) energy barriers-here the slowness has a purely dynamical origin: it is due to the presence of an adiabatic invariant, which freezes the dynamics of a tall breather. Consequently, relaxation proceeds via rare events, where energy is suddenly released towards the background.

Observation of Mode-Locked Spatial Laser Solitons.

A stable nonlinear wave packet, self-localized in all three dimensions, is an intriguing and much sought after object in nonlinear science in general and in nonlinear photonics in particular. We report on the experimental observation of mode-locked spatial laser solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback from an external cavity. These spontaneously emerging and long-term stable spatiotemporal structures have a pulse length shorter than the cavity round-trip time and may pave the way to completely independent cavity light bullets.

Optical Rogue Waves in Vortex Turbulence.

We present a spatiotemporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction, and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability to phase unbound turbulent states in complex Ginzburg-Landau and Swift-Hohenberg models with external driving. When the pumping is high and the external driving is low, synchronized oscillations are unstable and lead to spatiotemporal vortex-mediated turbulence with high excursions in amplitude.