Modulational instability, generation, and evolution of rogue waves in the generalized fractional nonlinear Schrödinger equations with power-law nonlinearity and rational potentials

In this paper, we investigate several properties of the modulational instability (MI) and rogue waves (RWs) within the framework of the generalized fractional nonlinear Schrödinger (FNLS) equations with rational potentials. We derive the dispersion relation for a continuous wave (CW), elucidating the relationship between the wavenumber and the instability growth rate of the CW solution in the absence of potentials. This relationship is primarily influenced by the power parameter σ, the Lévy index α, and the nonlinear coefficient g. Our theoretical findings are corroborated by numerical simulations, which demonstrate that MI occurs in the focusing context. Furthermore, we study the RW generations in both cubic and quintic FNLS equations with two types of time-dependent rational potentials, which make both cubic and quintic NLS equations support the exact RW solutions. Specifically, we show that the introduction of these two potentials allows for the excitations of controllable RWs in the defocusing regime. When these two potentials become the time-independent cases such that the stable W-shaped solitons with non-zero backgrounds are generated in these cubic and quintic FNLS equations. Moreover, we consider the excitations of higher-order RWs and investigate the conditions necessary for their generations. Our analysis reveals the intricate interplay between the system parameters and the potential configurations, offering insights into the mechanisms that facilitate the emergence of higher-order RWs. Finally, we find the separated controllable multi-RWs in the defocusing cubic FNLS equation with time-dependent multi-potentials. This comprehensive study not only enhances our understanding of MI and RWs in the fractional nonlinear wave systems, but also paves the way for future research in related nonlinear wave phenomena.

Rogue waves and instability arising from long-wave-short-wave resonance beyond the integrable regime

We consider instability and localized patterns arising from the long-wave-short-wave resonance in the nonintegrable regime numerically. We study the stability and instability of elliptic-function periodic waves with respect to subharmonic perturbations, whose period is a multiple of the period of the elliptic waves. We thus find the modulational instability (MI) of the corresponding dnoidal waves. Upon varying parameters of dnoidal waves, spectrally unstable ones can be transformed into stable states via the Hamiltonian Hopf bifurcation. For snoidal waves, we find a transition of the dominant instability scenario between the MI and the instability with a bubblelike spectrum. For cnoidal waves, we produce three variants of the MI. Evolution of the unstable states is also considered, leading to formation of rogue waves on top of the elliptic-wave and continuous-wave backgrounds.

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. In the second model, the drive is a pump laser leading to transverse self-organization by photon-atom scattering in a ring cavity. We numerically demonstrate the generation of multiparticle entangled states of atomic motion and discuss prospective experimental realizations of the models. For the cavity case, the calculations with adiabatically eliminated photonic sidebands show significant momentum entanglement generation can occur even in the "bad cavity" regime. The results highlight the potential for using self-organization of atomic motion in quantum technological applications.

Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape

Collective particle transport across periodic energy landscapes is ubiquitously present in many condensed matter systems spanning from vortices in high-temperature superconductors, frictional atomic sliding, driven skyrmions to biological and active matter. Here we report the emergence of fast solitons propagating against a rotating optical landscape. These experimentally observed solitons are stable cluster waves that originate from a coordinated particle exchange process which occurs when the number of trapped microparticles exceeds the number of potential wells. The size and speed of individual solitons rapidly increase with the particle diameter as predicted by theory and confirmed by numerical simulations. We show that when several solitons coexist, an effective repulsive interaction can stabilize their propagation along the periodic potential. Our experiments demonstrate a generic mechanism for cluster-mediated transport with potential applications to condensed matter systems on different length scales.

Formation, propagation, and excitation of matter solitons and rogue waves in chiral BECs with a current nonlinearity trapped in external potentials

In this paper, we investigate formation and propagation of matter solitons and rogue waves (RWs) in chiral Bose-Einstein condensates modulated by different external potentials, modeled by the chiral Gross-Pitaevskii (GP) equation with the current nonlinearity and external potentials. On the one hand, the introduction of two potentials (Pöschl-Teller and harmonic-Gaussian potentials) enables the discovery of exact soliton solutions in both focusing and defocusing cases. We analyze the interplay effects of current nonlinearity and potential on soliton stability via associated Bogoliubov-de Gennes equations. Moreover, multiple families of numerical solitons (ground-state and dipole modes) trapped in potentials are found, exhibiting distinctive structures. The interactions between solitons trapped in potentials are studied, which exhibit the inelastic trajectories and repulsive interactions. On the other hand, we introduce the time-dependent potentials such that the controlled RWs are found in both focusing and defocusing GP equations with current nonlinearity. Furthermore, through the interaction between potentials and current nonlinearity, it is possible to enlarge the region of modulational instability, leading to the generation of RWs and chiral solitons. High-order RWs are generated from several Gaussian perturbations on a continuous wave. The presence of current nonlinearity disrupts the structures of these high-order RWs, causing them to undergo a transform into chiral lower-amplitude solitons. Finally, various types of soliton excitations are investigated by varying the strengths of potential and current nonlinearity, showing the abundant dynamic transforms of chrital matter solitons.

Formation of Rogue Waves and Modulational Instability with Zero-Wavenumber Gain in Multicomponent Systems with Coherent Coupling

It is known that rogue waves (RWs) are generated by the modulational instability (MI) of the baseband type. Starting with the Bers-Kaup-Reiman system for three-wave resonant interactions, we identify a specific RW-building mechanism based on MI which includes zero wavenumber in the gain band. An essential finding is that this mechanism works solely under a linear relation between the MI gain and a vanishingly small wavenumber of the modulational perturbation. The same mechanism leads to the creation of RWs by MI in other multicomponent systems-in particular, in the massive Thirring model.

Rogue wave formation scenarios for the focusing nonlinear Schrödinger equation with parabolic-profile initial data on a compact support

We study the (1+1) focusing nonlinear Schrödinger equation for an initial condition with compactly supported parabolic profile and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural class of self-similar solutions, we provide a criterion for blowup in finite time, generalizing a result by Talanov et al. In the presence of dispersion, we numerically show that the same criterion determines, even beyond the semiclassical regime, whether the solution relaxes or develops a high-order rogue wave, whose onset time is predicted by the corresponding dispersionless catastrophe time. The sign of the chirp appears to determine the prevailing scenario among two competing mechanisms for rogue wave formation. For negative values, the numerical simulations are suggestive of the dispersive regularization of a gradient catastrophe described by Bertola and Tovbis for a different class of smooth, bell-shaped initial data. As the chirp becomes positive, the rogue wave seems to result from the interaction of counterpropagating dispersive dam break flows, as in the box problem recently studied by El, Khamis, and Tovbis. As the chirp and amplitude of the initial profile are relatively easy to manipulate in optical devices and water tank wave generators, we expect our observation to be relevant for experiments in nonlinear optics and fluid dynamics.

Dipolar physics: a review of experiments with magnetic quantum gases

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.

Interaction Control and Bright Solitons in Coherently Coupled Bose-Einstein Condensates

We demonstrate fast control of the interatomic interactions in a Bose-Einstein condensate by coherently coupling two atomic states with intra- and interstate scattering lengths of opposite signs. We measure the elastic and inelastic scattering properties of the system and find good agreement with a theoretical model describing the interactions between dressed states. In the attractive regime, we observe the formation of bright solitons formed by dressed-state atoms. Finally, we study the response of the system to an interaction quench from repulsive to attractive values, and observe how the resulting modulational instability develops into a bright soliton train.

Solitary matter wave in spin-orbit-coupled Bose-Einstein condensates with helicoidal gauge potential

We analytically and numerically study the different types of solitary wave in the two-component helicoidal spin-orbit coupled Bose-Einstein condensates (BECs). Adopting the multiscale perturbation method, we derive the analytical bright and dark solitary wave solutions of the system, and the stationary and moving bright (dark) solitary waves are obtained. The effects of spin-orbit coupling, the helicoidal gauge potential, the momentum, the Zeeman splitting, and the atomic interactions on the solitary wave types are discussed, and it is found that the coupling of these physical parameters can manipulate different types of solitary waves in the system. The results indicate that the helicoidal gauge potential breaks the symmetric properties of the energy band of the system and adjusts the energy band structure, thus further effecting the solitary wave properties, i.e., stationary or moving solitary wave, bright, or dark solitary wave. Correspondingly, the analytical predictions for exciting stationary or moving bright (dark) solitary wave in parameter space are obtained. In particular, the helicoidal gauge potential changes the solitary wave types drastically for the weak spin-orbit coupling, i.e., in the absence of the helicoidal gauge potential, only dark (bright) solitary wave solutions exist in the system with repulsive (attractive) atomic interaction; however, in the presence of the helicoidal gauge potential, both dark and bright solitary waves can exist in the system regardless of whether the atomic interaction is repulsive or attractive. In addition, we investigate the stability of solitary waves and obtain the stability regions of different types of solitary waves by applying the linear stability analysis. The dynamic evolution results of the solitary waves by the direct numerical simulation not only validate the linear stability analysis but also confirm the analytical prediction of the solitary waves. Finally, the collision effects between solitary waves are also presented by the numerical simulation. It is shown that the interactions between solitary waves in the system have both elastic and inelastic collisions, which are closely related to the position of solitary wave states in the linear energy band. Our results provide a potential way to adjust the types of solitary waves in BECs with helicoidal gauge potential.

Observation of Quasiparticle Pair Production and Quantum Entanglement in Atomic Quantum Gases Quenched to an Attractive Interaction

We report observations of quasiparticle pair production by a modulational instability in an atomic superfluid and present a measurement technique that enables direct characterization of quasiparticle quantum entanglement. By quenching the atomic interaction to attractive and then back to weakly repulsive, we produce correlated quasiparticles and monitor their evolution in a superfluid through evaluating the in situ density noise power spectrum, which essentially measures a "homodyne" interference between ground-state atoms and quasiparticles of opposite momenta. We observe large amplitude growth in the power spectrum and subsequent coherent oscillations in a wide spatial frequency band within our resolution limit, demonstrating coherent quasiparticle generation and evolution. The spectrum is observed to oscillate below a quantum limit set by the Peres-Horodecki separability criterion of continuous-variable states, thereby confirming quantum entanglement between interaction quench-induced quasiparticles.

Observation of Scale Invariance in Two-Dimensional Matter-Wave Townes Solitons

We report near-deterministic generation of two-dimensional (2D) matter-wave Townes solitons and a precision test on scale invariance in attractive 2D Bose gases. We induce a shape-controlled modulational instability in an elongated 2D matter wave to create an array of isolated solitary waves of various sizes and peak densities. We confirm scale invariance by observing the collapse of solitary-wave density profiles onto a single curve in a dimensionless coordinate rescaled according to their peak densities and observe that the scale-invariant profiles measured at different coupling constants g can further collapse onto the universal profile of Townes solitons. The reported scaling behavior is tested with a nearly 60-fold difference in soliton interaction energies and allows us to discuss the impact of a non-negligible magnetic dipole-dipole interaction (MDDI) on 2D scale invariance. We confirm that the effect of MDDI in our alkali cesium quasi-2D samples effectively conforms to the same scaling law governed by a contact interaction to well within our experiment uncertainty.

Self-Organization in Cold Atoms Mediated by Diffractive Coupling

This article discusses self-organization in cold atoms via light-mediated interactions induced by feedback from a single retro-reflecting mirror. Diffractive dephasing between the pump beam and the spontaneous sidebands selects the lattice period. Spontaneous breaking of the rotational and translational symmetry occur in the 2D plane transverse to the pump. We elucidate how diffractive ripples couple sites on the self-induced atomic lattice. The nonlinear phase shift of the atomic cloud imprinted onto the optical beam is the parameter determining coupling strength. The interaction can be tailored to operate either on external degrees of freedom leading to atomic crystallization for thermal atoms and supersolids for a quantum degenerate gas, or on internal degrees of freedom like populations of the excited state or Zeeman sublevels. Using the light polarization degrees of freedom on the Poincaré sphere (helicity and polarization direction), specific irreducible tensor components of the atomic Zeeman states can be coupled leading to spontaneous magnetic ordering of states of dipolar and quadrupolar nature. The requirements for critical interaction strength are compared for the different situations. Connections and extensions to longitudinally pumped cavities, counterpropagating beam schemes and the CARL instability are discussed.

"Extraordinary" modulation instability in optics and hydrodynamics

The classical theory of modulation instability (MI) attributed to Bespalov-Talanov in optics and Benjamin-Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.

Modulational instability and soliton generation in chiral Bose-Einstein condensates with zero-energy nonlinearity

By means of analytical and numerical methods, we address the modulational instability (MI) in chiral condensates governed by the Gross-Pitaevskii equation including the current nonlinearity. The analysis shows that this nonlinearity partly suppresses the MI driven by the cubic self-focusing, although the current nonlinearity is not represented in the system's energy (although it modifies the momentum), hence it may be considered as zero-energy nonlinearity. Direct simulations demonstrate generation of trains of stochastically interacting chiral solitons by MI. In the ring-shaped setup, the MI creates a single traveling solitary wave. The sign of the current nonlinearity determines the direction of propagation of the emerging solitons.

Probing Band Topology Using Modulational Instability

We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations of the nonlinear Bloch waves are sensitive to topological band inversions. At longer timescales, nonlinear wave mixing induces spreading of energy through the entire band and spontaneous creation of wave polarization singularities determined by the band Chern number. Our analytical and numerical results establish modulational instability as a tool to probe bulk topological invariants and create topologically nontrivial wave fields.

Modelling quantum aspects of disruption of a white dwarf star by a black hole

We study the final stages of the evolution of a binary system consisted of a black hole and a white dwarf star. We implement the quantum hydrodynamic equations and carry out numerical simulations. As a model of a white dwarf star we consider a zero temperature droplet of attractively interacting degenerate atomic bosons and spin-polarized atomic fermions. Such mixtures are investigated experimentally nowadays. We find that the white dwarf star is stripped off its mass while passing the periastron. Due to nonlinear effects, the accretion disk originated from the white dwarf becomes fragmented and the onset of a quantum turbulence with giant quantized vortices present in the bosonic component of the accretion disk is observed. The binary system ends its life in a spectacular way, revealing quantum features underlying the white dwarf star’s structure. We find a charged mass, falling onto a black hole, could be responsible for recently discovered ultraluminous X-ray bursts. The simulations show that final passage of a white dwarf near a black hole can cause a gamma-ray burst.

Observation of Universal Quench Dynamics and Townes Soliton Formation from Modulational Instability in Two-Dimensional Bose Gases

We experimentally study universal nonequilibrium dynamics of two-dimensional atomic Bose gases quenched from repulsive to attractive interactions. We observe the manifestation of modulational instability that, instead of causing collapse, fragments a large two-dimensional superfluid into multiple wave packets universally around a threshold atom number necessary for the formation of Townes solitons. We confirm that the density distributions of quench-induced solitary waves are in excellent agreement with the stationary Townes profiles. Furthermore, our density measurements in the space and time domain reveal detailed information about this dynamical process, from the hyperbolic growth of density waves, the formation of solitons, to the subsequent collision and collapse dynamics, demonstrating multiple universal behaviors in an attractive many-body system in association with the formation of a quasistationary state.

Geometrizing Quantum Dynamics of a Bose-Einstein Condensate

We show that quantum dynamics of Bose-Einstein condensates in the weakly interacting regime can be geometrized by a Poincaré disk. Each point on such a disk represents a thermofield double state, the overlap between which equals the metric of this hyperbolic space. This approach leads to a unique geometric interpretation of stable and unstable modes as closed and open trajectories on the Poincaré disk, respectively. The resonant modes that follow geodesics naturally equate fundamental quantities including the time, the length, and the temperature. Our work suggests a new geometric framework to coherently control quantum systems and reverse their dynamics using SU(1,1) echoes. In the presence of perturbations breaking the SU(1,1) symmetry, SU(1,1) echoes deliver a new means to measure these perturbations such as the interactions between excited particles.

Creation and Characterization of Matter-Wave Breathers

We report the creation of quasi-1D excited matter-wave solitons, "breathers," by quenching the strength of the interactions in a Bose-Einstein condensate with attractive interactions. We characterize the resulting breathing dynamics and quantify the effects of the aspect ratio of the confining potential, the strength of the quench, and the proximity of the 1D-3D crossover for the two-soliton breather. Furthermore, we demonstrate the complex dynamics of a three-soliton breather created by a stronger interaction quench. Our experimental results, which compare well with numerical simulations, provide a pathway for utilizing matter-wave breathers to explore quantum effects in large many-body systems.

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. The matter-wave dynamics is well reproduced in numerical simulations based on the nonpolynomial Schrödinger equation with three-body loss, allowing us to better understand the underlying behavior based on a wavelet transformation. Our analysis provides new understanding of collapse processes for solitons, and opens interesting connections to other nonlinear instabilities.

Subharmonic Entrainment Breather Solitons in Ultrafast Lasers

We study theoretically and experimentally the subharmonic entrainment (SHE) breather soliton in mode-locked lasers for the first time, in which the ratio of the breather period to the round-trip time is an integer. We build a non-Hermitian degeneracy map of breather soliton, and illustrate that SHE arises between the two exceptional points (EPs). We obtain SHE at the ratio of 20, observe the evolution of breather soliton when tuning the gain and/or cavity loss, and prove that this phenomenon can improve the stability of breather soliton. Our research brings insight into the EP physics of ultrafast lasers and makes the mode-locked laser a powerful test bed for non-Hermitian degeneracy, which may open a new course in ultrafast laser research.

Nondestructive dispersive imaging of rotationally excited ultracold molecules

A barrier to realizing the potential of molecules for quantum information science applications is a lack of high-fidelity, single-molecule imaging techniques. Here, we present and theoretically analyze a general scheme for dispersive imaging of electronic ground-state molecules. Our technique relies on the intrinsic anisotropy of excited molecular rotational states to generate optical birefringence, which can be detected through polarization rotation of an off-resonant probe laser beam. Using 23Na87Rb and 87Rb133Cs as examples, we construct a formalism for choosing the molecular state to be imaged and the excited electronic states involved in off-resonant coupling. Our proposal establishes the relevant parameters for achieving degree-level polarization rotations for bulk molecular gases, thus enabling high-fidelity nondestructive imaging. We additionally outline requirements for the high-fidelity imaging of individually trapped molecules.

Modified linear stability analysis for quantitative dynamics of a perturbed plane wave

We develop linear stability analysis (LSA) to quantitatively predict the dynamics of a perturbed plane wave in nonlinear systems. We take a nonintegrable fiber model with purely fourth-order dispersion as an example to demonstrate this method's effectiveness. For a Gaussian-type initial perturbation with cosine-type modulation on a plane wave, its propagation velocities, periodicity, and localization are predicted successfully, and the range of application is discussed. Importantly, the modulation-instability-induced growth of localized perturbation is proved different from the one of purely periodic perturbation and requires the modification of gain value for more accurate prediction. The method offers a needful supplement and improvement for LSA and paves a way to study the dynamics of a perturbed plane wave in more practical nonlinear systems.

Direct Measurements of Collisional Dynamics in Cold Atom Triads

The introduction of optical tweezers for trapping atoms has opened remarkable opportunities for manipulating few-body systems. Here, we present the first bottom-up assembly of atom triads. We directly observe atom loss through inelastic collisions at the single event level, overcoming the substantial challenge in many-atom experiments of distinguishing one-, two-, and three-particle processes. We measure a strong suppression of three-body loss, which is not fully explained by the presently availably theory for three-body processes. The suppression of losses could indicate the presence of local anticorrelations due to the interplay of attractive short range interactions and low dimensional confinement. Our methodology opens a promising pathway in experimental few-body dynamics.

Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases

Quantum droplets are ultradilute liquid states that emerge from the competitive interplay of two Hamiltonian terms, the mean-field energy and beyond-mean-field correction, in a weakly interacting binary Bose gas. We relate the formation of droplets in symmetric and asymmetric two-component one-dimensional boson systems to the modulational instability of a spatially uniform state driven by the beyond-mean-field term. Asymmetry between the components may be caused by their unequal populations or unequal intra-component interaction strengths. Stability of both symmetric and asymmetric droplets is investigated. Robustness of the symmetric solutions against symmetry-breaking perturbations is confirmed.

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. In addition, we observe signatures of higher-order solitons and the splitting of the wave packet after the quench. Our experimental results are compared to analytical predictions and to numerical simulations of the one-dimensional Gross-Pitaevskii equation.

Solitons in spin-orbit-coupled spin-2 spinor Bose-Einstein condensates

We investigate the different types of matter-wave solitons in spin-orbit-coupled spin-2 spinor Bose-Einstein condensates. Using mean-field theory and adopting the multiscale perturbation method, the original five-component Gross-Pitaevskii spin-orbit-coupled spin-2 spinor Bose-Einstein condensate model can be reduced to a single effective nonlinear Schrödinger equation, which allows us to find analytical soliton solutions of this system. In this way, for different regimes of the spin-orbit coupling, Raman coupling, and interatomic interactions, we find approximate bright and dark soliton solutions. Particularly, the type of solitons depends on the dispersion properties of the system. When the lowest-energy band has a single-well structure, we find there only exist positive mass bright or dark solitons due to the dispersion coefficient of effective nonlinear Shrödinger equation always positive. However, when the lowest-energy band has a double-well structure, there will appear positive (negative) mass bright or dark solitons because the sign of the dispersion coefficient can be positive (negative) under different momentum. We employ direct numerical simulation of the original five-component Gross-Pitaevskii equations to confirm the analytical results.

Nonlocal Pair Correlations in a Higher-Order Bose Gas Soliton

The truncated Wigner and positive-P phase-space representations are used to study the dynamics of a one-dimensional Bose gas. This allows calculations of the breathing quantum dynamics of higher-order solitons with 10^{3}-10^{5} particles, as in realistic Bose-Einstein condensation experiments. Although classically stable, these decay quantum mechanically. Our calculations show that there are large nonlocal correlations and nonclassical quantum entanglement.

Flemish Strings of Magnetic Solitons and a Nonthermal Fixed Point in a One-Dimensional Antiferromagnetic Spin-1 Bose Gas

Thermalization in a quenched one-dimensional antiferromagnetic spin-1 Bose gas is shown to proceed via a nonthermal fixed point through annihilation of Flemish-string bound states of magnetic solitons. A possible experimental situation is discussed.

Directional soliton and breather beams

Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the unidirectional nonlinear Schrödinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite; consequently, beam dynamics form. Spatiotemporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D + 1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large-amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose-Einstein condensates, solids, plasma, hydrodynamics, and optics.

Rogue Wave Type Solutions and Spectra of Coupled Nonlinear Schrödinger Equations

The formation of rogue oceanic waves may be the result of different causes. Various factors (winds, currents, dispersive focussing, depth, nonlinear focussing and instability) make this subject intriguing, and yet its understanding is quite relevant to practical issues. Here, we deal only with the nonlinear character of this dynamics, which has been recognised as the main ingredient to rogue wave formation. In this perspective, the formation of rogue waves requires a non-vanishing and unstable background such as a nonlinear regular wave train with attractive self-interaction. The simplest, best known model of such dynamics is the universal nonlinear Schrödinger equation. This has proven to serve as a good approximation in various contexts and over a broad range of experimental settings. This model aims to give the slow evolution of the envelope of one monochromatic wave due to nonlinearity. Here, we naturally consider the same problem for the envelopes of two weakly resonant monochromatic waves. As for the nonlinear Schrödinger equation, which is integrable, we adopt an integrable model to describe the interaction of two waves. This is the system of two coupled nonlinear Schrödinger equations (Manakov model) with self- and cross-interactions that may be both defocussing and focussing. We first discuss the linear stability properties of the background by computing the spectrum for all values of the parameters such as coupling constants and amplitudes. In particular, we relate the instability bands to properties of the spectrum and compute the gain function (or growth rate). We also relate to the stability spectrum the value of the spectral variable, which corresponds to a rogue wave solution. In contrast with the nonlinear Schrödinger equation, different types of single rogue wave exist that correspond to different values of the spectral variable even in the same spectrum. For these critical values, which are completely classified, we give the corresponding explicit expression of the rogue wave solution that follows from the well known Darboux–Dressing transformation method. Although not all systems of two coupled nonlinear Schrödinger equations that have been derived in water wave dynamics are integrable, our investigation contributes to the understanding of new effects due to wave coupling, at least for model equations that, even if not integrable, are close enough to the model considered here. For instance, our findings lead to investigate rogue waves generated by instabilities due to self- and cross-interactions of defocusing type. An illustrative selection of two coupled rogue waves solutions is displayed.

Rise and Fall of a Bright Soliton in an Optical Lattice

We study an ultracold atomic gas with attractive interactions in a one-dimensional optical lattice. We find that its excitation spectrum displays a quantum soliton band, corresponding to N-particle bound states, and a continuum band of other, mostly extended, states. For a system of a finite size, the two branches are degenerate in energy for weak interactions, while a gap opens above a threshold value of the interaction strength. We find that the interplay between degenerate extended and bound states has important consequences for both static and dynamical properties of the system. In particular, the solitonic states turn out to be protected from spatial perturbations and random disorder. We discuss how such dynamics implies that our system effectively provides an example of a quantum many-body system that, with the variation of the bosonic lattice filling, crosses over from integrable nonergodic to nonintegrable ergodic dynamics, through nonintegrable-nonergodic regimes.

Dynamical Critical Behavior of an Attractive Bose-Einstein Condensate Phase Transition

When matter undergoes a continuous phase transition on a finite timescale, the Kibble-Zurek mechanism predicts universal scaling behavior with respect to structure formation. The scaling is dependent on the universality class and is irrelevant to the details of the system. Here, we examine this phenomenon by controlling the timescale of the phase transition to a Bose-Einstein condensate using sympathetic cooling of an ultracold Bose thermal cloud with tunable interactions in an elongated trap. The phase transition results in a diverse number of bright solitons and gray solitons in the condensate that undergo attractive and repulsive interactions, respectively. The power law dependence of the average soliton number on the timescale of the phase transition is measured for each interaction and compared. The results support the Kibble-Zurek mechanism, in that the scaling behavior is determined by universality and does not rely on the interaction properties.

Single-shot condensation of exciton polaritons and the hole burning effect

A bosonic condensate of exciton polaritons in a semiconductor microcavity is a macroscopic quantum state subject to pumping and decay. The fundamental nature of this driven-dissipative condensate is still under debate. Here, we gain an insight into spontaneous condensation by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in a single-shot optical excitation regime, without averaging over multiple condensate realisations. We demonstrate that condensation is strongly influenced by an incoherent reservoir and that the reservoir depletion, the so-called spatial hole burning, is critical for the transition to the ground state. Condensates of photon-like polaritons exhibit strong shot-to-shot fluctuations and density filamentation due to the effective self-focusing associated with the reservoir depletion. In contrast, condensates of exciton-like polaritons display smoother spatial density distributions and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study fundamental properties of non-equilibrium condensation in the presence of a reservoir.

Observation of Roton Mode Population in a Dipolar Quantum Gas

The concept of a roton, a special kind of elementary excitation, forming a minimum of energy at finite momentum, has been essential to understand the properties of superfluid ⁴He 1. In quantum liquids, rotons arise from the strong interparticle interactions, whose microscopic description remains debated 2. In the realm of highly-controllable quantum gases, a roton mode has been predicted to emerge due to magnetic dipole-dipole interactions despite of their weakly-interacting character 3. This prospect has raised considerable interest 4-12; yet roton modes in dipolar quantum gases have remained elusive to observations. Here we report experimental and theoretical studies of the momentum distribution in Bose-Einstein condensates of highly-magnetic erbium atoms, revealing the existence of the long-sought roton mode. Following an interaction quench, the roton mode manifests itself with the appearance of symmetric peaks at well-defined finite momentum. The roton momentum follows the predicted geometrical scaling with the inverse of the confinement length along the magnetisation axis. From the growth of the roton population, we probe the roton softening of the excitation spectrum in time and extract the corresponding imaginary roton gap. Our results provide a further step in the quest towards supersolidity in dipolar quantum gases 13.

Self-Organized Lattices of Nonlinear Optochemical Waves in Photopolymerizable Fluids: The Spontaneous Emergence of 3-D Order in a Weakly Correlated System

Many of the extraordinary three-dimensional architectures that pattern our physical world emerge from complex nonlinear systems or dynamic populations whose individual constituents are only weakly correlated to each other. Shoals of fish, murmuration behaviors in birds, congestion patterns in traffic, and even networks of social conventions are examples of spontaneous pattern formation, which cannot be predicted from the properties of individual elements alone. Pattern formation at a different scale has been observed or predicted in weakly correlated systems including superconductors, atomic gases near Bose Einstein condensation, and incoherent optical fields. Understanding pattern formation in nonlinear weakly correlated systems, which are often unified through mathematical expression, could pave intelligent self-organizing pathways to functional materials, architectures, and computing technologies. However, it is experimentally difficult to directly visualize the nonlinear dynamics of pattern formation in most populations-especially in three dimensions. Here, we describe the collective behavior of large populations of nonlinear optochemical waves, which are poorly correlated in both space and time. The optochemical waves-microscopic filaments of white light entrapped within polymer channels-originate from the modulation instability of incandescent light traveling in photopolymerizable fluids. By tracing the three-dimensional distribution of optical intensity in the nascent polymerizing system, we find that populations of randomly distributed, optochemical waves synergistically and collectively shift in space to form highly ordered lattices of specific symmetries. These, to our knowledge, are the first three-dimensionally periodic structures to emerge from a system of weakly correlated waves. Their spontaneous formation in an incoherent and effectively chaotic field is counterintuitive, but the apparent contradiction of known behaviors of light including the laws of optical interference can be explained through the soliton-like interactions of optochemical waves with nearest neighbors. Critically, this work casts fundamentally new insight into the collective behaviors of poorly correlated nonlinear waves in higher dimensions and provides a rare, accessible platform for further experimental studies of these previously unexplored behaviors. Furthermore, it defines a self-organization paradigm that, unlike conventional counterparts, could generate polymer microstructures with symmetries spanning all the Bravais lattices.

Three-Component Soliton States in Spinor F=1 Bose-Einstein Condensates

Dilute-gas Bose-Einstein condensates are an exceptionally versatile test bed for the investigation of novel solitonic structures. While matter-wave solitons in one- and two-component systems have been the focus of intense research efforts, an extension to three components has never been attempted in experiments. Here, we experimentally demonstrate the existence of robust dark-bright-bright (DBB) and dark-dark-bright solitons in a multicomponent F=1 condensate. We observe lifetimes on the order of hundreds of milliseconds for these structures. Our theoretical analysis, based on a multiscale expansion method, shows that small-amplitude solitons of these types obey universal long-short wave resonant interaction models, namely, Yajima-Oikawa systems. Our experimental and analytical findings are corroborated by direct numerical simulations highlighting the persistence of, e.g., the DBB soliton states, as well as their robust oscillations in the trap.

First Observation of Bright Solitons in Bulk Superfluid ^{4}He

The existence of bright solitons in bulk superfluid ^{4}He is demonstrated by time-resolved shadowgraph imaging experiments and density functional theory (DFT) calculations. The initial liquid compression that leads to the creation of nonlinear waves is produced by rapidly expanding plasma from laser ablation. After the leading dissipative period, these waves transform into bright solitons, which exhibit three characteristic features: dispersionless propagation, negligible interaction in a two-wave collision, and direct dependence between soliton amplitude and the propagation velocity. The experimental observations are supported by DFT calculations, which show rapid evolution of the initially compressed liquid into bright solitons. At high amplitudes, solitons become unstable and break down into dispersive shock waves.

Collective Modes of a Soliton Train in a Fermi Superfluid

We characterize the collective modes of a soliton train in a quasi-one-dimensional Fermi superfluid, using a mean-field formalism. In addition to the expected Goldstone and Higgs modes, we find novel long-lived gapped modes associated with oscillations of the soliton cores. The soliton train has an instability that depends strongly on the interaction strength and the spacing of solitons. It can be stabilized by filling each soliton with an unpaired fermion, thus forming a commensurate Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We find that such a state is always dynamically stable, which paves the way for realizing long-lived FFLO states in experiments via phase imprinting.