Compact Solitons Research Articles

Towards a compact soliton microcomb fully referenced on atomic reference

Towards a compact soliton microcomb fully referenced on atomic reference

The Heterotic-Ricci Flow and Its Three-Dimensional Solitons

We introduce a novel curvature flow, the Heterotic-Ricci flow, as the two-loop renormalization group flow of the Heterotic string common sector and study its three-dimensional compact solitons. The Heterotic-Ricci flow is a coupled curvature evolution flow, depending on a non-negative real parameter κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}, for a complete Riemannian metric and a three-form H on a manifold M. Its most salient feature is that it involves several terms quadratic in the curvature tensor of a metric connection with skew-symmetric torsion H. When κ=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa = 0$$\\end{document} the Heterotic-Ricci flow reduces to the generalized Ricci flow and hence it can be understood as a modification of the latter via the second-order correction prescribed by Heterotic string theory, whereas when H=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H=0$$\\end{document} and κ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa >0$$\\end{document} the Heterotic-Ricci flow reduces to a constrained version of the RG-2 flow and hence it can be understood as a generalization of the latter via the introduction of the three-form H. Solutions of Heterotic supergravity with trivial gauge bundle, which we call Heterotic solitons, define a particular class of three-dimensional solitons for the Heterotic-Ricci flow and constitute our main object of study. We prove a number of structural results for three-dimensional Heterotic solitons, obtaining, in particular, the complete classification of compact three-dimensional strong Heterotic solitons as hyperbolic three-manifolds or quotients of the Heisenberg group equipped with a left-invariant metric. Furthermore, we prove that all Einstein three-dimensional Heterotic solitons have constant dilaton and leave as open the construction of a Heterotic soliton with non-constant dilaton. In this direction, we prove that Einstein Heterotic solitons with constant dilaton are rigid and therefore cannot be deformed into a solution with non-constant dilaton. This is, to the best of our knowledge, the first rigidity result for compact supergravity solutions in the literature.

Compact gap solitons and compact edge states of exciton–polariton condensates with spin–orbit coupling in a one-dimensional flatband lattice

We propose that the compact gap solitons and compact edge states can be excited in a flatband of the incoherently-pumped exciton–polariton condensate under a one-dimensional periodic potential lattice. The combined effects of spin–orbit coupling and periodic potential depth on the flatband structures are investigated. Then how the compact gap solitons and edge states are localized and extended inside only a fraction of a single lattice site will be studied with varying pump strengths, pump spot-sizes as well as energy detuning.

Q-capacitor formulation of the ℂPN nonlinear sigma model

A multi-component ℂPN model’s scalar electrodynamics is investigated. The model contains Q-balls/shells, which are non-topological compact solitons with time dependency eiωt . Because of the compacton nature of solutions, Q-shells with another compact Q-ball or Q-shell inside their cavity can exist. Even if compactons do not overlap, they can interact with one another via the electromagnetic field. They look similar to the capacitor in the standard electromagnetism. We focus on the structure of such Q-capacitor with opposite charges.

Photorefraction‐Assisted Self‐Emergence of Dissipative Kerr Solitons

AbstractGenerated in high‐Q optical microresonators, dissipative Kerr soliton microcombs constitute broadband optical frequency combs with chip sizes and repetition rates in the microwave to millimeter‐wave range. For frequency metrology applications such as spectroscopy, optical atomic clocks, and frequency synthesizers, octave‐spanning soliton microcombs generated in dispersion‐optimized microresonators are required, which allow self‐referencing for full frequency stabilization. In addition, field‐deployable applications require the generation of such soliton microcombs to be simple, deterministic, and reproducible. Here, a novel scheme to generate self‐emerging solitons in integrated lithium‐niobate microresonators is demonstrated. The single soliton features a broadband spectral bandwidth with dual dispersive waves, allowing 2f–3f self‐referencing. Via harnessing the photorefractive effect of lithium niobate to significantly extend the soliton existence range, a spontaneous yet deterministic single‐soliton formation is observed. The soliton is immune to external perturbation and can operate continuously for over 13 h without active feedback control. Finally, via integration with a pre‐programmed distributed feedback (DFB) laser, turnkey soliton generation is demonstrated. With further improvement of microresonator Q and hybrid integration with chip‐scale laser chips, compact soliton microcomb devices with electronic actuation can be created, which can become central elements for future LiDAR, microwave photonics, and optical telecommunications.

Supercontinuum generation in As2S3 chalcogenide waveguide pumped by all-fiber structured dual-femtosecond solitons.

Supercontinuum sources with high compactness are essential for applications such as optical sensing, airborne detection and communication systems. In the past decades, the adoption of bulky optical parametric amplifier to pump various chalcogenide glass waveguides are widely reported for on-chip mid-infrared supercontinuum generation, but this usually leads to a large volume of the whole system, and is not practical. Therefore, integrating advanced femtosecond fiber lasers with optical waveguides using nano-fabrication technology are highly desired. However, the scarcity of compact pump sources and the dispersion-matched high-nonlinearity waveguide in short wavelength regions have hindered the advancement of integrated supercontinuum source performances in the near and mid-infrared region. In this study, we demonstrate a broadband supercontinuum source from As2S3 waveguide pumped by a compact dual-femtosecond solitons pulse source. The laser is completely fiber structured, and its wavelength can be readily tuned from 2 to 2.3 µm using Raman soliton self-frequency shift technology in a Tm3+-doped fiber amplifier. Furthermore, the As2S3 waveguide is designed with controllable dispersion and high nonlinearity for a broadband supercontinuum generation. These results will advance the development of on-chip supercontinuum sources based on chalcogenide waveguides.

Ell -convex Legendre curves and geometric inequalities

In this paper we consider ell -convex Legendre curves, which are natural generalizations of strictly convex curves. We generalize various optimal geometric inequalities, isoperimetric inequality, Bonnesen’s inequality and Green–Osher inequality, for strictly convex curves to ones for ell -convex Legendre curves. Moreover we generalize the inverse curvature curve flow for this class of Legendre curves and prove that it always converges to a compact soliton after rescaling. Unlike in the class of regular curves, there are infinitely many compact solitons, which include circles and astroids.

Self‐Starting Switchable Multifunctional Solitons Fiber Laser

Modern solitons fiber lasers systems sought for imaging, micromachining, metrology, spectroscopy, and sensing applications, require multifunctional light sources with fully controlled switching features to avail the necessary optical signal. Existing single cavity fiber laser systems have limitations on the generation of multistate solitons due to the intrinsic dispersion, nonlinearity, filtering, gain, and loss. Herein, for the very first time, a compact multifunctional solitons fiber laser controlled by the 3D maneuvering of the polarization beam splitter (PBS) to select the appropriate polarization state for various mode‐locked operations is demonstrated. For single soliton state operation, conventional solitons (CSs), quasi‐coherent noise‐like pulses (QC‐NLPs) and harmonic mode‐locking (HML) are achieved independently, and these different states can be easily and efficiently switched by steering the PBS position. Versatile hybrid dual‐wavelength mode‐locked operations (2‐CSs states, 1‐CS state and 1‐QC‐NLP state, and 2‐QC‐NLPs states) are additional functionalities achievable when the PBS position is steered to suitable positions. The hybrid dual‐wavelength mode‐locked operation has excellent long‐term stability even functioning at maximum output power. It is envisaged that the proposed work provides a compact switchable multifunctional solitons fiber laser system that can be potentially applied in optics signal processing, micromachining, spectroscopy, and optical sensing, etc.

Triviality results for compact k-Yamabe solitons

In this paper, we show that any compact gradient k-Yamabe soliton must have constant σk-curvature. Moreover, we provide a certain condition for a compact k-Yamabe soliton to be gradient.

Wave dark matter and ultra-diffuse galaxies

ABSTRACT Dark matter (DM) as a Bose–Einstein condensate, such as the axionic scalar field particles of String Theory, can explain the coldness of DM on large scales. Pioneering simulations in this context predict a rich wave-like structure, with a ground state soliton core in every galaxy surrounded by a halo of excited states that interfere on the de Broglie scale. This de Broglie scale is largest for the low-mass galaxies as momentum is lower, providing a simple explanation for the wide cores of dwarf spheroidal galaxies. Here we extend these ‘wave dark matter’ (ψDM) predictions to the newly discovered class of ‘ultra-diffuse galaxies’ (UDG) that resemble dwarf spheroidal galaxies but with more extended stellar profiles. Currently, the best-studied example, ‘Dragon Fly 44’ (DF44), has a uniform velocity dispersion of ≃33 km s−1, extending to at least 3 kpc, that we show is reproduced by our ψDM simulations with a soliton radius of ≃0.5 kpc. In the ψDM context, we show that relatively flat dispersion profile of DF44 lies between massive galaxies with compact dense solitons, as may be present in the Milky Way on a scale of 100 pc and lower mass galaxies where the velocity dispersion declines centrally within a wide, low-density soliton, like Antlia II, of radius 3 kpc.

Precision Measurement Noise Asymmetry and Its Annual Modulation as a Dark Matter Signature

Dark matter may be composed of self-interacting ultralight quantum fields that form macroscopic objects. An example of which includes Q-balls, compact non-topological solitons predicted by a range of theories that are viable dark matter candidates. As the Earth moves through the galaxy, interactions with such objects may leave transient perturbations in terrestrial experiments. Here we propose a new dark matter signature: an asymmetry (and other non-Gaussianities) that may thereby be induced in the noise distributions of precision quantum sensors, such as atomic clocks, magnetometers, and interferometers. Further, we demonstrate that there would be a sizeable annual modulation in these signatures due to the annual variation of the Earth velocity with respect to dark matter halo. As an illustration of our formalism, we apply our method to 6 years of data from the atomic clocks on board GPS satellites and place constraints on couplings for macroscopic dark matter objects with radii R<104km, the region that is otherwise inaccessible using relatively sparse global networks.

Classification of Generalized Kähler‐Ricci Solitons on Complex Surfaces

AbstractUsing toric geometry we give an explicit construction of the compact steady solitons for pluriclosed flow first constructed in by the first author in 2019. This construction also reveals that these solitons are generalized Kähler in two distinct ways, with vanishing and nonvanishing Poisson structure. This gives the first examples of generalized Kähler structures with nonvanishing Poisson structure on nonstandard Hopf surfaces, completing the existence question for such structures. Moreover, this gives a complete answer to the existence question for generalized Kähler‐Ricci solitons on compact complex surfaces. In the setting of generalized Kähler geometry with vanishing Poisson structure, we show that these solitons are unique. We show that these solitons are global attractors for the generalized Kähler‐Ricci flow among metrics with maximal symmetry. © 2020 Wiley Periodicals LLC

On Traveling Waves of the Nonlinear Schrödinger Equation Escaping a Potential Well

In this paper, we consider the NLS equation with focusing nonlinearities in the presence of a potential. We investigate the compact soliton motions that correspond to a free soliton escaping the well created by the potential. We exhibit the dynamical system driving the exiting trajectory and construct associated nonlinear dynamics for untrapped motions. We show that the nature of the potential/soliton is fundamental, and two regimes may exist: one where the tail of the potential is fat and dictates the motion, and one where the tail is weak and the soliton self-interacts with the potential defects, hence leading to different motions.

Chip-based soliton microcomb module using a hybrid semiconductor laser

Photonic chip-based soliton microcombs have shown rapid progress and have already been used in many system-level applications. There has been substantial progress in realizing soliton microcombs that rely on compact laser sources, culminating in devices that only utilize a semiconductor gain chip or a self-injection-locked laser diode as the pump source. However, generating single solitons with electronically detectable repetition rates from a compact laser module has remained challenging. Here we demonstrate a current-initiated, Si3N4 chip-based, 99-GHz soliton microcomb driven directly by a compact, semiconductor-based laser. This approach does not require any complex soliton tuning techniques, and single solitons can be accessed by tuning the laser current. Further, we demonstrate a generic, simple, yet reliable, packaging technique to facilitate the fiber-chip interface, which allows building a compact soliton microcomb package that can benefit from the fiber systems operating at high power (> 100 mW). Both techniques can exert immediate impact on chip-based nonlinear photonic applications that require high input power, high output power, and interfacing chip-based devices to mature fiber systems.

Real-time temporal-spectral analysis of complex dynamics involving multiple soliton states in a dual-wavelength passively mode-locked fiber ring laser

We present an experimental study of complex dissipative solitons dynamics in a passively mode-locked fiber ring laser. Recently, thanks to real-time spectroscopy techniques such as the dispersive Fourier transform (DFT), it has been possible to study the complex internal dynamics of soliton molecules. However, most of the works have been limited to the study of intermolecular or intramolecular dynamics involving a small number of solitons within a single compact soliton packet, to which the DFT technique applies naturally. In this work, we study the dynamics of complex arrangements of multiple solitons, extending the analysis to regimes where multiple soliton packets at different wavelengths coexist and interact in the cavity, probing simultaneously the internal dynamics of various short-lived soliton molecules, as well as the collective dynamics of the different soliton packets distributed in the cavity, all of which is made possible by simultaneous analysis in the temporal and spectral domains. This allows to relate temporal dynamics at different time scales, as well as temporal and spectral events. In particular, we report the experimental observation of the dynamics of the Kelly sidebands that flank the soliton spectra, and relate it to temporal and spectral events such as extinctions of soliton packets with pulsating amplitude, spectral narrowing, and with energy fluctuations.

Classification of solitons for pluriclosed flow on complex surfaces

We give a classification of compact solitons for the pluriclosed flow on complex surfaces. First, by exploiting results from the Kodaira classification of surfaces, we show that the complex surface underlying a soliton must be Kahler except for the possibility of steady solitons on minimal Hopf surfaces. Then, we construct steady solitons on all class 1 Hopf surfaces by exploiting a symmetry ansatz.

On complete Finslerian Yamabe solitons

Here it is shown that any Finslerian compact Yamabe soliton with bounded above scalar curvature is of constant scalar curvature. Furthermore, this extension of Yamabe solitons is developed for inequalities and among the others, it is proved that a forward complete non-compact shrinking Yamabe soliton has finite fundamental group and its first cohomology group vanishes, providing the scalar curvature is strictly bounded above.

Evolution of the Steklov eigenvalue under geodesic curvature flow

On a two-dimensional compact Riemannian manifold with boundary, we prove that the first nonzero Steklov eigenvalue is nondecreasing along the unnormalized geodesic curvature flow if the initial metric has positive geodesic curvature and vanishing Gaussian curvature. Using the normalized geodesic curvature flow, we also obtain some estimate for the first nonzero Steklov eigenvalue. On the other hand, we prove that the compact soliton of the geodesic curvature flow must be the trivial one.

Gravitational wave emission from collisions of compact scalar solitons

We numerically investigate the gravitational waves generated by the head-on collision of equal-mass, self-gravitating, real scalar field solitons (oscillatons) as a function of their compactness $\mathcal{C}$. We show that there exist three different possible outcomes for such collisions: (1) an excited stable oscillaton for low $\mathcal{C}$, (2) a merger and formation of a black-hole for intermediate $\mathcal{C}$, and (3) a pre-merger collapse of both oscillatons into individual black-holes for large $\mathcal{C}$. For (1), the excited, aspherical oscillaton continues to emit gravitational waves. For (2), the total energy in gravitational waves emitted increases with compactness, and possesses a maximum which is greater than that from the merger of a pair of equivalent mass black-holes. The initial amplitudes of the quasi-normal modes in the post-merger ring-down in this case are larger than that of corresponding mass black-holes -- potentially a key observable to distinguish black-hole mergers with their scalar mimics. For (3), the gravitational wave output is indistinguishable from a similar mass, black-hole--black-hole merger.

Strong Gravitational Lensing by Wave Dark Matter Halos

Abstract Wave dark matter (WaveDM) has recently gained attention as a viable candidate to account for the dark matter content of the universe. In this paper we explore the extent to which, and under what conditions, dark matter halos in this model are able to reproduce strong-lensing systems. First, we explore analytically the lensing properties of the model, finding that a pure WaveDM density profile, the soliton profile, produces a weaker lensing effect than similar cored profiles. Then, we analyze models with a soliton embedded within a Navarro, Frenk, and White (NFW) profile, as has been found in numerical simulations of structure formation. We use a benchmark model with a boson mass of m a = 10−22 eV, for which we see that there is a bimodality in the contribution of the external NFW part of the profile, and some of the free parameters associated with it are not well constrained. We find that for configurations with boson masses 10−23 to 10−22 eV, a range of masses preferred by dwarf galaxy kinematics, the soliton profile alone can fit the data, but its size is incompatible with the luminous extent of the lens galaxies. Likewise, boson masses of the order of 10−21 eV, which would be consistent with Lyα constraints and consist of more compact soliton configurations, necessarily require the NFW part in order to reproduce the observed Einstein radii. We then conclude that lens systems impose a conservative lower bound m a > 10−24 eV and that the NFW envelope around the soliton must be present to satisfy the observational requirements.