Soliton States Research Articles

THz frequency combs form dispersion-compensated antenna-coupled ring quantum cascade lasers

We report comb operation of RF injected ring Quantum Cascade Lasers. A coupled waveguide approach is implemented for dispersion compensation while passive bullseye antenna improves the device power extraction and far field. Phase sensitive measurements are presented which hints at the presence of soliton state.

Pattern Formation in One-Dimensional Polaron Systems and Temporal Orthogonality Catastrophe

Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity momentum and interactions. Following an interspecies interaction quench the temporal orthogonality catastrophe is identified, provided that bath-impurity interactions are sufficiently stronger than the intraspecies bath ones, thus generalizing the results of the confined case. This catastrophe originates from the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. For initially moving impurities, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated, resulting in a final polaronic state with reduced velocity. Our results clearly demonstrate the crucial role of non-linear excitations for determining the behavior of the one-dimensional Bose polaron.

Localization and spin dynamics of spin-orbit-coupled Bose-Einstein condensates in deep optical lattices.

We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.

Quantum Dark Solitons in the 1D Bose Gas: From Single to Double Dark-Solitons

We study quantum double dark-solitons, which give pairs of notches in the density profiles, by constructing corresponding quantum states in the Lieb–Liniger model for the one-dimensional Bose gas. Here, we expect that the Gross–Pitaevskii (GP) equation should play a central role in the long distance mean-field behavior of the 1D Bose gas. We first introduce novel quantum states of a single dark soliton with a nonzero winding number. We show them by exactly evaluating not only the density profile but also the profiles of the square amplitude and phase of the matrix element of the field operator between the N-particle and (N−1)-particle states. For elliptic double dark-solitons, the density and phase profiles of the corresponding states almost perfectly agree with those of the classical solutions, respectively, in the weak coupling regime. We then show that the scheme of the mean-field product state is quite effective for the quantum states of double dark solitons. Assigning the ideal Gaussian weights to a sum of the excited states with two particle-hole excitations, we obtain double dark-solitons of distinct narrow notches with different depths. We suggest that the mean-field product state should be well approximated by the ideal Gaussian weighted sum of the low excited states with a pair of particle-hole excitations. The results of double dark-solitons should be fundamental and useful for constructing quantum multiple dark-solitons.

Integrated, Ultra‐Compact High‐Q Silicon Nitride Microresonators for Low‐Repetition‐Rate Soliton Microcombs

AbstractMultiple applications of relevance in photonics, such as spectrally efficient coherent communications, microwave synthesis or the calibration of astronomical spectrographs, would benefit from soliton microcombs operating at repetition rates <50GHz. However, attaining soliton microcombs with low repetition rates using photonic integration technologies represents a formidable challenge. Expanding the cavity volume results in a drop of intracavity intensity that can only be offset by an encompassing rise in quality factor. In addition, reducing the footprint of the microresonator on an integrated circuit requires race‐track designs that typically result into modal coupling losses and disruptions into the dispersion, preventing the generation of the dissipative single soliton state. Here, we report the generation of sub‐50GHz soliton microcombs in dispersion‐engineered silicon nitride microresonators. In contrast to other approaches, the authors' devices feature an optimized racetrack design that minimizes the coupling to higher‐order modes and reduces the footprint size by an order of magnitude to ≈1mm2. The statistical intrinsic Q reaches 19 million, and soliton microcombs at 20.5 and 14.0 GHz repetition rates are successfully generated. Importantly, the fabrication process is entirely subtractive, meaning that the devices can be directly patterned on the silicon nitride film.

Dark discrete breather modes in a monoaxial chiral helimagnet with easy-plane anisotropy

Nonlinearity and discreteness are two pivotal factors for an emergence of discrete breather excitations in various media. We argue that these requirements are met in the forced ferromagnetic phase of the monoaxial chiral helimagnet $\mathrm{Cr}{\mathrm{Nb}}_{3}\mathrm{S}{}_{6}$ due to the specific domain structure of the compound. The stationary, time-periodic breather modes appear as the discrete breather lattice solutions whose period mismatches with a system size. Thanks to easy-plane single-ion anisotropy intrinsic to $\mathrm{Cr}{\mathrm{Nb}}_{3}\mathrm{S}{}_{6}$, these modes are of the dark type with frequencies lying within the linear spin-wave band, close to its bottom edge. They represent cnoidal states of magnetization, similar to the well-known soliton lattice ground state, with differing but limited number of embedded $2\ensuremath{\pi}$ kinks. The linear stability of these dark breather modes is verified by means of Floquet analysis. Their energy, which is controlled by two parameters, namely, the breather lattice period and amplitude, falls off linearly with a growth of the kink number. These results may pave a path to design spintronic resonators on the base of chiral helimagnets.

Breather solitons in AlN microresonators

In this work, we demonstrate the generation of breather solitons in an aluminum nitride (AlN) microresonator. Our study shows different techniques for excitation of breather solitons together with stimulated Raman scattering (SRS) by pumping the fundamental transverse electric (TE00) mode. With suitable pump power and laser scan speed, we can eliminate the Raman effect and achieve a single soliton comb (FSR ∼ 374 GHz) beyond 4/5 of an octave-spanning bandwidth (1200–2100 nm). We have also demonstrated the breather and single soliton (FSR ∼ 364 GHz) states by pumping the first-order TE (TE10) mode using another device with a similar geometry. Our study adds significant development in the dynamics of solitons in the AlN platform.

Stationary optical solitons with Kudryashov's quintuple power–law of refractive index having nonlinear chromatic dispersion

This paper implements extended trial function algorithm to retrieve stationary optical soliton solutions to the governing nonlinear Schrödinger's equation with Kudryashov's lately proposed quintuple power law of refractive index. This studied model comes with nonlinear chromatic dispersion. Both, linear temporal evolution as well as generalized temporal evolution are taken into account.

Sphalerons and resonance phenomenon in kink-antikink collisions

We show that in some kink-antikink (KAK) collisions sphalerons, i.e., unstable static solutions - rather than the asymptotic free soliton states - can be the source of the internal degrees of freedom (normal modes) which trigger the resonance phenomenon responsible for the fractal structure in the final state formation.

Creation of single chiral soliton states in monoaxial helimagnets

In monoaxial helimagnets, the Dzyaloshinskii–Moriya interaction favors inhomogeneous distributions of the magnetization with chiral modulations of solitonic character. In addition to the helical magnetic state at zero field, a chiral soliton lattice can be stabilized when a magnetic field perpendicular to the chiral axis is applied. When the magnetic field is increased, the system undergoes a phase transition to the uniform state at a critical field Bc. Above Bc, a single chiral soliton comprises the lowest level excitation over the stable uniform state, surviving as a metastable configuration. How to retain a single chiral soliton metastable state has not been addressed yet. Using micromagnetic simulations, we analyze this possibility by injecting spin polarized currents and put forward a feasible protocol to obtain a state with a single chiral soliton from the chiral soliton lattice. Our proposal could be relevant in the experimental study of metastable solitons for technological applications.

Transient soliton dynamics in a mode-locked fiber laser: from stationary to pulsation.

We report the experimental observation of the transformation process from a stationary soliton to a pulsating soliton in a mode-locked fiber laser. The detailed soliton dynamics, including soliton parameter changings and sideband variation in the transition, are analyzed by the dispersive Fourier transformation technique. This Letter unveils the great enhancement of intracavity periodic perturbations resulting from the slight increase of soliton intensity induced soliton modulation instability, leading to the occurrence of parametric sidebands and multi-periodic pulsing instability. Our experimental results can shed some light on the intrinsic mechanism of soliton pulsation, as well as contribute to the study of soliton stability and laser dynamics.

Incoherent localized structures and hidden coherent solitons from the gravitational instability of the Schrödinger-Poisson equation.

The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in the framework of the Schrödinger-Poisson (or Newton-Schrödinger) equation accounting for the gravitational interaction. By increasing the amount of nonlinearity, the system self-organizes into a large-scale incoherent localized structure that contains "hidden" coherent soliton states: The solitons can hardly be identified in the usual spatial or spectral domains, but their existence can be unveiled in the phase-space representation (spectrogram). We develop a theoretical approach that provides the coupled description of the coherent soliton component [governed by the Schrödinger-Poisson equation (SPE)] and of the incoherent structure [governed by a wave turbulence Vlasov-Poisson equation (WT-VPE)]. We demonstrate theoretically and numerically that the incoherent structure introduces an effective trapping potential that stabilizes the hidden coherent soliton and we show that the incoherent structure belongs to a family of stationary solutions of the WT-VPE. The analysis reveals that the incoherent structure evolves in the strongly nonlinear regime and that it is characterized by a compactly supported spectral shape. By relating the analytical properties of the hidden soliton to those of the stationary incoherent structure, we clarify the quantum-to-classical (i.e., SPE-to-VPE) correspondence in the limit ℏ/m→0: The hidden soliton appears as the latest residual quantum correction preceding the classical limit described by the VPE. This study is of potential interest for self-gravitating Boson models of fuzzy dark matter. Although we focus our paper on the Schrödinger-Poisson equation, we show that the regime of hidden solitons stabilized by an incoherent structure is general for long-range wave systems featured by an algebraic decay of the interacting potential. This work should stimulate nonlinear optics experiments in highly nonlocal nonlinear (thermal) media that mimic the long-range nature of gravitational interactions.

Dissipative Kerr solitons at the edge state of the Su-Schrieffer—Heeger model

We investigate analytically and numerically dynamics of dissipative Kerr solitons (DKS) at the edge state of the Su-Schrieffer–Heeger model. We demonstrate that four-wave mixing processes can lead to the formation of DKSs in the edge state of the resonator chain which subsequently initiates photon transfer to the bulk states. We discuss how the edge state soliton can be stabilized by limiting its width within the band gap. Our results contribute to advanced dispersion engineering via mode hybridization in chains of resonators — one of promising ways to achieve broadband frequency combs generation on chip.

Many-body dark solitons in one-dimensional hard-core Bose gases

The existence and stability of solitonic states in one-dimensional repulsive Bose-Einstein condensates is investigated within a fully many-body framework by considering the limit of infinite repulsion (Tonks-Girardeau gas). A class of stationary, shape-invariant states propagating at constant velocity are explicitly found and compared to the known solution of the Gross-Pitaevskii equation. The typical features attributed to nonlinearity are thus recovered in a purely linear theory, provided the full many-particle physics is correctly accounted for. However, the formation dynamics predicted by the Gross-Pitaevskii approximation considerably differs from the exact many-body evolution.

Soliton molecules in femtosecond fiber lasers: universal binding mechanism and direct electronic control

Sequences of ultrashort pulses form the basis of extremely precise laser applications ranging from femtosecond spectroscopy, to material microprocessing, to biomedical imaging. Dynamic patterns of temporal solitons—termed “soliton molecules”—inside mode-locked cavities provide yet unexplored means for generating reconfigurable arrangements of ultrashort pulses. Here, we demonstrate the external control of solitonic bound states in widespread erbium-doped fiber lasers via direct electronic modulation of the semiconductor pump source. This straightforward approach allows for switching between discrete soliton doublet states of picosecond separations, employing and relying on laser-intrinsic soliton interactions. We analyze the externally induced dynamics based on real-time switching data acquired by time-stretch dispersive Fourier transform spectroscopy and identify a universal bound-state formation mechanism different from broadly considered models. Owing to the ease of implementation and its intrinsic tunability, our control scheme is readily applicable to various laser platforms enabling, e.g., rapid multipulse measurements and tailored nonlinear light–matter interactions.

Temporal dissipative structures in optical Kerr resonators with transient loss fluctuation.

Dissipative structures are the result of spontaneous symmetry breaking in a dynamic open system, which is induced by either the nonlinear effect or loss fluctuations. While optical temporal dissipative solitons in nonlinear Kerr cavities has been widely studied, their operation is limited to the red-detuned regime. Here, we demonstrate an emergent dissipative soliton state in optical nonlinear cavities in the presence of loss fluctuations, which is accessible by self-evolution of the system on resonance. Based on a modified dissipative and Kerr-nonlinear cavity model, we numerically investigate the effect of the loss modulation on the intracavity field pattern, and in transmission observe a single and bright soliton pulse state at the zero detuning. The effect of the optical saturable absorption is also numerically investigated, which is recognized as an effective approach to the transient loss fluctuation in the cavity. The estimated power efficiency of the resonant bright soliton can be higher than that of the conventional dissipative Kerr soliton, which is determined by the loss modulation depth and the pump intensity. The self-starting soliton state on system's resonance is potentially of wide interest, which physically contributes to insights of the temporal structure formation in dissipative cavities. On application aspect, it may constitute a way to the generation of ultra-fast soliton pulse trains as well as the generation of soliton micro-combs.

Multifrequency Solitons in Commensurate-Incommensurate Photonic Moiré Lattices.

We predict that photonic moiré patterns created by two mutually twisted periodic sublattices in quadratic nonlinear media allow the formation of parametric solitons under conditions that are strongly impacted by the geometry of the pattern. The question addressed here is how the geometry affects the joint trapping of multiple parametrically coupled waves into a single soliton state. We show that above the localization-delocalization transition the threshold power for soliton excitation is drastically reduced relative to uniform media. Also, the geometry of the moiré pattern shifts the condition for phase matching between the waves to the value that matches the edges of the eigenmode bands, thereby shifting the properties of all soliton families. Moreover, the phase-mismatch bandwidth for soliton generation is dramatically broadened in the moiré patterns relative to latticeless structures.

Quantum limited timing jitter of soliton molecules in a mode-locked fiber laser.

Soliton molecules in mode-locked lasers are expected to be ideal self-organization patterns, which warrant stability and robustness against perturbations. However, recent ultra-high resolution optical cross-correlation measurements uncover an intra-molecular timing jitter, even in stationary soliton molecules. In this work, we found that the intra-molecular timing jitter has a quantum origin. Numerical simulation indicates that amplified spontaneous emission (ASE) noise induces a random quantum diffusion for soliton pulse timing, which cannot be compensated by soliton binding mechanism. By suppressing indirectly coupled timing jitter at close-to-zero cavity dispersion, a record-low 350 as rms intra-soliton-molecular jittering is obtained from an Er-fiber laser in experiment. This work provides insight into the fundamental limits for the instability of multi-soliton patterns.

Autosetting soliton pulsation in a fiber laser by an improved depth-first search algorithm.

Soliton pulsation is one of the most fascinating phenomena in ultrafast fiber lasers, owing to its rich nonlinear dynamics and potential generation of high peak power pulse. However, it is still a challenge to efficiently search for pulsating soliton in fiber lasers because it requires a fine setting of laser cavity parameters. Here, we report the autosetting soliton pulsation in a passively mode-locked fiber laser. The parameters of electronic polarization controller are intelligently adjusted to search for pulsating soliton state by the improved depth-first search algorithm. Moreover, the intensity modulation depth of pulsating soliton could be flexibly controlled. These findings indicate that the intelligent control of a fiber laser is an effective way to explore on-demand soliton dynamics and is also beneficial to the optimization of ultrafast laser performance.

Stationary Hermite-Gaussian solitons and their control for nonlinear Schrödinger equation with complex potential

We report stationary Hermite-Gaussian (HG) solitons for nonlinear Schrödinger equation with complex potential. It is found that complex potential exhibits parity-time (PT) symmetry property for specific choice of gain function and corresponding solutions are quite stable compared to the one for non-PT potential. Our exact analysis takes recourse to construct one parameter family of complex potentials using isospectral Hamiltonian approach and thus enabling one to control the behaviour of HG solitons.