Soliton Tunneling Research Articles

Nonlinear-Optical Analogies in Nuclear-Like Soliton Reactions: Selection Rules, Nonlinear Tunneling and Sub-Barrier Fusion–Fission

Abstract The main goal of our study is to reveal unexpected but intriguing analogies arising between optical solitons and nuclear physics, which still remain hidden from us. We consider the main cornerstones of the concept of nonlinear optics of nuclear reactions and the well-dressed repulsive-core solitons. On the base of this model, we reveal the most intriguing properties of the nonlinear tunneling of nucleus-like solitons and the soliton self-induced sub-barrier transparency effect. We describe novel interesting and stimulating analogies between the interaction of nucleus-like solitons on the repulsive barrier and nuclear sub-barrier reactions. The main finding of this study concerns the conservation of total number of nucleons (or the baryon number) in nuclear-like soliton reactions. We show that inelastic interactions among well-dressed repulsive-core solitons arise only when a “cloud” of “dressing” spectral side-bands appears in the frequency spectra of the solitons. This property of nucleus-like solitons is directly related to the nuclear density distribution described by the dimensionless small shape-squareness parameter. Thus the Fourier spectra of nucleus-like solitons are similar to the nuclear form factors. We show that the nuclear-like reactions between well-dressed solitons are realized by “exchange” between “particle-like” side bands in their spectra.

Quantum transport of charge density wave electrons in layered materials

The charge density wave (CDW) is a condensate that often forms in layered materials. It is known to carry electric current en masse, but the transport mechanism remains poorly understood at the microscopic level. Its quantum nature is revealed by several lines of evidence. Experiments often show lack of CDW displacement when biased just below the threshold for nonlinear transport, indicating the CDW never reaches the critical point for classical depinning. Quantum behavior is also revealed by oscillations of period h/2e in CDW conductance vs. magnetic flux, sometimes accompanied by telegraph-like switching, in TaS3 rings above 77 K. Here we discuss further evidence for quantum CDW electron transport. We find that, for temperatures ranging from 9 to 474 K, CDW current-voltage plots of three trichalcogenide materials agree almost precisely with a modified Zener-tunneling curve and with time-correlated soliton tunneling model simulations. In our model we treat the Schrödinger equation as an emergent classical equation that describes fluidic Josephson-like coupling of paired electrons between evolving topological states. We find that an extension of this ‘classically robust’ quantum picture explains both the h/2e magnetoconductance oscillations and switching behavior in CDW rings. We consider potential applications for thermally robust quantum information processing systems.

Controlled generation of soliton spectral tunneling by double pulses injection.

Numerical simulations of a simple and direct method to generate soliton spectral tunneling (SST) based on two input pulses are reported in the paper. An intense pump pulse and a weak probe pulse with a time delay are transmitted in a photonic crystal fiber with three zero-dispersion wavelengths. Our results demonstrate that the distance and the state of soliton tunneling are obviously influenced by the probe-pump delay. Therefore, the velocity and efficiency of SST can be effectively regulated by varying the relative time delay, thus affecting the SST formation. This scenario appears promising for designing a "soliton ejector", in which real-time control of the soliton ejection process can be achieved through phase modulation between pulses.

Quantum tunneling of three-spine solitons through excentric barriers

Macromolecular protein complexes catalyze essential physiological processes that sustain life. Various interactions between protein subunits could increase the effective mass of certain peptide groups, thereby compartmentalizing protein α-helices. Here, we study the differential effects of applied massive barriers upon the soliton-assisted energy transport within proteins. We demonstrate that excentric barriers, localized onto a single spine in the protein α-helix, reflect or trap three-spine solitons as effectively as concentric barriers with comparable total mass. Furthermore, wider protein solitons, whose energy is lower, require heavier massive barriers for soliton reflection or trapping. Regulation of energy transport, delivery and utilization at protein active sites could thus be achieved through control of the soliton width, or of the effective mass of the protein subunits.

Coherent, time-correlated tunneling of density wave electrons

A growing body of evidence reveals that charge density wave (CDW) transport is a high-temperature cooperative quantum phenomenon. According to the time-correlated soliton tunneling (ST) model, quantum solitons, or electron-phonon correlates within the CDW condensate, act much like electrons tunneling through a Coulomb-blockade tunnel junction. Pair creation of charged fluidic soliton droplets is prevented by their electrostatic energy below a Coulomb-blockade threshold electric field. Above threshold, the quantum fluid flows in a periodic fashion, via a hybrid between Zener-like and coherent Josephson-like tunneling. We summarize the time-correlated ST model and compare model simulations with experiment. The ST model shows excellent agreement with coherent voltage oscillations, and with CDW current-voltage characteristics. Finally, we discuss implications for physics and potential applications.

Generation of mid-infrared supercontinuum by designing circular photonic crystal fiber

A circular photonic crystal fiber (C-PCF) based on As2Se3 is designed, which has three zero dispersion wavelengths and flat dispersion. Using this fiber, a wide mid-infrared supercontinuum (MIR-SC) can be generated by launching a femtosecond pulse in the first anomalous dispersion region. The simulation results show that the MIR-SC is formed by soliton self-frequency shift and direct soliton spectrum tunneling on the long wavelength side and self-phase modulation, soliton fission on the short wavelength side. Further, optical shocking and four-wave mixing (FWM) are not conducive to the long-wavelength extension of MIR-SC, while the number and intensity of fundamental solitons have a greater effect on the short-wavelength extension of MIR-SC. The generation of optical shocking waves, FWM waves and fundamental solitons can be obviously affected by changing the fiber length and input pulse parameters, so that the spectrum range and flatness can be adjusted with great freedom. Finally, under the conditions of 4000 W pulse peak power, 30 fs pulse width, 47 mm fiber length, and 0 initial chirp, a wide MIR-SC with a coverage range of 2.535 μm–16.6 μm is obtained. These numerical results are encouraging because they demonstrate that the spread of MIR-SC towards the red and blue ends can be manipulated by choosing the appropriate incident pulse and designing optimized fiber parameters, which contributes to applications in such diverse areas as spectroscopy, metrology and tomography.

Nonlinear tunneling of solitons in a variable coefficients nonlinear Schrödinger equation with $$\mathscr {PT}$$-symmetric Rosen–Morse potential

Nonlinear tunneling of solitons in a variable coefficients nonlinear Schrödinger equation with $$\mathscr {PT}$$-symmetric Rosen–Morse potential

Quantum fluidic charge density wave transport

We discuss charge density wave transport as the periodic flow of a quantum fluid of electron–phonon correlates, viewed as quantum solitons, within the condensate. Pair creation of charged soliton droplets is prevented by their electrostatic energy below a Coulomb-blockade threshold electric field. Above threshold, the quantum fluid flows in drip-like fashion as microscopic entities tunnel coherently from one charging energy macrostate to the next. We summarize the time-correlated soliton tunneling model and compare simulations of coherent oscillations, narrow band noise, and current–voltage characteristics with experiment. We also explore the possibility of collective quantum behavior at room temperature in some materials. Finally, we discuss potential applications in quantum information processing.

Design of photonic crystal fibers with flat dispersion and three zero dispersion wavelengths for coherent supercontinuum generation in both normal and anomalous regions

A photonic crystal fiber (PCF) structure with three-zero dispersion wavelengths (ZDWs) and a flat dispersion curve was designed by adjusting the structural parameters (the diameters of small air holes inserted between standard lattices in the first and third rings) and fiber core size to obtain the required shape, number of extreme points and the dynamic range of waveguide dispersion (Dw) curve. A quantitative method which was realized by fixing the positions of the ZDWs and tailoring different dispersion slopes was proposed to design another PCF with the same ZDWs and a slightly larger dispersion slope. Both of the designed PCFs were used for contrast experiments of supercontinuum (SC) generation. The simulation results show that the flat dispersion can produce the coherent SC in both normal and anomalous dispersion regions for the designed two PCFs. The degree of flatness and the wavelength range of coherent SC are determined by the great time-domain compression due to the direct soliton spectrum tunneling (DSST) resulting from the mismatch between self-phase modulation and gradually decreasing dispersion. A wide, flat, and coherent SC with a wavelength range of 1281–2200 nm and power range of −14.8 ~ −9.4 dB was obtained for the PCF with flatter dispersion by pumping in the anomalous dispersion region with 50 fs incident pulse. This study is instructive for PCF design in different application scenarios and finds a new way for the generation of wide flat coherent spectrum.

Periodic oscillations and nonlinear tunneling of soliton for Hirota-MB equation in inhomogeneous fiber

Under investigation in this paper is an inhomogeneous Hirota-Maxwell Bloch equation, which describes the propagation of optical soliton inhomogeneous fiber. For considered equation, corresponding Lax pair is constructed. Via the Darboux transformation method and symbolic computation, one and two soliton solutions are attained. For obtained one soliton solution, nonlinear tunneling of soliton through dispersion barrier on exponential background have been discussed. Using obtained two soliton solutions, periodic oscillation of solitons and their interactions are studied. Especially, soliton fission from the merged two solitons is observed which can be used to construct the soliton based ultrafast switching. Influence of the variable coefficients and erbium on the soliton solutions are analyzed. By keeping third order dispersion as periodic function and other coefficients are consider as constants, collision less propagation also have been discussed. We hope that our analytical results will be helpful to understand the soliton tunneling and periodic oscillation in an inhomogeneous erbium doped fiber experimentally.

Optical event horizon-based complete transformation and control of dark solitons.

We propose a manipulation approach to vary the wave speed, as well as the grayness, of dark solitons under the optical event horizon arising from the interaction between a dark soliton and a probe wave. To the best of our knowledge, the optical event horizon effect is demonstrated for the first time to be capable of inducing a reversible conversion between a black soliton and a gray one. This reversible soliton transformation and control process originates from the intrinsic competition between the probe-induced nonlinear phase shift and the internal phase of the dark soliton. In a cascaded system consisting of two optical event horizons, we also observe the new optical soliton tunneling phenomena where a dark soliton can be reset longitudinally purposely. The results may find applications in information cloaking such as effectively hiding the presence of intermediate fiber section to the receiver.

Hydrodynamic optical soliton tunneling.

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

Black and gray soliton interactions and cascade compression in the variable coefficient nonlinear Schrödinger equation

We present the theoretical study of dark soliton dynamics in inhomogeneous fiber system by means of a variable coefficient nonlinear Schrödinger equation (Vc-NLSE). The dark soliton interaction in the dispersion-managed system with gain/loss and cascade compression of solitons by the nonlinear tunneling phenomena are studied in detail. Numerically, we study the dark soliton propagation in the continuous wave background, and the obtained soliton solution is found to be robust against perturbations. The elastic collision behavior of the dark solitons are observed by means of asymptotic analysis. For better insight, we study the impact of the blackness factor in the phase profile and also on the interaction dynamics of the different dark soliton settings, such as black and gray soliton. Additionally, we extend the study to the investigation of tunneling of the dark soliton across the barrier/well with a particular emphasize on the role of blackness parameter in the nonlinear tunneling phenomena, and demonstrated a cascaded compression of soliton in the inhomogeneous system.

Schrödinger solitons in gravitational-like potentials with embedded barriers and wells: Possible applications for the optical soliton supercontinuum generation and the ocean coast line protection

Inspirited by many remarkable but, obviously, only formal analogies appearing within the framework of the nonlinear Schrödinger equation model from nonlinear femtosecond optics, Bose–Einstein condensates and plasmas, to ocean extreme waves and hurricanes, we conclude that these important mathematical parallels offer novel possibilities to perform “optic hydrodynamics” experiments in the nonlinear fiber-optics systems. Specifically, we present the results of the wide-range computer experiments of the soliton dynamics in the external gravitational-like potentials with embedded barriers and wells. We show that the external gravitational-like potential adds significant new physics both to the nonlinear soliton tunneling through classically forbidden potential barriers and to the solitonic analog of the quantum-mechanical Ramsauer–Townsend effect. The main special feature of a soliton in the external gravitational-like potential lies in the fact that its velocity is no longer constant, but depends linearly on time. This soliton acceleration changes dramatically the wave-particle duality of a soliton giving rise, by virtue of the Galilean symmetry, the appearance of its own solitonic analog of the “accelerating de Broglie wavelength”. Guided by this constructive (but obviously only formal) analogy, we reveal the hidden role of the soliton self-interaction (binding) energy both for the soliton nonlinear tunneling and the solitonic nonlinear analog of the Ramsauer–Townsend effect in the effective gravitational-like external potentials with superimposed barriers and wells.

Ultrashort dark solitons interactions and nonlinear tunneling in the modified nonlinear Schrödinger equation with variable coefficient

Abstract We present the study of the dark soliton dynamics in an inhomogeneous fiber by means of a variable coefficient modified nonlinear Schrodinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. The ultrashort dark soliton pulse evolution and interaction is studied by using the Hirota bilinear (HB) method. In particular, we give much insight into the effect of self-steepening (SS) on the dark soliton dynamics. The study reveals a shock wave formation, as a major effect of SS. Numerically, we study the dark soliton propagation in the continuous wave background, and the stability of the soliton solution is tested in the presence of photon noise. The elastic collision behaviors of the dark solitons are discussed by the asymptotic analysis. On the other hand, considering the nonlinear tunneling of dark soliton through barrier/well, we find that the tunneling of the dark soliton depends on the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or valley and retains its shape after the tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well.

Longitudinal soliton tunneling in optical fiber.

We report the observation of the longitudinal soliton tunneling effect in axially varying optical fibers. A fundamental soliton, initially propagating in the anomalous dispersion region of a fiber, can pass through a normal dispersion barrier without being substantially affected. We perform experimental studies by means of spectral and temporal characterizations that show the evidence of the longitudinal soliton tunneling process. Our results are well supported by numerical simulations using the generalized nonlinear Schrödinger equation.

Landau-Zener tunneling of solitons.

We consider Landau-Zener tunneling of solitons in a weakly coupled two-channel system, for this purpose we construct a simple mechanical system using two weakly coupled chains of nonlinear oscillators with gradually decreasing (first chain) and increasing (second chain) masses. The model allows us to consider soliton propagation and Landau-Zener tunneling between the chains. It is shown that soliton tunneling characteristics become drastically dependent on its amplitude in nonlinear regime. The validity of the developed tunneling theory is justified via comparison with direct numerical simulations on oscillator ladder system.

Influence of generalized external potentials on nonlinear tunneling of nonautonomous solitons: Soliton management

Soliton control and management using generalized external potentials in an inhomogeneous fiber to the design of high speed optical devices and ultrahigh capacity transmission systems are investigated based on solving the variable-coefficient generalized nonautonomous nonlinear Schrödinger equation with the help of symbolic computation. We construct Lax pair for GNLS equation by means of AKNS method and two soliton solutions are obtained by virtue of the Darboux transformation. With symbolic computation, we manipulate the control parameters and external potentials to investigate the propagation behaviors of nonautonomous solitons. Moreover, the main evolution features of obtained two soliton solutions are exposed by some interesting figures through computer simulation. Especially, we analyze the influence of external potentials such as periodic, exponential and parabolic potential on soliton propagation. Finally, soliton propagation under the absence (vanishing) of external potential is also discussed. Obtained results confirmed that external potentials has strong influence on the soliton dynamics. Our results might provide a new method to achieve the soliton pulse compression while they passing through the potential barrier or well under the influence of external potentials.

Hidden possibilities in soliton switching through tunneling in erbium doped birefringence fiber with higher order effects

In this paper, coupled higher order nonlinear Schrödinger–Maxwell–Bloch equations are studied for the ultrashort pulse propagation in erbium-doped birefringent fiber system. Lax pair is constructed for the CHNLS–MB system. Through the Darboux method and symbolic computation, analytic two-soliton solution is obtained. To analyze the specific problem, we design an optimal system by properly choosing the special form of variable coefficients. Here, using obtained two-soliton solution, tunneling of femtosecond soliton through barrier and well is investigated. While solitons are passing through barrier and well, some unexpected behavior is observed and hidden possibilities in switching action through tunneling is investigated.

Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation

We investigated the soliton solution for N coupled nonlinear Schrödinger (CNLS) equations. These equations are coupled due to the cross-phase-modulation (CPM). Lax pair of this system is obtained via the Ablowitz–Kaup–Newell–Segur (AKNS) scheme and the corresponding Darboux transformation is constructed to derive the soliton solution. One and two soliton solutions are generated. Using two soliton solutions of 3 CNLS equation, nonlinear tunneling of soliton for both with and without exponential background has been discussed. Finally cascade compression of optical soliton through multi-nonlinear barrier has been discussed. The obtained results may have promising applications in all-optical devices based on optical solitons, study of soliton propagation in birefringence fiber systems and optical soliton with distributed dispersion and nonlinearity management.