Soliton Tunneling Research Articles

Dispersion management and cascade compression of femtosecond nonautonomous soliton in birefringent fiber

In this paper, we investigated the nonlinear tunneling of soliton in coupled higher order nonlinear Schrodinger (CHNLS) equations. Corresponding Lax pair for this equation is acquired through the Ablowitz-Kaup-Newell-Segur (AKNS) method and two soliton solutions is derived using Darboux transformation. Using two soliton solution of CHNLS equation, nonlinear tunneling of soliton has been investigated. Ultimately, cascade compressions of optical soliton have been investigated by soliton passing through number of nonlinear tunneling barrier. The obtained results may have promising applications in all-optical devices based on optical solitons.

Coherent quantum transport of charge density waves

Recent experiments show oscillations of dominant period $h/2e$ in conductance vs magnetic flux of charge density wave (CDW) rings above 77 K, revealing macroscopically observable quantum behavior. The time-correlated soliton tunneling model discussed here is based on coherent, Josephson-like tunneling of microscopic quantum solitons of charge $2e$. The model interprets the CDW threshold electric field as a Coulomb blockade threshold for soliton pair creation, often much smaller than the classical depinning field but with the same impurity dependence (e.g., $\ensuremath{\sim}{n}_{i}^{2}$ for weak pinning). This picture draws upon the theory of time-correlated single-electron tunneling to interpret CDW dynamics above threshold. Similar to Feynman's derivation of the Josephson current-phase relation for a superconducting tunnel junction, the picture treats the Schr\"odinger equation as an emergent classical equation to describe the time-evolution of Josephson-coupled order parameters related to soliton dislocation droplets. Vector or time-varying scalar potentials can affect the order parameter phases to enable magnetic quantum interference in CDW rings or lead to interesting behavior in response to oscillatory electric fields. The ability to vary both magnitudes and phases is an aspect important to future applications in quantum computing.

Soliton self-induced sub-barrier transparency and the controllable ‘shooting out’ effect

We demonstrate both the existence of the self-induced sub-barrier transparency in soliton tunneling through classically forbidden localized potential barriers and controllable ‘shooting out’ the high-energy solitons from arbitrary -soliton superpositions.

Geiger–Nuttall law for Schrödinger solitons

Based on the formal analogy between soliton tunneling through a classically forbidden potential barrier and –particle tunneling and decay we introduce a ‘toy solitonic model of a nucleus’ and show that the analog of the Geiger–Nuttall law can be discovered for Schrödinger solitons. We reveal and explain the analogy with virtual particle–antiparticle pair production and annihilation mechanisms and show how the nonlinear particle-like wave packet is being ‘dressed in a coat of virtual pairs’ and transformed into the soliton. In computational experiments with different soliton parameters and for different profiles of the barriers, including the charged sphere Coulomb potential, we demonstrate how the scaling symmetry breaking reveals the hidden role of the soliton self-interaction (binding) energy in the soliton scattering on external potentials and its dramatic impact on the wave-particle duality of solitons.

Vortex–bright-soliton dipoles: Bifurcations, symmetry breaking, and soliton tunneling in a vortex-induced double well

The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein condensates through bifurcations from suitable eigenstates of the underlying linear system is examined. These dipoles can have their bright solitary structures be in phase (symmetric) or out of phase (anti-symmetric). The dynamical robustness of each of these two possibilities is considered and the out-of-phase case is found to exhibit an intriguing symmetry-breaking instability that can in turn lead to tunneling of the bright wavefunction between the two vortex "wells". We interpret this phenomenon by virtue of a vortex-induced double well system, whose spontaneous symmetry breaking leads to asymmetric vortex-bright dipoles, in addition to the symmetric and anti-symmetric ones. The theoretical prediction of these states is corroborated by detailed numerical computations.

Nonlinear tunneling of nonautonomous optical solitons in combined nonlinear Schrödinger and Maxwell–Bloch systems

We consider the nonlinear Schrödinger–Maxwell–Bloch (NLS–MB) equation with variable coefficients. We construct the Lax pair for the NLS–MB system through AKNS formalism. We derived the two-soliton solution using the Darboux transformation. Finally we demonstrate the nonlinear tunneling of two solitons through dispersion and the nonlinear barrier or well. Our result shows that solitons can be compressed through the tunneling barrier or well with exponential decay for the special choice of variable coefficients.

Tunneling of optical lattice solitons at interfaces

The nonlinear wave propagation and scattering processes in discrete optical heterostructures is studied both analytically and numerically. The presented theory describes the reflection and tunneling of lattice solitons at interfaces. In particular, the derived expressions allow us to construct the reflected and transmitted pulses from the incident one. In the range of validity, the analytical results are in very good agreement with the numerical simulations. It is demonstrated that optical heterostructures represent an effective tool for controlling and manipulating nonlinear light pulses and beams.

Particle-wave duality in quantum tunneling of a bright soliton

One of the most fundamental difference between classical and quantum mechanics is observed in the particle tunneling through a localized potential: the former predicts a discontinuous transmission coefficient (T) as a function in incident velocity between one (complete penetration) and zero (complete reflection); while in the latter T always changes smoothly with a wave nature. Here we report a systematic study of the quantum tunneling property for a bright soliton, which behaves as a classical particle (wave) in the limit of small (large) incident velocity. In the intermediate regime, the classical and quantum properties are combined via a finite (but not full) discontinuity in the tunneling transmission coefficient. We demonstrate that the formation of a localized bound state is essential to describe such inelastic collisions, showing a nontrivial nonlinear effect on the quantum transportation of a bright soliton.

Extended object tunneling: Current-carrying states of Abrikosov vortices in a superconductor with artificial nanobarriers

We consider the structure and dynamics of two-dimensional fluxons created by a magnetic field in a type-II superconductor film with critical temperature ${T}_{1}$ in the presence of nanostripes of material with a higher critical temperature ${T}_{2}.$ The width of the stripes is of the order of the coherence length $\ensuremath{\xi}$. Such a stripe plays the role of a potential barrier for vortices. When subjected to the current $J$ parallel to the stripe, vortices move toward the barrier. Below the critical current ${J}_{c}$, the flux flow is effectively halted by the barrier, while above ${J}_{c}$, flux penetrates the stripe and passes the barrier. The mechanism of the barrier penetration (``soliton tunneling'' occurs even at zero temperature) is rather unusual: the vortices adjust their shape, and upon passing the barrier, they shrink their cores. The critical current and the I-V curves are calculated numerically and analytically using variational approach.

Quantum mechanisms of density wave transport

We report on new developments in the quantum picture of correlated electron transport in charge and spin density waves. The model treats the condensate as a quantum fluid in which charge soliton domain wall pairs nucleate above a Coulomb blockade threshold field. We employ a time-correlated soliton tunneling model, analogous to the theory of time-correlated single electron tunneling, to interpret the voltage oscillations and nonlinear current-voltage characteristics above threshold. An inverse scaling relationship between threshold field and dielectric response, originally proposed by Grüner, emerges naturally from the model. Flat dielectric and other ac responses below threshold in NbSe3 and TaS3, as well as small density wave phase displacements, indicate that the measured threshold is often much smaller than the classical depinning field. In some materials, the existence of two distinct threshold fields suggests that both soliton nucleation and classical depinning may occur. In our model, the ratio of electrostatic charging to pinning energy helps determine whether soliton nucleation or classical depinning dominates.

Resonant Tunneling of Fast Solitons through Large Potential Barriers

AbstractWe rigorously study the resonant tunneling of fast solitons through large potential barriers for the nonlinear Schrödinger equation in one dimension. Our approach covers the case of general nonlinearities, both local and Hartree (nonlocal).

Numerical simulation of resonant tunneling of fast solitons for the nonlinear Schrödinger equation

In a recent paper [4], we showed that the phenomenon of resonant tunneling, well known in linear quantum mechanical scattering theory, takes place for fast solitons of the Nonlinear Schrödinger (NLS) equation in the presence of certain large potentials. Here, we illustrate numerically this situation for the one dimensional cubic NLS equation withtwo classes of potentials, namely the 'box' potential and a repulsive 2-delta potential. In particular, under the resonant condition, we show that the transmitted wave is close to a soliton, calculate the transmitted mass of the solution and show that it converges to the total mass of the solution as the velocity of the soliton is increased.

Enigmas of optical and matter-wave soliton nonlinear tunneling

The method of mathematical analogies opens the possibility to study optical and matter-wave solitons in parallel and, due to the evident complexity of experiments with matter wave solitons, offers remarkable possibilities in studies of the BEC systems by performing experiments in the nonlinear optical systems and vice versa. We discuss previous misinterpretations of the binding soliton energy and investigate all possible scenarios of nonlinear soliton tunneling of Schrödinger solitons including soliton splitting on a potential barrier, leading to partial reflection and partial transmission, sub-barrier soliton tunneling and over-barrier soliton reflection. We reveal the most significant modifications of soliton tunneling scenarios due to increasing the binding energy, and show that the self-compressing soliton resembles more the classical particle case than a quantum mechanical behavior. The enhancement of the soliton binding energy is of decisive importance in the testing of a long-standing theoretical result which predicts that an optical soliton can tunnel between two regions of anomalous dispersion across a forbidden region of normal dispersion (enhanced soliton spectral tunneling effect).

Spectral tunneling of lattice nonlocal solitons

We address spectral tunneling of walking spatial solitons in photorefractive media with nonlocal diffusion of the nonlinear response and an imprinted shallow optical lattice. In contrast to materials with local nonlinearities, where solitons travelling across the lattice close to the Bragg angle suffer large radiative losses, in photorefractive media with diffusion nonlinearity resulting in self-bending solitons survive when their propagation angle approaches and even exceeds the Bragg angle. In the spatial frequency domain this effect can be considered as tunneling through the band of spatial frequencies centered around the Bragg frequency where the spatial group velocity dispersion is positive.

Soliton tunneling in the nonlinear Schrödinger equation with variable coefficients and an external harmonic potential

We report on the nonlinear tunneling effects of spatial solitons of the generalized nonlinear Schrödinger equation with distributed coefficients in an external harmonic potential. By using the homogeneous balance principle and the F-expansion technique we find the spatial bright and dark soliton solutions. We then display tunneling effects of such solutions occurring under special conditions; specifically when the spatial solitons pass unchanged through the potential barriers and wells affected by special choices of the diffraction and/or the nonlinearity coefficients. Our results show that the solitons display tunneling effects not only when passing through the nonlinear potential barriers or wells but also when passing through the diffractive barriers or wells. During tunneling the solitons may also undergo a controllable compression.

Spatial soliton tunneling, compression and splitting

We numerically investigate the tunneling of spatial solitons through a focusing Kerr nonlinear optical lattice with longitudinal potential barrier, and find that the position of input beams apparently affects the tunneling behaviors of spatial solitons, which exhibit compression or splitting when passing through the barrier, and that the transverse modulation frequency of lattice and the intensity of input beams strongly affect the ability of tunneling. Based on these properties, we present a scheme for compressing soliton and splitting soliton into stable twin beams. The obtained results may have promising applications in all-optical devices based on spatial solitons.

Drift instability and tunneling of lattice solitons

We derive an analytic formula for the lateral dynamics of solitons in a general inhomogeneous nonlinear media, and show that it can be valid over tens of diffraction lengths. In particular, we show that solitons centered at a lattice maximum can be "mathematically unstable" but "physically stable." We also derive an analytic upper bound for the critical velocity for tunneling, which is valid even when the standard Peierls-Nabarro potential approach fails.

Observation of Soliton Tunneling Phenomena and Soliton Ejection

We study, theoretically and experimentally, the nonlinear dynamics of a wave packet launched inside a trap potential. Increasing the power of the wave packet transforms its dynamics from linear tunneling through a potential barrier, to soliton tunneling, and eventually, above a well-defined threshold, to the ejection of a soliton from the potential trap.

Cascade compression induced by nonlinear barriers in propagation of optical solitons

We investigate the nonlinear tunneling of optical solitons through both dispersion and nonlinear barriers by employing the exact solution of the generalized nonlinear Schrödinger equation with variable coefficients. The extensive numerical simulations show that the optical solitons can be efficiently compressed when they pass through adequate engineered nonlinear barriers. A cascade compression system in a dispersion decreasing fiber with nonlinear barriers on an exponential background is proposed and the cascade compression of optical pulses is further investigated in detail. Finally, the stability to various initial perturbations of the cascade compressed optical soliton and the interaction between two neighboring compressed solitons were investigated too.

Collective rotational tunneling of methyl groups and quantum solitons in 4-methylpyridine: Neutron scattering studies of single crystals

The structure of the 4-methylpyridine crystal has been determined at 10 and 260 K with the single-crystal neutron-diffraction technique. The space-group symmetries are ${I4}_{1}/a$ and ${I4}_{1}/amd,$ respectively. In both cases, there are eight molecular entities in the unit cell. The rotational axes of the methyl groups are aligned along the c axis. The shortest intermolecular distances occur between face-to-face methyl groups. The next shortest distances correspond to infinite chains of rotors parallel to the orthogonal axes a and b. The angular probability densities of the methyl groups are clear evidence of orientational disorder. The incoherent scattering function ${S(Q}_{a}{,Q}_{b},\ensuremath{\omega})$ has been measured with the inelastic neutron scattering technique at 1.7 K. The energy-transfer ranges, $\ensuremath{\Elzxh}\ensuremath{\omega}=\ifmmode\pm\else\textpm\fi{}(500\ifmmode\pm\else\textpm\fi{}60)\ensuremath{\mu}\mathrm{eV},$ encompass transitions due to rotational tunneling. The anisotropy in $\mathbf{Q}$ is distinctive of dynamics in one dimension. These are represented with the quantum sine-Gordon equation that is an approximation to the Hamiltonian for an infinite chain of coupled rotors. Spots of intensity observed for neutron-energy loss at $|{Q}_{a}|$ or $|{Q}_{b}|\ensuremath{\approx}1.55{\mathrm{\AA{}}}^{\ensuremath{-}1}$ are distinctive of stationary states for breathers. Weaker peaks at $|{Q}_{a}|$ or $|{Q}_{b}|\ensuremath{\approx}1.0{\mathrm{\AA{}}}^{\ensuremath{-}1}$ reveal collective tunneling. This is a thermally activated process arising from rather heavy pseudoparticles composed of large numbers (from 22 to 25) of kinks or antikinks. Quantization of the kinetic momentum arises from the chain discreteness and from conservation of the angular momentum. Traveling states are stationary when the kinetic energy is within the tunneling energy band. In the ground state, the chain dynamics are represented with a single collective angular coordinate. The incoherent scattering function for neutron-energy-gain reveals bound excited states with lifetimes of several days.