Soliton Tunneling Research Articles

Condensate bright solitons under transverse confinement

We investigate the dynamics of Bose-condensed bright solitons made of alkali-metal atoms with negative scattering length and under harmonic confinement in the transverse direction. Contrary to the 1D case, the 3D bright soliton exists only below a critical attractive interaction which depends on the extent of confinement. Such a behavior is also found in multi-soliton condensates with box boundary conditions. We obtain numerical and analytical estimates of the critical strength beyond which the solitons do not exist. By using an effective 1D nonpolynomial nonlinear Schr\"odinger equation (NPSE), which accurately takes into account the transverse dynamics of cigar-like condensates, we numerically simulate the dynamics of the "soliton train" reported in a recent experiment (Nature {\bf 417} 150 (2002)). Then, analyzing the macroscopic quantum tunneling of the bright soliton on a Gaussian barrier we find that its interference in the tunneling region is strongly suppressed with respect to non-solitonic case; moreover, the tunneling through a barrier breaks the solitonic nature of the matter wave. Finally, we show that the collapse of the soliton is induced by the scattering on the barrier or by the collision with another matter wave when the density reaches a critical value, for which we derive an accurate analytical formula.

Low frequency dynamics of disordered XY spin chains and pinned density waves: from localized spin waves to soliton tunneling.

A long-standing problem of the low-energy dynamics of a disordered XY spin chain is reexamined. The case of a rigid chain is studied, where the quantum effects can be treated quasiclassically. It is shown that, as the frequency decreases, the relevant excitations change from localized spin waves to two-level systems to soliton-antisoliton pairs. The linear-response correlation functions are calculated. The results apply to other periodic glassy systems such as pinned density waves, planar vortex lattices, stripes, and disordered Luttinger liquids.

Nonlinear tunneling of temporal and spatial optical solitons through organic thin films and polymeric waveguides

Nonlinear optical organic materials will be the key elements for future high-bit-rate telecommunications and ultrafast photonic technologies. We show that the process of nonlinear tunneling of optical solitons through a strong nonlinear thin film barrier, for example, a nonlinear organic thin film barrier, exhibits jump-like nonadiabatic evolution, which eventually leads to the soliton “fission reactions”. Nonlinear “fission reaction” is attended by generation of “colored” solitons with different frequencies and group velocities. It seems very attractive to use the nonlinear soliton tunneling effect through thin film of polydiacetylene para-toluene sulfonate in developing a whole class of basically novel all-optical soliton logic devices.

Nanotransport in polyacetylene single fiber: Toward the intrinsic properties

The electrical transport properties of iodine doped polyacetylene (PA) nanofibers were measured as function of temperature in micron and sub-micron scale. Polyacetylenc fiber network measured in micron scale shows weaker temperature dependence of resistivity and smaller negative magnetoresistance (MR) at T=1.5K compared to those of hulk PA film. The reaction of Au electrodes with dopant became serious in submicron experiment, so that stripes of Pt electrodes with 100nm separation were patterned on top of the SiO 2 substrate to prevent the reaction. Non-ohmic I-V charactersitics are observed in PA nanofiber. The gate dependence shows the charge carrier to be hole with mobility μ FET ∼ 4.4×10 -5 cm 2 /Vs at 233K. The non-ohmic I-V dependence at high electric fields could be originated from the soliton tunneling conduction in PA nanofiber.

Leaving the BPS bound: Tunneling of classically saturated solitons

We discuss quantum tunneling between classically BPS saturated solitons in two-dimensional theories with N=2 supersymmetry and a compact space dimension. Genuine BPS states form shortened multiplets of dimension two. In the models we consider there are two degenerate shortened multiplets at the classical level, but there is no obstruction to pairing up through quantum tunneling. The tunneling amplitude in the imaginary time is described by instantons. We find that the instanton is nothing but the 1/4 BPS saturated ``wall junction,'' considered previously in the literature in other contexts. Two central charges of the superalgebra allow us to calculate the instanton action without finding the explicit solution (it is checked, though, numerically, that the saturated solution does exist). We present a quantum-mechanical interpretation of the soliton tunneling.

Time-correlated tunneling of solitons in charge and spin density waves

We consider a model in which an electric field induces quantum nucleation of kink-antikink pairs in a charge or spin density wave. Pair nucleation events, prevented by the electrostatic energy below a pair creation threshold, become correlated in time above threshold. The model provides a natural explanation for the observed small density wave displacement below threshold, narrow-band noise, coherent oscillations, and mode-locking at high drift frequencies.

Time-correlated macroscopic quantum tunneling of density wave solitons

We consider a model in which an electric field induces quantum nucleation of soliton–antisoliton pairs in a charge or spin density wave. Coulomb blockade prevents pair creation until the applied field exceeds a sharp threshold value. Above threshold, the pair creation events become correlated in time, by analogy to time-correlated single electron tunneling. We find that, when the electrostatic energy is small compared to the pinning energy, the phase polarization below threshold can be quite small, as indicated by a number of experiments.

Time-correlated soliton tunneling in charge and spin density waves

We consider a model in which an electric field induces quantum nucleation of kink-antikink pairs in a pinned charge or spin density wave. Pair nucleation events, prevented by Coulomb blockade below a pair creation threshold, become correlated in time above threshold. The model provides a natural explanation for the observed (i) small density wave polarization below threshold in NbSe (3), (ii) narrow band noise, (iii) coherent oscillations, and (iv) mode-locking at high drift frequencies.

Theory of time-correlated tunneling of density wave solitons

We discuss a model in which an applied field induces quantum nucleation of soliton-antisoliton (S-S') pairs in a pinned charge or spin density wave. Coulomb blockade prevents pair creation until the electric field exceeds a sharp threshold value, which can be much smaller than the classical depinning field. Above threshold, the pair creation events become correlated in time, by analogy to time-correlated single electron tunneling. We compute the phase polarization and find that, depending on parameters, the predicted phase polarization can either be extremely small below threshold, as observed in NbSe 3 , or quite substantial, as observed in blue bronze. The lack of significant phase polarization below threshold in NbSe 3 , indicated by several experiments, suggests that the measured threshold field is a quantum S-S' pair creation threshold rather than a classical depinning field.

Soliton tunneling with sub-barrier kinetic energies.

We investigate (theoretically and numerically) the dynamics of a soliton moving in an asymmetrical potential well with a finite barrier. For large values of the width of the well, the width of the barrier, and/or the height of the barrier, the soliton behaves classically. On the other hand, we obtain the conditions for the existence of soliton tunneling with sub-barrier kinetic energies. We apply these results to the study of soliton propagation in disordered systems.

Self-Bouncing of Quadratic Solitons

We introduce a new kind of soliton-impurity interaction by examining the phenomena generated by colliding multiple-wave solitons in quadratic nonlinear media with localized perturbations. We examine different models for the impurities and find regimes of soliton self-bouncing, tunneling, and trapping, depending on the impurity type. We show that the transition between the different regimes is governed, e.g., by the soliton energy, and in one of the models we derive a Snell-type law for the process. We propose an optical setting to observe the soliton bouncing predicted.

Soliton compression and splitting in double-core nonlinear optical fibers

We consider compression of higher-order solitons in asymmetric and symmetric dual-core fibers (couplers) by means of numerical simulations of the corresponding coupled nonlinear Schrödinger equations. We demonstrate that an asymmetric coupler with different dispersion coefficients in its two cores provides almost the same degree of compression for the soliton tunneling from the core with a larger dispersion into the one with a smaller dispersion as the single-core fiber with the same jump of the dispersion coefficients. The pedestal around the compressed soliton is smaller when using the coupler; however, the necessary compression length is larger for the coupler than for the single-core fiber. An advantage of using the coupler is that it allows one to avoid a junction between two pieces of the fiber with different dispersions, which is inevitable if one uses the single-core fiber. Next, we consider compression of a higher-order soliton in a symmetric coupler. We demonstrate that, using the so-called soliton effect, one can achieve a record compression ratio (approximately 20), which is larger than that for any other known soliton compressor, with a very small share of the total energy in the pedestal. The corresponding compression length is still larger than for the single-core fiber, but the compression quality is much better. Lastly, the symmetric coupler allows, in some cases, to split the incoming pulse into two nearly identical compressed pulses outcoming from the two cores.

Tunneling of an optical soliton through a fiber junction

Two cases involving soliton tunneling through a finite-length junction between two long optical fibers are considered. First, it is shown that a junction with a certain length and a properly chosen dispersion, intermediate to that of the adjacent main fibers, can give rise to efficient chirp-free pulse compression. Second, conditions for solitons to survive tunneling through a junction dominated by linear dispersive effects are investigated.

Fully three-dimensional collisions of bistable light bullets

To break cylindrical symmetry and to achieve fully three-dimensional collisions of bistable light bullets, we have investigated the effect of a varying impact parameter. Novel effects such as soliton tunneling and spiral arm formation have been observed, some of which have no direct one-dimensional analog. The extreme stability and attractorlike behavior of optical bullets is demonstrated.

Tunneling of solitons and charge-density waves through impurities

In the presence of impurity potentials which couple directly to the phase of the charge-density waves the ground state as well as soliton excitations are pinned. The quantum-mechanical tunneling of a sine-Gordon soliton through an impurity potential is calculated. The small tunneling probability for even a moderate impurity potential means that the conductivity due to solitons will be greatly reduced. We also study the electric field and temperature dependence of a charge-density wave pinned by impurities when quasiclassical tunneling is taken into account. The temperature dependence is found to be dominated by simple thermal excitation and the conductivity is activated in both the strong- and weak-pinning limits.