Quasi-discrete microwave solitons in a split ring resonator-based left-handed coplanar waveguide

We study the propagation of quasi-discrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split ring resonators. By considering the relevant transmission line analogue, we derive a nonlinear lattice model which is studied analytically by means of a quasi-discrete approximation. We derive a nonlinear Schr{\"o}dinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasi-discrete microwave solitons. Our numerical findings are in good agreement with the analytical predictions, and suggest that the predicted structures are quite robust and may be observed in experiments

Fluctuating and dissipative dynamics of dark solitons in quasi-condensates

The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long lived soliton trajectories within each ensemble of numerical realizations (S.P. Cockburn {\it et al.}, Phys. Rev. Lett. 104, 174101 (2010)). Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based upon the dissipative Gross-Pitaevskii model (with the same {\it ab initio} damping). Probing the regime for which $0.8 k_{B}T < \mu < 1.6 k_{B}T$, we find average soliton lifetimes to scale with temperature as $\tau\sim T^{-4}$, in agreement with predictions previously made for the low-temperature regime $k_{B}T\ll\mu$. The model is also shown to capture the experimentally-relevant decrease in the visibility of an oscillating soliton due to the presence of background fluctuations.Comment: 17 pages, 14 figure

Quasidiscrete microwave solitons in a split-ring-resonator-based left-handed coplanar waveguide

We study the propagation of quasidiscrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split-ring resonators. By considering the relevant transmission line analog, we derive a nonlinear lattice model which is studied analytically by means of a quasidiscrete approximation. We derive a nonlinear Schrödinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasidiscrete microwave solitons. Our numerical findings are in good agreement with the analytical predictions, and suggest that the predicted structures are quite robust and may be observed in experiments. © 2011 American Physical Society

Fluctuating and dissipative dynamics of dark solitons in quasicondensates

The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark-soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long-lived soliton trajectories within each ensemble of numerical realizations. Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based upon the dissipative Gross-Pitaevskii model (with the same ab initio damping). Probing the regime for which 0.8 kBT&amp;lt;μ&amp;lt;1.6 kBT, we find average soliton lifetimes to scale with temperature as τ∼T-4, in agreement with predictions previously made for the low-temperature regime kBTμ. The model is also shown to capture the experimentally relevant decrease in the visibility of an oscillating soliton due to the presence of background fluctuations. © 2011 American Physical Society