Postdoctoral position in optical and matter-wave solitons

A postdoctoral research position is open for work on a project on solitons in optical fibers and Bose-Einstein condensates. The main focus of the project is to study interaction between solitons with the aim of increasing the bit-rate of data transfer in optical fibers. Both analytical and numerical methods will be used. See more details about the project below.

Duration of the job will be for one year with possible extension for another two years depending on production and hence availability of funds. Experience with numerical methods for solving nonlinear partial differential equations and in symbolic programming with Mathematica is required.

A tax-free salary of 3000.00 US$ per month will be paid.

Interested applicants should apply through the online application form on the website of the United Arab Emirates University (http://www.uaeu.ac.ae/) and/or by emailing their CV to Usama Al Khawaja u.alkhawaja@uaeu.ac.ae. The position is open until filled.

Project Summary:

Title: Using solitons and soliton molecules as data carriers to increase the bit rate of optical telecommunications

Key words: matter-wave solitons, optical solitons, Bose-Einstein condensation, Gross-Pitaevskii equation, exact solutions.

The main goal of this project is to increase the bit rate of optical communications using solitons and soliton molecules by devising methods to overcome the problem of soliton-soliton interaction. In addition, we aim at understanding the nonlinear transport of optical and matter-wave solitons in inhomogeneous and time-dependent media. Specific models corresponding to transport of solitons in optical fibers with localized or extended impurities and matter-wave solitons in atom waveguide chips will be considered. Here is a list of the objectives and methods used to achieve this goal:

Objectives

i) Obtaining analytic exact formula for the force of interaction between solitons in the presence of time-dependent external potential and nonlinearity. From this formula we should obtain the exact conditions for the formation of soliton molecules and soliton coalescence and their stability analysis.

ii)  Obtaining analytic formula for the force of interaction between solitons and surfaces in terms of the distance between the soliton and the surface and the phase of the soliton.

iii) Obtaining the resonant tunneling conditions for a soliton scattered by a potential barrier and a potential well and calculating the transmission coefficient for different combinations of them.

iv) Deriving the condition of integrability of the most general Gross-Pitaevskii equation (GPE) and finding new exact solutions for the integrable cases (see project description for details). 

v) Applying the findings of the above objectives in one or more of the following applications: optical communication, all-optical switches and routers, optical data storage, and matter-wave soliton laser.

vi) We will work on writing and publishing a handbook of all integrable Gross-Pitaevskii equations. All previously-known integrable GPEs will be assembled with their solutions in addition to the new ones that we hope to discover. This will be a valuable handbook for researchers in the nonlinear optics and Bose-Einstein condensation communities.

Methods

i) Inverse-Scattering Method: Will be used to obtain the new exact solutions and to investigate the integrability of the Gross-Pitaevskii equation. Modulational instability analysis will then be used to test the stability of the new solutions.

ii) Numerical method: The Split-Step Crank-Nicholson Method will be used which has proved to be very accurate in the kind of problems to be addressed. Other numerical methods will be used if needed.

iii) Variational method: This is a rather simple method that sometimes captures the main physics features of the problem addressed. It also gives analytical description and insight beyond numerical techniques, but it is of course less accurate than exact methods.